Ingenieria de Procesos de Separacion

  • 0 0 0
  • Like this paper and download? You can publish your own PDF file online for free in a few minutes! Sign Up
File loading please wait...
Citation preview

www.FreeLibros.me

*OHFOJFSÎBEFQSPDFTPT EFTFQBSBDJÓO 4&(6/%"&%*$*¶/ 1)*--*1$8"/,"5

53"%6$$*¶/

7JSHJMJP(PO[ÃMF[Z1P[P *OHFOJFSP2VÎNJDP 6OJWFSTJEBE/BDJPOBM"VUÓOPNBEF.ÊYJDP

3&7*4*¶/5­$/*$"

4FSHJP"OUPOJP(ÓNF[5PSSFT %FQBSUBNFOUPEF*OHFOJFSÎBEF1SPDFTPTF)JESÃVMJDB *OHFOJFSÎB2VÎNJDB 6OJWFSTJEBE"VUÓOPNB.FUSPQPMJUBOB 6OJEBE*[UBQBMBQB

www.FreeLibros.me

%BUPTEFDBUBMPHBDJÓOCJCMJPHSÃàDB 8"/,"5 1)*--*1$ *OHFOJFSÎBEFQSPDFTPTEFTFQBSBDJÓO 4FHVOEBFEJDJÓO 1&"340/&%6$"$*¶/ .ÊYJDP  *4#/ ¦SFB$JFODJBT 'PSNBUP3DN

1ÃHJOBT

"VUIPSJ[FEUSBOTMBUJPOGSPNUIF&OHMJTIMBOHVBHFFEJUJPO FOUJUMFE4FQBSBUJPO1SPDFTT&OHJOFFSJOH OEFEJUJPOCZ1IJMMJQ $8BOLBU QVCMJTIFECZ1FBSTPO&EVDBUJPO *OD QVCMJTIJOHBT1SFOUJDF)BMM*OD $PQZSJHIU¥"MMSJHIUTSFTFSWFE *4#/ 5SBEVDDJÓOBVUPSJ[BEBEFMBFEJDJÓOFOJEJPNBJOHMÊTUJUVMBEB4FQBSBUJPO1SPDFTT&OHJOFFSJOH OEFEJUJPOQPS1IJMMJQ $8BOLBU QVCMJDBEBQPS1FBSTPO&EVDBUJPO *OD QVCMJDBEBDPNP1SFOUJDF)BMM $PQZSJHIU¥5PEPTMPT EFSFDIPTSFTFSWBEPT &TUBFEJDJÓOFOFTQBÒPMFTMBÙOJDBBVUPSJ[BEB &EJDJÓOFOFTQBÒPM &EJUPS  &EJUPSEFEFTBSSPMMP 4VQFSWJTPSEFQSPEVDDJÓO

3VCÊO'VFSUF3JWFSB FNBJMSVCFOGVFSUF!QFBSTPOFEDPN #FSOBSEJOP(VUJÊSSF[)FSOÃOEF[ (VTUBWP3JWBT3PNFSP

4&(6/%"&%*$*¶/  %3¥QPS1FBSTPO&EVDBDJÓOEF.ÊYJDP 4"EF$7 "UMBDPNVMDPPQJTP $PM*OEVTUSJBM"UPUP  /BVDBMQBOEF+VÃSF[ &EPEF.ÊYJDP $ÃNBSB/BDJPOBMEFMB*OEVTUSJB&EJUPSJBM.FYJDBOB3FH/ÙN 1SFOUJDF)BMMFTVOBNBSDBSFHJTUSBEBEF1FBSTPO&EVDBDJÓOEF.ÊYJDP 4"EF$7 3FTFSWBEPTUPEPTMPTEFSFDIPT/JMBUPUBMJEBEOJQBSUFEFFTUBQVCMJDBDJÓOQVFEFOSFQSPEVDJSTF SFHJTUSBSTFP USBOTNJUJSTF QPSVOTJTUFNBEFSFDVQFSBDJÓOEFJOGPSNBDJÓO FOOJOHVOBGPSNBOJQPSOJOHÙONFEJP TFBFMFDUSÓOJDP  NFDÃOJDP GPUPRVÎNJDP NBHOÊUJDPPFMFDUSPÓQUJDP QPSGPUPDPQJB HSBCBDJÓOPDVBMRVJFSPUSP TJOQFSNJTPQSFWJPQPS FTDSJUPEFMFEJUPS &MQSÊTUBNP BMRVJMFSPDVBMRVJFSPUSBGPSNBEFDFTJÓOEFVTPEFFTUFFKFNQMBSSFRVFSJSÃUBNCJÊOMBBVUPSJ[BDJÓOEFM FEJUPSPEFTVTSFQSFTFOUBOUFT *4#/ *NQSFTPFO.ÊYJDP1SJOUFEJO.FYJDP 

www.FreeLibros.me

1BSB%PU $IVDLZ+FOOJF

www.FreeLibros.me

www.FreeLibros.me

$POUFOJEP

Prefacio Agradecimientos Acerca del autor Nomenclatura Capítulo 1 1.1. 1.2. 1.3. 1.4. 1.5. 1.6. 1.7.

2.5. 2.6. 2.7. 2.8. 2.9. 2.10.

Introducción a la ingeniería de procesos de separación

Importancia de las separaciones El concepto de equilibrio Transferencia de masa Métodos para resolver los problemas Prerrequisitos Otras fuentes sobre ingeniería de procesos de separación Resumen–Objetivos Referencias Tarea

Capítulo 2 2.1. 2.2. 2.3. 2.4.

xv xvii xix xxi

Destilación instantánea

Método básico de destilación instantánea Forma y fuentes de los datos de equilibrio Representación gráfica del equilibrio binario vapor-líquido Destilación instantánea binaria 2.4.1. Procedimiento secuencial de solución Ejemplo 2-1. Separador de evaporación instantánea para etanol y agua 2.4.2. Procedimiento de solución simultánea Equilibrio vapor-líquido con varios componentes Destilación instantánea de varios componentes Convergencia simultánea con varios componentes Cálculo de los tamaños Uso de tambores de destilación existentes Resumen–Objetivos Referencias Tarea Apéndice al capítulo 2 Simulación en computadora de la destilación instantánea

1 1 2 4 5 7 8 9 9 10

12 12 14 16 21 21 24 27 29 34 40 45 49 50 51 52 59 WJJ

www.FreeLibros.me

WJJJ

Capítulo 3

$POUFOJEP

Introducción a la destilación en columna

3.1. 3.2. 3.3. 3.4.

Desarrollo de una cascada de destilación Equipo de destilación Especificaciones Balances externos de la columna &KFNQMP#BMBODFTFYUFSOPTQBSBEFTUJMBDJÓOCJOBSJB 3.5. Resumen–Objetivos Referencias Tarea

Capítulo 4

Destilación en columna: balances internos, etapa por etapa

65 65 72 74 76  81 81 81

86

4.1. Balances internos 4.2. Métodos de solución de etapa por etapa, para destilación binaria &KFNQMP$ÃMDVMPTFUBQBQPSFUBQBDPOFMNÊUPEPEF-FXJT 4.3. Introducción al método de McCabe-Thiele 4.4. Línea de alimentación &KFNQMP$ÃMDVMPTEFMBMÎOFBEFBMJNFOUBDJÓO 4.5. Método completo de McCabe-Thiele &KFNQMP.ÊUPEPEF.D$BCF5IJFMF 4.6. Perfiles para destilación binaria 4.7. Calentamiento con vapor directo &KFNQMP"OÃMJTJTEF.D$BCF5IJFMFEFDBMFOUBNJFOUP DPOWBQPSEJSFDUP 4.8. Procedimiento general de análisis McCabe-Thiele  &KFNQMP%FTUJMBDJÓODPOEPTBMJNFOUBDJPOFT 4.9. Otras situaciones en las columnas de destilación 4.9.1. Condensadores parciales 4.9.2. Vaporizadores totales 4.9.3. Corrientes laterales o líneas de salida 4.9.4. Vaporizadores intermedios y condensadores intermedios 4.9.5. Columnas de agotamiento y enriquecimiento 4.10. Condiciones límite de operación 4.11. Eficiencias 4.12. Problemas de simulación 4.13. Usos nuevos para columnas viejas 4.14. Reflujo subenfriado y vapor sobrecalentado al plato inferior 4.15. Comparaciones entre los métodos analíticos y los gráficos 4.16. Resumen–Objetivos Referencias Tarea Apéndice al capítulo 4 Simulaciones de destilación binaria en computadora

86 90  97 101  109  112 114

Capítulo 5

161

Introducción a la destilación de varios componentes

5.1. Dificultades de cálculo  &KFNQMP#BMBODFTFYUFSOPTVTBOEPSFDVQFSBDJPOFTGSBDDJPOBSJBT 5.2. Perfiles para destilación de varios componentes 5.3. Resumen–Objetivos Referencias Tarea

www.FreeLibros.me

 118  125 125 126 126 128 129 130 133 135 136 138 140 142 143 144 158

161  167 172 172 172

$POUFOJEP

Capítulo 6

JY

Procedimientos de cálculo exacto para destilación de varios componentes

6.1. 6.2. 6.3. 6.4.

Introducción a la solución matricial para destilación de varios componentes Balances de masa de componentes en forma de matrices Proposición inicial para tasas de flujo Cálculos de punto de burbuja &KFNQMP5FNQFSBUVSBEFQVOUPEFCVSCVKB 6.5. Método θ de convergencia  &KFNQMP$ÃMDVMPEFNBUSJDFTZDPOWFSHFODJBDPOθ 6.6. Balances de energía en forma matricial 6.7. Resumen–Objetivos Referencias Tarea Apéndice al capítulo 6 Simulaciones en computadora de columnas de destilación de varios componentes

Capítulo 7

Métodos abreviados aproximados para destilación de varios componentes

7.1. Reflujo total: Ecuación de Fenske  &KFNQMP&DVBDJÓOEF'FOTLF 7.2. Reflujo mínimo: Ecuaciones de Underwood  &KFNQMP&DVBDJPOFTEF6OEFSXPPE 7.3. Correlación de Gilliland para la cantidad de etapas a relación de reflujo finita  &KFNQMP$PSSFMBDJÓOEF(JMMJMBOE 7.4. Resumen–Objetivos Referencias Tarea

Capítulo 8

Introducción a métodos complejos de destilación

8.1. Ruptura de azeótropos con otros separadores  &KFNQMP4FDBEPEFCFODFOPQPSEFTUJMBDJÓO 8-2. Procesos de destilación azeotrópica binaria heterogénea 8.2.1. Azeótropos heterogéneos binarios 8.2.2. Secado de compuestos orgánicos parcialmente miscibles con agua  &KFNQMP%FTUJMBDJÓOQPSBSSBTUSFDPOWBQPSEFBHVB 8.3. Destilación por arrastre de vapor 8.4. Procesos de destilación a dos presiones 8.5. Sistemas ternarios complejos de destilación 8.5.1. Curvas de destilación 8.5.2. Curvas de residuo 8.6. Destilación extractiva 8.7. Destilación azeotrópica con solvente agregado 8.8. Destilación con reacción química 8.9. Resumen–Objetivos Referencias Tarea Apéndice al capítulo 8 Simulación de sistemas complejos de destilación

Capítulo 9

Destilación intermitente

9.1. Destilación intermitente binaria: Ecuación de Rayleigh

www.FreeLibros.me

176 176 178 181 181  184  191 194 195 195 200

205 205  210  215  219 219 220

225 225  227 227 230  234 238 239 240 243 245 251 255 258 258 260 270

276 278

Y

$POUFOJEP

9.2. Destilación intermitente binaria simple  &KFNQMP%FTUJMBDJÓOTJNQMFEF3BZMFJHI 9.3. Destilación intermitente a nivel constante 9.4. Destilación intermitente por arrastre con vapor de agua 9.5. Destilación intermitente en varias etapas 9.5.1. Relación de reflujo constante  &KFNQMP%FTUJMBDJÓOJOUFSNJUFOUFFOWBSJBTFUBQBT 9.5.2. Relación de reflujo variable 9.6. Tiempo de operación 9.7. Resumen–Objetivos Referencias Tarea

Capítulo 10

Diseño de columnas de platos y empacadas

279  283 284 285 286  290 291 292 292 293

301

10.1. Descripción de los equipos en las columnas de platos 10.1.1. Platos, bajantes y vertederos 10.1.2. Entradas y salidas 10.2. Eficiencias de platos  &KFNQMP&TUJNBDJÓOEFMBFàDJFODJBHFOFSBM 10.3. Cálculo del diámetro de la columna  &KFNQMP$ÃMDVMPEFMEJÃNFUSPQBSBVOBDPMVNOBEFQMBUPT 10.4. Distribución y consideraciones hidráulicas para platos perforados &KFNQMP%JTUSJCVDJÓOEFQMBUPZDÃMDVMPTIJESÃVMJDPT 10.5. Diseño de platos de válvulas 10.6. Introducción al diseño de columnas empacadas 10.7. Partes internas de las columnas empacadas 10.8. Altura del empaque. Método de la Hetp 10.9. Inundación de la columna empacada y cálculo del diámetro  &KFNQMP$ÃMDVMPEFMEJÃNFUSPEFVOBDPMVNOBFNQBDBEB 10.10. Consideraciones económicas 10.11. Resumen–Objetivos Referencias Tarea

301 304 306 309  314  320  327 329 329 331 333  341 345 345 348

Capítulo 11

354

Economía y conservación de energía en la destilación

11.1. Costos de destilación 11.2. Efectos de la operación sobre los costos  &KFNQMP&TUJNBDJÓOEFMDPTUPQBSBVOBEFTUJMBDJÓO 11.3. Cambios en capacidades de la planta 11.4. Conservación de la energía en la destilación 11.5. Síntesis de secuencias de columnas para destilación de varios componentes casi ideales  &KFNQMP4FDVFODJBDJÓOEFDPMVNOBTDPOIFVSÎTUJDBT 11.6. Síntesis de sistemas de destilación para mezclas ternarias no ideales  &KFNQMP%FTBSSPMMPEFQSPDFTPTQBSBTFQBSBSVOBNF[DMB UFSOBSJBDPNQMFKB 11.7. Resumen–Objetivos Referencias Tarea

www.FreeLibros.me

354 359  366 366 370  376  380 380 382

$POUFOJEP

Capítulo 12

YJ

Absorción y arrastre

385

12.1. Equilibrios de absorción y arrastre 12.2. Líneas de operación para absorción  &KFNQMP"OÃMJTJTHSÃàDPEFMBBCTPSDJÓO 12.3. Análisis del arrastre 12.4. Diámetro de la columna 12.5. Solución analítica: La ecuación de Kremser  &KFNQMP"OÃMJTJTEFTFQBSBEPSEFBSSBTUSFDPOMBFDVBDJÓO EF,SFNTFS 12.6. Absorbedores y separadores de arrastre con varios solutos diluidos 12.7. Solución matricial para absorbedores y separadores de arrastre con soluciones concentradas 12.8. Absorción irreversible 12.9. Resumen–Objetivos Referencias Tarea Apéndice al capítulo 12 Simulaciones de absorción y arrastre en computadora

Capítulo 13

Extracción inmiscible, lavado, lixiviación y extracción supercrítica

387 389  394 396 397  403 406 410 411 412 413 421

424

13.1. Procesos y equipos de extracción 13.2. Extracción a contracorriente 13.2.1. Método de McCabe-Thiele para sistemas diluidos  &KFNQMP&YUSBDDJÓOEJMVJEBBDPOUSBDPSSJFOUFDPOGBTFTJONJTDJCMFT 13.2.2. Método de Kremser para sistemas diluidos 13.3. Extracción fraccionada diluida 13.4. Extracción en una etapa y con flujo cruzado  &KFNQMP&YUSBDDJÓOEFVOBQSPUFÎOBDPOVOBFUBQBZáVKPDSV[BEP 13.5. Extracción con fases inmiscibles y concentradas 13.6. Extracción intermitente 13.7. Procedimientos generalizados de McCabe-Thiele y de Kremser 13.8. Lavado  &KFNQMP-BWBEP 13.9. Lixiviación 13.10. Extracción con fluido supercrítico 13.11. Aplicación a otras separaciones 13.12. Resumen–Objetivos Referencias Tarea

424 428 428  434 435 439  443 444 445 448  452 454 457 457 457 459

Capítulo 14

Extracción de sistemas parcialmente miscibles

468

14.1. Equilibrios en extracción 14.2. Cálculos en mezclado y la regla de la palanca 14.3. Sistemas de una etapa y flujo cruzado  &KFNQMP&YUSBDDJÓOFOVOBFUBQB 14.4. Cascadas de extracción a contracorriente 14.4.1. Balances externos de masa 14.4.2. Puntos de diferencia y cálculos de etapa por etapa 14.4.3. Problema completo de extracción  &KFNQMP&YUSBDDJÓOBDPOUSBDPSSJFOUF

468 471 474  477 477 479 483 

www.FreeLibros.me

YJJ

$POUFOJEP

14.5. 14.6. 14.7. 14.8.

Relación entre los diagramas de McCabe-Thiele y triangulares Flujo mínimo de solvente Simulaciones de la extracción en computadora Lixiviación con tasas de flujo variables  &KFNQMP$ÃMDVMPTQBSBMJYJWJBDJÓO 14.9. Resumen–Objetivos Referencias Tarea Apéndice al capítulo 14 Simulación de la extracción en computadora

Capítulo 15

Análisis de la transferencia de masa

15.1. Fundamentos de la transferencia de masa 15.2. Análisis de las columnas de destilación con altura y número de unidades de transferencia (HTU y NTU)  &KFNQMP%FTUJMBDJÓOFOVOBDPMVNOBFNQBDBEB 15.3. Relación entre HETP y HTU 15.4. Correlaciones de transferencia de masa para torres empacadas 15.4.1. Correlaciones detalladas para empaques aleatorios  &KFNQMP&TUJNBDJÓOEF)(Z)- 15.4.2. Correlaciones sencillas 15.5. Análisis HTU-NTU de absorbedores y separadores de arrastre  &KFNQMP"CTPSDJÓOEF40 15.6. Análisis HTU-NTU de absorbedores concurrentes 15.7. Transferencia de masa en un plato  &KFNQMP&TUJNBDJÓOEFMBFàDJFODJBEFQMBUP 15.8. Resumen–Objetivos Referencias Tarea

Capítulo 16

Introducción a los procesos de separación con membrana

16.1. Equipos de separación con membrana 16.2. Conceptos relacionados con las membranas 16.3. Permeación de gases 16.3.1. Permeación de mezclas binarias de gases 16.3.2 Permeación binaria en sistemas perfectamente mezclados  &KFNQMP1FSNFBEPEFHBTCJFONF[DMBEPTPMVDJÓO BOBMÎUJDBTFDVFODJBM  &KFNQMP1FSNFBDJÓOEFHBTCJFONF[DMBEPTPMVDJPOFT TJNVMUÃOFBTBOBMÎUJDBZHSÃàDB 16.3.3 Permeación de varios componentes en sistemas perfectamente mezclados  &KFNQMP1FSNFBDJÓOHBTFPTBQFSGFDUBNFOUFNF[DMBEB EFWBSJPTDPNQPOFOUFT 16.4. Ósmosis inversa 16.4.1. Análisis de la ósmosis y la ósmosis inversa  &KFNQMP¶TNPTJTJOWFSTBTJOQPMBSJ[BDJÓOEFDPODFOUSBDJÓO 16.4.2. Determinación experimental de las propiedades de las membranas  &KFNQMP%FUFSNJOBDJÓOEFMBTQSPQJFEBEFTEFNFNCSBOBT QBSBÓTNPTJTJOWFSTB

www.FreeLibros.me

485 486 488 489  492 492 493 499

501 501 504  511 513 513  520 521  526 528  531 531 532

535 537 541 544 544 547   555  558 558  564 

$POUFOJEP

YJJJ

16.4.3.  

Determinación de la polarización de concentración &KFNQMP¶TNPTJTJOWFSTBDPOQPMBSJ[BDJÓOEFDPODFOUSBDJÓO &KFNQMP$ÃMDVMPEFMBPQFSBDJÓOEFÓTNPTJTJOWFSTBDPO QPMBSJ[BDJÓOEFDPODFOUSBDJÓO 16.4.4. Ósmosis inversa con soluciones concentradas 16.5. Ultrafiltración  &KFNQMP6MUSBàMUSBDJÓODPOGPSNBDJÓOEFHFM 16.6. Pervaporación  &KFNQMP1FSWBQPSBDJÓODÃMDVMPEFGBDUJCJMJEBE  &KFNQMP1FSWBQPSBDJÓOEFTBSSPMMPEFVOEJTFÒPGBDUJCMF 16.7. Efectos de la pauta de flujo general  &KFNQMP&GFDUPTEFMBQBVUBEFáVKPTPCSFMBQFSNFBDJÓOEFHBTFT 16.7.1. Permeación binaria con flujo cruzado 16.7.2. Permeación binaria concurrente 16.7.3. Flujo binario a contracorriente 16.8 Resumen–Objetivos Referencias Tarea Apéndice al capítulo 16 hojas de cálculo para cálculos con pautas de flujo, para permeación de gases 16.A.1. Flujo cruzado 16.A.2. Flujo concurrente 16.A.3. Flujo a contracorriente

Capítulo 17

Introducción a la adsorción, cromatografía e intercambio iónico

17.1. Sorbentes y equilibrio de sorción 17.1.1. Definiciones 17.1.2. Tipos de sorbente 17.1.3. Comportamiento de equilibrio en adsorción  &KFNQMP&RVJMJCSJPEFBETPSDJÓO 17.2. Análisis del movimiento de soluto para sistemas lineales: fundamentos y aplicaciones a la cromatografía 17.2.1. Movimiento del soluto en una columna 17.2.2. Teoría del movimiento del soluto para isotermas lineales 17.2.3. Aplicación de la teoría lineal del movimiento del soluto a ciclos de purga y a la cromatografía de elución  &KFNQMP"OÃMJTJTMJOFBMEFMNPWJNJFOUPEFMTPMVUPFO DSPNBUPHSBGÎBEFFMVDJÓO 17.3. Análisis de movimiento de soluto para sistemas lineales: Adsorción térmica y con variación de presión, y movimiento simulado de lecho 17.3.1. Adsorción con oscilación de temperatura  &KFNQMP3FHFOFSBDJÓOUÊSNJDBDPOJTPUFSNBMJOFBM 17.3.2. Adsorción con oscilación de presión  &KFNQMP4JTUFNBEFBETPSDJÓODPOPTDJMBDJÓOEFQSFTJÓO 17.3.3. Lechos móviles simulados  &KFNQMP4JTUFNBEFMFDIPNÓWJMTJNVMBEP 17.4. Análisis de movimiento no lineal del soluto 17.4.1. Ondas difusas  &KFNQMP0OEBEJGVTB

www.FreeLibros.me

566   573 573  579   588  590 592 594 595 596 597 603 603 605 607

609 610 610 612 615  621 623 625 626  631 631  641  649  654 655 

YJW

17.5.

17.6.

17-7.

17.8. 17.9. 17.10.

$POUFOJEP

17.4.2. Ondas de choque  &KFNQMP0OEBEFDIPRVFBVUPBàMBEPSB Intercambio iónico 17.5.1. Equilibrio en el intercambio iónico 17.5.2. Movimiento de los iones  &KFNQMP.PWJNJFOUPEFJPOFTQBSBJOUFSDBNCJP EJWBMFOUFNPOPWBMFOUF Transferencia de masa y energía 17.6.1. Transferencia de masa y difusión 17.6.2. Balances de masa en la columna 17.6.3. Transferencia de masa con parámetro agrupado 17.6.4. Balances de energía y transferencia de calor 17.6.5. Deducción de la teoría del movimiento del soluto 17.6.6. Simuladores detallados Soluciones de transferencia de masa para sistemas lineales 17.7.1. Solución de Lapidus y Amundson para equilibrio local con dispersión 17.7.2. Superposición en sistemas lineales  &KFNQMP4PMVDJÓOEF-BQJEVTZ"NVOETPOQBSBFMVDJÓO 17.7.3. Cromatografía lineal  &KFNQMP%FUFSNJOBDJÓOEFMPTQBSÃNFUSPTEFVOBJTPUFSNB MJOFBM / ZMBSFTPMVDJÓO FODSPNBUPHSBGÎBMJOFBM Método LUB para sistemas no lineales  &KFNQMP.ÊUPEP-6# Lista de control para diseño y operación en la práctica Resumen–Objetivos Referencias Tarea Apéndice al capítulo 17 Introducción al simulador Aspen Chromatography

658  663 664 667  672 672 674 675 676 677 678 678 679 680  683  687  691 693 693 696 708

Guía de localización de problemas en Aspen Plus para separaciones

713

Respuestas a problemas seleccionados

717

±OEJDF



www.FreeLibros.me

1SFGBDJP

&OFMTJHMP99* MBTTFQBSBDJPOFTTJHVFOTJFOEPUBOJNQPSUBOUFT PNÃT RVFEVSBOUFFMTJHMPQB TBEP&MEFTBSSPMMPEFOVFWBTJOEVTUSJBT DPNPMBCJPUFDOPMPHÎBZMBOBOPUFDOPMPHÎB ZMBNBZPS JNQPSUBODJBEFFMJNJOBSIVFMMBTEFDPNQVFTUPTIBOMMFWBEPBMBTTFQBSBDJPOFTBMQSJNFSQMBOP -PTJOHFOJFSPTRVÎNJDPTEFCFOFOUFOEFSZEJTFÒBSOVFWPTQSPDFTPTEFTFQBSBDJÓO DPNPTF QBSBDJPOFTDPONFNCSBOBT BETPSDJÓOZDSPNBUPHSBGÎB BEFNÃTEFMBTTFQBSBDJPOFTOPSNBMFT DPOFUBQBTEFFRVJMJCSJP DPNPEFTUJMBDJÓO BCTPSDJÓOZFYUSBDDJÓO%BEPRVFBIPSBTFJODMVZFO MBTTFQBSBDJPOFTFONFNCSBOB BETPSDJÓO DSPNBUPHSBGÎBFJOUFSDBNCJPJÓOJDP IFDBNCJBEPFM UÎUVMPEFFTUBTFHVOEBFEJDJÓO EF4FQBSBDJPOFTDPOFUBQBTEFFRVJMJCSJP &RVJMJCSJVN4UBHFE 4FQBSBUJPOT B*OHFOJFSÎBEFQSPDFTPTEFTFQBSBDJÓO 4FQBSBUJPO1SPDFTT&OHJOFFSJOH QBSBSF áFKBSFTUBDPCFSUVSBNÃTBNQMJB  1BSBTBUJTGBDFSFTUBEFNBOEBEFOVFWBTTFQBSBDJPOFT IFBHSFHBEPEPTDBQÎUVMPTBMMJCSP &MOVFWPDBQÎUVMP FOTFQBSBDJPOFTDPONFNCSBOBTJODMVZFQFSNFBDJÓO FTEFDJS QFOFUSB DJÓO P JOàMUSBDJÓO  EF HBT  ÓTNPTJT JOWFSTB  VMUSBàMUSBDJÓO Z QFSWBQPSBDJÓO $PNP FKFNQMPT EFMVTPEFFTUPTNÊUPEPTEFTFQBSBDJÓODPONFNCSBOBFTUÃOMBQVSJàDBDJÓOEFIJESÓHFOPZ EJÓYJEP EF DBSCPOP  QVSJàDBDJÓO EF BHVB  QSPDFTPT GBSNBDÊVUJDPT Z QVSJàDBDJÓO EFM FUBOPM  SFTQFDUJWBNFOUF&MOVFWPDBQÎUVMPFTVOBFYUFOTBJOUSPEVDDJÓOBMBBETPSDJÓO DSPNBUPHSB GÎBFJOUFSDBNCJPJÓOJDP&TBTTFQBSBDJPOFTTFTVFMFOVTBSQBSBQSPDFTBSTVTUBODJBTRVÎNJDBTZ GBSNBDÊVUJDBTEFBMUBDBMJEBE5BNCJÊO MBBETPSDJÓOZFMJOUFSDBNCJPJÓOJDPTFVTBODPOGSF DVFODJBQBSBUSBUBNJFOUPEFBHVB"VORVFOJMBTTFQBSBDJPOFTDPONFNCSBOBOJQPSBETPSDJÓO TFTVFMFOIBDFSUSBCBKBSFOGPSNBEFTFQBSBDJPOFTDPOFUBQBTEFFRVJMJCSJP FTTPSQSFOEFOUF RVFUFOHBONVDIBTDPOFYJPOFTDPOMPTQSPDFTPTDPOFUBQBTEFFRVJMJCSJP  &TJOFWJUBCMFRVFMBTFHVOEBFEJDJÓOTFBNÃTMBSHBRVFMBQSJNFSB)FUSBUBEPEFFWJUBS FTUPFMJNJOBOEPBMHPEFMNBUFSJBMPSJHJOBMZDPNCJOBOEPBMHVOPTDBQÎUVMPT&MNBUFSJBMBDFSDB EFMFRVJMJCSJP FMBOUFSJPSDBQÎUVMP TFSFQBSUFBIPSBFOUPEPFMUFYUP QPSMPRVFTFQSFTFOUBEF NBOFSBiKVTUPBUJFNQPu BNFEJEBRVFTFOFDFTJUB -PTDBQÎUVMPTZPSJHJOBMFT TPCSFFM NÊUPEPEF.D$BCF5IJFMFQBSBBOBMJ[BSMBEFTUJMBDJÓOCJOBSJB TFIBODPNCJOBEPFOVOPTPMP  FMOVFWPDBQÎUVMP&MNÊUPEPEF.D$BCF5IJFMFTFTJHVFVTBOEPDPNPNFEJPEFWJTVBMJ[B DJÓOZHVÎBQBSBMPDBMJ[BSQSPCMFNBT BVORVFZBOPTFVTBFO&6" QBSBEJTFÒPTEFUBMMBEPT 4FDPOTFSWBSPOUSFTDBQÎUVMPTTPCSFEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT MPTOVFWPTDBQÎUVMPT B

QFSPFOGPSNBTJNQMJàDBEB&MBMDBODFEFMDBQÎUVMPTPCSFEFTUJMBDJÓODPNQMFKB FMOVFWP YW

www.FreeLibros.me

YWJ

1SFGBDJP

DBQÎUVMP TFIBBNQMJBEPQBSBSFáFKBSMPTBWBODFTFOMBDPNQSFOTJÓOEFMBEFTUJMBDJÓOFY USBDUJWBZB[FPUSÓQJDB5BNCJÊOTFIBBNQMJBEPMBFYQPTJDJÓOEFMBEFTUJMBDJÓOJOUFSNJUFOUF FM OVFWPDBQÎUVMP   -PTEPTDBQÎUVMPTPSJHJOBMFTTPCSFEJTFÒPEFDPMVNOBTTFIBODPNCJOBEPFOFMOVFWPDBQÎ UVMP-BJOGPSNBDJÓOFDPOÓNJDB EFMBOUFSJPSDBQÎUVMP TFIBDPOEFOTBEP QPSRVFFOHF OFSBMTFFOTFÒBFOMBTDMBTFTEFEJTFÒP4JOFNCBSHP FMNBUFSJBMTPCSFDPOTFSWBDJÓOEFFOFSHÎB ZTFDVFODJBDJÓOEFMBTDPMVNOBTEFEFTUJMBDJÓOEFFTFDBQÎUVMP TFIBBNQMJBEP QBSBBCBSDBS BMHVOPTEFMPTBWBODFTFOEFTUJMBDJÓODPNQMFKB FOFMOVFWPDBQÎUVMP-PTDBQÎUVMPTZ BOUFSJPSFTTFIBODPNCJOBEPFOFMOVFWPDBQÎUVMP VTBOEPFMNÊUPEPEF.D$BCF5IJFMFZ MBFDVBDJÓOEF,SFNTFSQBSBFYUSBDDJÓOJONJTDJCMF MBWBEP MJYJWJBEPZFYUSBDDJÓOTVQFSDSÎUJDB -BTFDDJÓOTPCSFIVNJEJàDBDJÓOTFIBFMJNJOBEPEFMDBQÎUVMP FMOVFWPDBQÎUVMP

QPSRVF QBSFDÎBGVFSBEFMVHBS  5PEPTMPTDBQÎUVMPTJODMVZFOVOBHSBODBOUJEBEEFQSPCMFNBTQBSBSFTPMWFSGVFSBEFMBVMB EF DMBTFT  RVF TVSHJFSPO B NFEJEB RVF DPOUJOVBCB MB FOTFÒBO[B EF MB NBUFSJB FO MB 1VSEVF 6OJWFSTJUZUBNCJÊOTFIBOBHSFHBEPWBSJPTQSPCMFNBTEFTJNVMBDJÓO  &OWJTUBEFRVFIPZMPTTJNVMBEPSFTEFQSPDFTPTFVTBONVDIPFOMBQSÃDUJDBDPNFSDJBM  IFJODMVJEPFOUPEPFMUFYUPFKFNQMPTZQSPCMFNBTEFUBSFBTPCSFTJNVMBDJÓOEFQSPDFTPT)PZ FOTFÒPFMDVSTPEFTFQBSBDJPOFT EFUSFTDSÊEJUPT QBSBQSJODJQJBOUFT FO1VSEVF FOEPTDMBTFTZ EPTIPSBTEFMBCPSBUPSJPEFDÓNQVUPQPSTFNBOB&OFMMBCPSBUPSJPEFDÓNQVUPTFJODMVZFVOB QSVFCBQBSBFWBMVBSMBDBQBDJEBEEFMPTBMVNOPTQBSBVTBSFMTJNVMBEPS"VORVFZPVTP"TQFO 1MVTDPNPTJNVMBEPS TFQVFEFVTBSDVBMRVJFSTJNVMBEPSEFQSPDFTPT-PTOVFWPTDBQÎUVMPT    ZUJFOFOBQÊOEJDFTRVFQSFTFOUBOJOTUSVDDJPOFTQBSBNBOFKBS"TQFO1MVT&MBQÊOEJDF EFMDBQÎUVMPUJFOFIPKBTEFDÃMDVMP&YDFM DPOQSPHSBNBTEF7JTVBM#BTJDQBSBQFSNFBDJÓOEF HBTFOáVKPDSV[BEP DPODVSSFOUFZBDPOUSBDPSSJFOUF0QUÊQPSVTBSIPKBTEFDÃMDVMPFOMVHBS EFVOQSPHSBNBNBUFNÃUJDPEFNBZPSOJWFM QPSRVFMBTIPKBTEFDÃMDVMPTFDPOTJHVFOFOUPEBT QBSUFT &M BQÊOEJDF EFM DBQÎUVMP  DPOUJFOF CSFWFT JOTUSVDDJPOFT QBSB NBOFKBS FM TJNVMBEPS DPNFSDJBM"TQFO$ISPNBUPHSBQIZFTQPTJCMFTPMJDJUBSIPKBTEFJOTUSVDDJPOFTNÃTEFUBMMBEBTBM BVUPS FOFMDPSSFPFMFDUSÓOJDPXBOLBU!FDOQVSEVFFEV  &MNBUFSJBMEFMBTFHVOEBFEJDJÓOIBTJEPQSPCBEPBNQMJBNFOUFFOFMDVSTPEFTFQBSBDJP OFTQBSBQSJODJQJBOUFTFOMB6OJWFSTJEBE1VSEVF"VORVFFOTFÒPFMNBUFSJBMBOJWFMEFQSJODJ QJBOUFT MPTDBQÎUVMPTBEFCFOTFSQBSBJOUFSNFEJPT ZUPEPFMNBUFSJBMFTBEFDVBEPQBSBMPT OJWFMFTTVQFSJPSFT-BTFHVOEBFEJDJÓOFTEFNBTJBEPMBSHBQBSBDVCSJSTFFOVOTFNFTUSF QFSP FTQPTJCMFDVCSJSMBQPSDPNQMFUP DPOTJNVMBDJPOFTFODPNQVUBEPSB FOEPTTFNFTUSFT.VDIBT FTDVFMBT  DPNP 1VSEVF  BTJHOBO VO TPMP DVSTP TFNFTUSBM EF USFT DSÊEJUPT QBSB FTUF NBUFSJBM $PNPFTEFNBTJBEPNBUFSJBM FOFTUFDBTPEFCFOTFMFDDJPOBSTFMPTUFNBT

www.FreeLibros.me

"HSBEFDJNJFOUPT

.VDIBTQFSTPOBTBZVEBSPOBFTDSJCJSMBQSJNFSBFEJDJÓO&M%S.BSKBO#BDFZFMQSPGFTPS+PF $BMPIJDJFSPORVFDPNFO[BSBBFTDSJCJSMB"17*OD (MJUTDI*ODZ5IF/PSUPO$P BNB CMFNFOUFNFTVNJOJTUSBSPOGPUPHSBGÎBT$ISJT3PFTFMZ#BSC/BVHMF)JMEFCSBOEIJDJFSPOMBT QSJNFSBTJMVTUSBDJPOFT1BSBUFSNJOBSMBQSJNFSBFEJDJÓOGVFFTFODJBMMBBZVEBTFDSFUBSJBMEF $BSPMZO#MVF %FCSB#PXNBO +BO(SBZZ#FDLZ8BUTPO.JTBZVEBOUFTBDBEÊNJDPT.BHEJFM "HPTUP $ISJT#VFIMFS .BSHSFU4IBZ 4VOH4VQ4VIZ/BSBTJOIBO4VOEBSBNBZVEBSPOBMP DBMJ[BSFSSPSFT-PTQSPGFTPSFT3PO"OESFT +BNFT$BSVUIFST ,BSM5$IVBOH "MEFO&NFSZ Z %BWJE 1 ,FTTMFT  BTÎ DPNP $IBSMFT (JMMBSE BZVEBSPO B SFWJTBS QBSUFT EFM UFYUP 5BNCJÊO UFOHPEFVEBDPOMPTQSPGFTPSFTEFMPTRVFBQSFOEÎFTUFNBUFSJBM-PXFMM,PQQFM RVFEFTQFSUÓ NJJOUFSÊTFOMBTTFQBSBDJPOFT FOFMOJWFMMJDFODJBUVSB8JMMJBN34DIPXBMUFS RVJFOBNQMJÓ NJTIPSJ[POUFTNÃTBMMÃEFMBTTFQBSBDJPOFTDPOFUBQBTEFFRVJMJCSJPFOMPTFTUVEJPTTVQFSJPSFT Z$+VETPO,JOH RVJFODPOTVTBSUÎDVMPT TVMJCSPZTVFKFNQMPQFSTPOBMNBOUVWPWJWPTNJT JOUFSFTFTTJFOEPZPQSPGFTPSZBENJOJTUSBEPS "HSBEF[DPUBNCJÊOMBBZVEBEF-FF.FBEPXT +FOOJ-BZOFZ,BSFO)FJEFFOMBQSFQB SBDJÓO EF MB TFHVOEB FEJDJÓO *HVBMNFOUF B MPT SFWJTPSFT +PIO )FZEFJMMFS  4UFXBSU 4MBUFS Z +PF4IBFJXJU[QPSTVTUBOÙUJMFTSFWJTJPOFT-PTÃOJNPTZBQSFNJPTPDBTJPOBMFTEFNJFEJUPS  #FSOBSE (PPEXJO  GVFSPO EF NVDIB BZVEB QBSB RVF QSFQBSBSB FTUB UBO EFNPSBEB TFHVOEB FEJDJÓO 1PSÙMUJNP OPIBCSÎBUFSNJOBEPMBTFHVOEBFEJDJÓOTJOFMBNPSZFMBQPZPEF%PU NJFT QPTB ZNJTIJKPT$IVDLZ+FOOJF

YWJJ

www.FreeLibros.me

www.FreeLibros.me

"DFSDBEFMBVUPS

1IJMMJQ $ 8BOLBU PTUFOUB FM UÎUVMP EF 1SPGFTPS %JTUJOHVJEP $MJGUPO - -PXFMM  FO *OHFOJFSÎB 2VÎNJDBZFT%JSFDUPSEF1SPHSBNBTEF-JDFODJBUVSBFOFM%FQBSUBNFOUPEF&EVDBDJÓOFO*O HFOJFSÎB EF MB 1VSEVF 6OJWFSTJUZ )B FTUBEP JOWPMVDSBEP FO MB JOWFTUJHBDJÓO Z FOTFÒBO[B EF TFQBSBDJPOFTEVSBOUFNÃTEFBÒPT ZUJFOFHSBOJOUFSÊTFOFMNFKPSBNJFOUPEFMBFOTFÒBO[BZ FMBQSFOEJ[BKFEFMBJOHFOJFSÎB&TBVUPSEFEPTMJCSPTBDFSDBEFDÓNPFOTFÒBSZUSFTTPCSFQSPDF TPTEFTFQBSBDJÓO)BSFDJCJEPWBSJPTQSFNJPTOBDJPOBMFTEFJOWFTUJHBDJÓOZPUSPTQSFNJPTMPDBMFT ZOBDJPOBMFTBMBFOTFÒBO[B

YJY

www.FreeLibros.me

www.FreeLibros.me

/PNFODMBUVSB

 $BQÎUVMPTB B BQ BQ BQ BQ B5 B5 B5 " # $ " # $ % & " # $ % "& #& $& %& "BDUJWB "D "E "EV "BHVKFSP "* "OFUB C # $ $#. $G- $P $Q $Q $Q UBNBÒP $Q8 $T $TC E % % % %JB %′DPM %UPUBM F

ÃSFBJOUFSGBDJBMQPSVOJEBEEFWPMVNFO QJFQJFPNN ÃSFBTVQFSàDJBMWPMVNFO NN DPOTUBOUFTFOMBFDVBDJÓO  ZMBUBCMB DPOTUBOUFTFOMBFDVBDJÓOEF"OUPJOF 

DPOTUBOUFTFOMBFDVBDJÓO 

DPOTUBOUFTFOMBGPSNBNBUSJDJBMEFCBMBODFTEFNBTB  FDVBDJPOFT  Z 

DPOTUBOUFTFOMBGPSNBNBUSJDJBMEFCBMBODFTEFFOFSHÎB FDVBDJÓO 

ÃSFBBDUJWBEFQMBUP QJFPN ÃSFBUSBOTWFSTBMEFMBDPMVNOB QJFPN ÃSFBEFCBKBOUF QJFPN ÃSFBEFáVKPCBKPFMNBOEJMEFMBCBKBOUF FDVBDJÓO 

QJF ÃSFBEFMPTBHVKFSPTFOMBDPMVNOB QJF ÃSFBJOUFSGBDJBMFOUSFEPTGBTFT QJFPN ÃSFBOFUB FDVBDJÓO 

QJFPN DPOTUBOUFEFFRVJMJCSJPMJOFBM ZNY C UBTBEFáVKPEFDPMBTPGPOEPT DBOUJEBEEFDPNQPOFOUFT DPTUPEFNÓEVMPFTDVFUP DBQÎUVMP DPFàDJFOUFEFDBSHBEFWBQPS FDVBDJÓO 

DPFàDJFOUFEFPSJàDJP FDVBDJÓO 

DBQBDJEBEDBMPSÎàDB #UVMCž' #UVMCNPMž' PDBMHž$PDBMHNPMž$ FUD DPTUPCBTFEFDPNQSB DBQÎUVMP GBDUPSEFUBNBÒPEFFNQBRVF UBCMB DBQBDJEBEDBMPSÎàDBEFMBHVB GBDUPSEFDBQBDJEBEFOJOVOEBDJÓO FDVBDJÓO 

GBDUPSEFDBQBDJEBE FDVBDJÓO 

GBDUPSEFBNPSUJHVBNJFOUP FDVBDJÓO 

EJGVTJWJEBE DNTQQJFI EJÃNFUSPEFMBDPMVNOB QJFTPN EJÃNFUSPEFMBDPMVNOB WÊBTFUBCMB QJFT DBOUJEBEUPUBMEFEFTUJMBEP DBQÎUVMP

áVKPEFNPMFTPLHEFEFTUJMBEP LH NPMIPMCNPMI BSSBTUSFBCTPMVUP NPMFTI YYJ

www.FreeLibros.me

YYJJ

& ® &L &.- &.7 &P &QU FTQ ®U G7' G Y

GL 7'

' ' ' ' ' '% 'MW '1 'N 'Q 'R 'T 'TPMW 'TÓMJEP 'X H ( (′ I I I I I I} IG I' IP IQ IUPUBM ) ) ) )( )- )0( )0- )&51 )56 +"

/PNFODMBUVSB

UBTBEFáVKPEFMFYUSBDUP DBQÎUVMPTZ

LHI NBTBEFFYUSBDUP LH WBMPSEFMBGVODJÓOEFFOFSHÎBQBSBUBOUFPL FDVBDJÓO 

FàDBDJBTEF.VSQIFF EFMÎRVJEPZWBQPS FDVBDJPOFT  Z 

FàDJFODJBHFOFSBM FDVBDJÓO 

FàDJFODJBQVOUVBM FDVBDJÓO  P B

FTQBDJPFOUSFNBOEJMEFMBCBKBOUFIBTUBFMQMBUP FDVBDJÓO 

QJFT SFUFODJÓOEFGBTFEFFYUSBDUPFOUBORVFNÃTTFEJNFOUBEPS LH GSBDDJÓOWBQPSJ[BEB GVODJÓOEFFRVJMJCSJP DBQÎUVMP GVODJÓOEF3BDIGPSE3JDFQBSBUBOUFP, FDVBDJÓO   GBDUPSEFFNQBRVF àHVSBZUBCMBTZ HSBEPTEFMJCFSUBE FDVBDJÓO

DBSHBBMQPDJMMPEFMEFTUJMBEPS DBQÎUVMP

NPMFTPLH NBTBEFBMJNFOUBDJÓOFOFYUSBDDJÓOJOUFSNJUFOUF LH UBTBEFáVKPEFBMJNFOUBDJÓO LHNPMIPMCNPMI PLHI FUD UBTBEFáVKPEFMEJMVZFOUF DBQÎUVMP

LHI LA LK

A′ šA 2  Z#< # $17 # 5−5SFG >



EPOEFY"ZZ"TPOMBTGSBDDJPOFTNPMEFMDPNQPOFOUF"FOFMMÎRVJEPZFMWBQPS SFTQFDUJWBNFOUF$Q FTMBDBQBDJEBEDBMPSÎàDBNPMBS 5SFGFTMBUFNQFSBUVSBEFSFGFSFODJBRVFTFIBZBFTDPHJEPZ FTFM DBMPSMBUFOUFEFFWBQPSBDJÓOBMB5SFG1BSBTJTUFNBTCJOBSJPT Y#−Y"ZZ#−Z"

 1SPDFEJNJFOUPTFDVFODJBMEFTPMVDJÓO

&OFMQSPDFEJNJFOUPTFDVFODJBMEFTPMVDJÓO QSJNFSPTFSFTVFMWFOMBTSFMBDJPOFTEFCBMBODFEFNBTB ZEFFRVJMJCSJP ZEFTQVÊTMBTFDVBDJPOFTEFCBMBODFEFFOFSHÎBZEFFOUBMQÎB&OPUSBTQBMBCSBT MPT EPTDPOKVOUPTEFFDVBDJPOFTFTUÃOEFTBDPQMBEPT&MQSPDFEJNJFOUPTFDVFODJBMEFTPMVDJÓOTFBQMJDB

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOJOTUBOUÃOFB

DVBOEPTFVTBFMÙMUJNPHSBEPEFMJCFSUBEQBSBFTQFDJàDBSVOBWBSJBCMFSFMBDJPOBEBDPOMBTDPOEJDJP OFTEFMUBNCPSEFEFTUJMBDJÓO-BTPQDJPOFTQPTJCMFTTPO 'SBDDJÓONPMFOWBQPS Z 'SBDDJÓONPMFOMÎRVJEP Y 'SBDDJÓOFWBQPSBEBEFMBBMJNFOUBDJÓO G7' 'SBDDJÓOEFMBBMJNFOUBDJÓOFOFMMÎRVJEPSFNBOFOUF R-' 5FNQFSBUVSBEFMUBNCPSEFEFTUJMBDJÓO 5UBNC 4JTFFTQFDJàDBVOBEFMBTDPOEJDJPOFTEFFRVJMJCSJP Z YP5UBNC FOUPODFTTFQVFEFOEFUFSNJOBS MBTPUSBTEPTDPOMBTFDVBDJPOFT  P 

PCJFODPOMBSFQSFTFOUBDJÓOHSÃàDBEFMPTEBUPTEF FRVJMJCSJP1PSFKFNQMP TJTFFTQFDJàDBZ YTFPCUJFOFDPOMBFDVBDJÓO 

Z5UBNCDPOMBFDVBDJÓO  &OMPTCBMBODFTEFNBTB FDVBDJPOFT  Z 

MBTÙOJDBTJODÓHOJUBTTPO-Z7 ZMBTEPT FDVBDJPOFTQVFEFOSFTPMWFSTFFOGPSNBTJNVMUÃOFB 4JTFFTQFDJàDBMBGSBDDJÓOFWBQPSBEBPMBGSBDDJÓOEFMMÎRVJEPSFNBOFOUF TFEFCFOSFTPMWFS TJNVMUÃOFBNFOUFMBTFDVBDJPOFT 

  Z  -BGPSNBNÃTDÓNPEBEFIBDFSMPFTDPNCJOBS MPTCBMBODFTEFNBTB"MEFTQFKBSZEFMBFDVBDJÓO  SFTVMUB 





-BFDVBDJÓO  FTMBFDVBDJÓOEFPQFSBDJÓORVF QBSBVOTJTUFNBEFVOBTPMBFUBQB SFMBDJPOBMBT DPNQPTJDJPOFTEFMBTEPTDPSSJFOUFTRVFTBMFOEFMBFUBQB-BFDVBDJÓO  TFQVFEFFYQSFTBSFO UÊSNJOPTEFMBGSBDDJÓOFWBQPSBEB G7' PEFMBGSBDDJÓOEFMMÎRVJEPSFNBOFOUF R-' %FBDVFSEPDPOFMCBMBODFHFOFSBMEFNBTB FDVBDJÓO 







&OUPODFT MBFDVBDJÓOEFPQFSBDJÓOTFUSBOTGPSNBFO 





-BBMUFSOBUJWB FOUÊSNJOPTEF-' FT 





ZMBFDVBDJÓOEFPQFSBDJÓOFT 





"VORVFDPOEJGFSFOUFGPSNB MBTFDVBDJPOFT 

  Z  TPONÊUPEPTFRVJWBMFOUFTQBSB PCUFOFSZ YP[6TBSFNPTFOUPODFTMBFDVBDJÓOEFPQFSBDJÓORVFTFBNÃTDPOWFOJFOUF

www.FreeLibros.me

 %FTUJMBDJÓOJOTUBOUÃOFBCJOBSJB



"IPSBTFEFCFOSFTPMWFSTJNVMUÃOFBNFOUFMBFDVBDJÓOEFFRVJMJCSJP  ZMBFDVBDJÓOEFPQF SBDJÓO FDVBDJPOFT P -BGPSNBFYBDUBEFIBDFSMPEFQFOEFEFMBGPSNBEFMPTEBUPT EFFRVJMJCSJP1BSBTJTUFNBTCJOBSJPT VOBTPMVDJÓOHSÃàDBFTNVZDÓNPEB-BTFDVBDJPOFT 

  Z  SFQSFTFOUBOVOBTPMBMÎOFBSFDUB MMBNBEBMÎOFBEFPQFSBDJÓO FOVOBHSÃàDBEFZFO GVODJÓOEFY&TUBMÎOFBSFDUBUFOESÃ 





Z 





5BNCJÊOTFQVFEFOHSBàDBSMPTEBUPTEFFRVJMJCSJPBMBQSFTJÓOQUBNC FOFMEJBHSBNBZY-BJOUFS TFDDJÓOEFMBDVSWBEFFRVJMJCSJPZMBMÎOFBEFPQFSBDJÓOFTMBTPMVDJÓOTJNVMUÃOFBEFMPTCBMBODFT EFNBTBFOFRVJMJCSJP&TUBHSÃàDBEFZFOGVODJÓOEFY RVFNVFTUSBMBTMÎOFBTEFFRVJMJCSJPZEF PQFSBDJÓO TFMMBNBEJBHSBNBEF.D$BCF5IJFMF ZTFWFFOMBàHVSBQBSBFMDBTPEFMBTFQBSBDJÓO EFFUBOPMBHVB-PTEBUPTEFFRVJMJCSJPTPOEFMBUBCMB ZMBDVSWBEFFRVJMJCSJPFTJEÊOUJDBBMBEF MBàHVSB&MQVOUPTPMVDJÓOJOEJDBMBTDPODFOUSBDJPOFTEFWBQPSZMÎRVJEPRVFTBMFOEFMUBNCPS EFFWBQPSBDJÓOJOTUBOUÃOFB-BàHVSBNVFTUSBUSFTMÎOFBTEJGFSFOUFTEFPQFSBDJÓO DVBOEP7' WBSÎBEFB QBTBOEPQPS WFBFMFKFNQMP 5UBNCTFQVFEFDBMDVMBSDPOMBFDVBDJÓO  P FOVOEJBHSBNBEFUFNQFSBUVSBDPNQPTJDJÓO 0USPTEPTQVOUPTRVFTFVTBODPOGSFDVFODJBFOFMEJBHSBNBEF.D$BCF5IJFMFTPOMBBCTDJTBBM PSJHFO Z EFMBMÎOFBEFPQFSBDJÓOZTVJOUFSTFDDJÓODPOMBSFDUBZY$VBMRVJFSBEFFTPTQVOUPT UBNCJÊOTFQVFEFEFUFSNJOBSBMHFCSBJDBNFOUFQBSBFOUPODFTHSBàDBSDPOFMMPTMBMÎOFBEFPQFSBDJÓO

línea de operación pendiente = L/V

'*(63" %*"(3"."%&.$$"#& 5)*&-&1"3"%&45*-"$*¶/*/45"/5¦/&" #*/"3*"4&*-6453"1"3"&-&+&.1-0

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOJOTUBOUÃOFB

-BJOUFSTFDDJÓOEFMBMÎOFBEFPQFSBDJÓODPOMBMÎOFBZYTFVTBDPOGSFDVFODJBQPSRVFFTGÃDJM EFHSBàDBS&TUFQVOUPTFQVFEFEFUFSNJOBSSFTPMWJFOEPTJNVMUÃOFBNFOUFMBFDVBDJÓO  ZMB FDVBDJÓOZY"MTVTUJUVJSZYFOMBFDVBDJÓO  SFTVMUB 

PCJFO 

PUBNCJÊO 

DPNP7 -' FMSFTVMUBEPFTZ[ ZFODPOTFDVFODJB 

YZ[

-BJOUFSTFDDJÓOFTUÃFOMBDPNQPTJDJÓOEFMBBMJNFOUBDJÓO &TJNQPSUBOUFEBSTFDVFOUBEFRVFMBMÎOFBZYOPUJFOFJNQPSUBODJBGVOEBNFOUBM4FVTBDPO GSFDVFODJBFOMPTNÊUPEPTHSÃàDPTEFTPMVDJÓOQPSRVFTJNQMJàDBMPTDÃMDVMPT4JOFNCBSHP OPTF EFCFVTBSBDJFHBT &TPCWJPRVFTFQVFEFVTBSMBUÊDOJDBHSÃàDBTJTFFTQFDJàDBZ YP5UBNC&MPSEFOFORVFTF EFUFSNJOBOMPTQVOUPTFOFMEJBHSBNBEFQFOEFSÃEFMBJOGPSNBDJÓODPORVFDVFOUBVOPQBSBDP NFO[BS &+&.1-0 4FQBSBEPSEFFWBQPSBDJÓOJOTUBOUÃOFBQBSBFUBOPMZBHVB 6OBDÃNBSBEFEFTUJMBDJÓOJOTUBOUÃOFBUSBCBKBBL1BZTFQBSBVOBNF[DMBEFFUBOPM BHVB-BNF[DMBRVFTFBMJNFOUBFTNPMEFFUBOPMB y$VÃMFTMBDPNQPTJDJÓONÃYJNB EFMWBQPS C y$VÃMFTMBDPNQPTJDJÓONÎOJNBEFMMÎRVJEPRVFTFQVFEFPCUFOFSTJTFEFKB WBSJBS7' D 4J7' yDVÃMFTTPOMBTDPNQPTJDJPOFTEFMMÎRVJEPZEFMWBQPS E 3FQJUB FMQBTPDQBSBDVBOEP'TFBLHNPMIPSB 4PMVDJÓO " %FGJOB%FTFBNPTBOBMJ[BSFMGVODJPOBNJFOUPEFVOTFQBSBEPSEFFWBQPSBDJÓOJOTUBO UÃOFBBBUN B $BMDVMFZNÃY C $BMDVMFYNÎO D ZE$BMDVMFZZYQBSB7' # &YQMPSF0CTFSWFRVFQUBNCL1BBUN&OUPODFTTFEFCFOVTBSEBUPTQBSB FTUBQSFTJÓO&TPTEBUPTFTUÃOEJTQPOJCMFTFOMBUBCMBZFOMBàHVSB$PNPQUBNC Z7'QBSBMBQBSUFDTPOEBUPT TFVTBSÃVOQSPDFEJNJFOUPTFDVFODJBMEFTPMVDJÓO1BSB MBTQBSUFTBZCCVTDBSFNPTWBMPSFTMÎNJUFEF7' $ 1MBOFF6TBSFNPTFMEJBHSBNBZYRVFTFWFFOMBàHVSB1BSBUPEPTMPTDBTPTIBSF NPTVOCBMBODFEFNBTBQBSBEFEVDJSVOBMÎOFBEFPQFSBDJÓO0CTFSWFRVF 7' &OUPODFT OVFTUSPTWBMPSFTNÃYJNPZNÎOJNP EF7'EFCFOFTUBSEFOUSPEFFTUFJOUFSWBMP % )ÃHBMP"DPOUJOVBDJÓOTFNVFTUSBFMFTRVFNB

#BMBODFTEFNBTB 





'7 '[7Z -Y

%FTQFKFZ 

%FBDVFSEPDPOFMCBMBODFHFOFSBM -'¢7  DVBOEP7' 7 -'Z-7' DVBOEP7' 7  ' -  'Z-7  '<  '> DVBOEP7' 7' -Z-7' &OUPODFT MBTQFOEJFOUFT ¢-7 TPO¢ ¢Z¢ 4JEFTQFKBNPTMBJOUFSTFDDJÓOZY WFSFNPTRVFFTUÃFOZY[ FOUPEPTMPT DBTPT 1PSMPUBOUP QPEFNPTUSB[BSUSFTMÎOFBTEFPQFSBDJÓORVFQBTFOQPSZY[ DPO QFOEJFOUFTEF¢ ¢Z¢&TBTMÎOFBTEFPQFSBDJÓOTFNVFTUSBOFOMBàHVSB B -BZNÃYJNBFTQBSB7' Z C -BYNÎOJNBFTQBSB7' Y D $VBOEP7'FT ZZY E $VBOEP' DPO7' FMSFTVMUBEPFTFYBDUBNFOUFJHVBMRVFFMEFMB QBSUFD&MáVKPEFBMJNFOUBDJÓOJOáVJSÃTPCSFFMEJÃNFUSPEFMUBNCPSZMBFOFSHÎB RVFTFOFDFTJUBFOFMQSFDBMFOUBEPS & $PNQSVFCF1PEFNPTWFSJàDBSMBTTPMVDJPOFTDPOFMCBMBODFEFNBTB '[7Z -Y B         DPSSFDUP C         DPSSFDUP D         

 0CTFSWFRVF7  'Z-  '  &MSFTVMUBEPFT DPSSFDUPEFOUSPEFMBFYBDUJUVEEFMBHSÃàDB E -BDPNQSPCBDJÓOFTTJNJMBSBMBEFMQVOUPD 5BNCJÊOQPESFNPTWFSJàDBSBKVTUBOEPMPTEBUPTEFFRVJMJCSJPBVOBFDVBDJÓODÙCJDB ZSFTPMWFSTJNVMUÃOFBNFOUFMBTFDVBDJPOFTEFFRVJMJCSJPZPQFSBDJÓO NJOJNJ[BOEPFMSFTJ EVP-PTDÃMDVMPTDPODVFSEBODPOMBTPMVDJÓOHSÃàDB ' (FOFSBMJDF &M NÊUPEP QBSB PCUFOFS FM SFTVMUBEP VTBOEP MPT WBMPSFT EF 7' FO TVT MÎNJUFTFYUSFNPTEFZ TFQVFEFVTBSQBSBPUSPTDBTPTEJWFSTPT&OHFOFSBM FM

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOJOTUBOUÃOFB

áVKPEFBMJNFOUBDJÓOOPBGFDUBSÃMBTDPNQPTJDJPOFTPCUFOJEBTFOFMEJTFÒPEFTFQB SBEPSFT FO FUBQBT &M áVKP EF BMJNFOUBDJÓO TÎ BGFDUB B MBT OFDFTJEBEFT EF DBMPS Z BM EJÃNFUSPEFMFRVJQP 6OBWF[DBMDVMBEBTMBTDPOEJDJPOFTFOFMJOUFSJPSEFMUBNCPSEFEFTUJMBDJÓOTFQSPDFEFBIBDFS FMCBMBODFEFFOFSHÎB$POPDJEPTZ YZ5UBNC TFDBMDVMBODPOGBDJMJEBEMBTFOUBMQÎBT)WZI-DPOMBT FDVBDJPOFT  P  Z  &OUPODFT MBÙOJDBJODÓHOJUBFOMBFDVBDJÓO  FTMBFOUBMQÎBEF BMJNFOUBDJÓO I'$VBOEPTFDPOPDFI' TFQVFEFPCUFOFSMBUFNQFSBUVSBEFFOUSBEBEFMBBMJNFOUB DJÓO 5' DPOMBFDVBDJÓO  P C  -B DBOUJEBE EF DBMPS RVF TF SFRVJFSF FO FM DBMFOUBEPS  2I  TF EFUFSNJOB DPO VO CBMBODF EF FOFSHÎBFOFMDBMFOUBEPS 





:BRVFMBFOUBMQÎBIMTFQVFEFDBMDVMBSBQBSUJSEF5MZ[ MBÙOJDBJODÓHOJUBFT2I RVFDPOUSPMBFM UBNBÒPEFMDBMFOUBEPS -BQSFTJÓOEFFOUSBEB Q' RVFTFSFRVJFSF FTiTFNJBSCJUSBSJBu4FQVFEFVTBSDVBMRVJFSQSF TJÓOMPTVàDJFOUFNFOUFBMUBQBSBFWJUBSMBFCVMMJDJÓOBMBUFNQFSBUVSB5' 6OSFTVMUBEPBEJDJPOBMZÙUJMFTFMDÃMDVMPEF7'DVBOEPTFDPOPDFOUPEBTMBTGSBDDJPOFTNPMB SFT Y Z [ "MSFTPMWFSMBTFDVBDJPOFT  Z 

SFTVMUB 





$POFTUPTFUFSNJOBFMQSPDFEJNJFOUPTFDVFODJBM FYDFQUPQPSFMEJNFOTJPOBNJFOUPEFMUBNCPS EFFWBQPSBDJÓOJOTUBOUÃOFB RVFTFEFTDSJCJSÃEFTQVÊT0CTFSWFRVFMBTWFOUBKBTEFFTUFQSPDFEJ NJFOUP TPO RVF MPT CBMBODFT EF NBTB Z FOFSHÎB FTUÃO EFTBDPQMBEPT Z RVF TF QVFEFO SFTPMWFS FO GPSNBJOEFQFOEJFOUF1PSFMMPOPTFSFRVJFSFVONÊUPEPDPOUBOUFPT 4JTFDVFOUBDPOVOBFDVBDJÓOBEFDVBEBQBSBMPTEBUPTEFFRVJMJCSJP TFQVFEFUFOFSMBTPMVDJÓO TJNVMUÃOFBEFMBFDVBDJÓOEFPQFSBDJÓO  P ZMBFDVBDJÓOEFFRVJMJCSJP FOGPSNBBOBMÎ UJDB1PSFKFNQMP MPTTJTUFNBTJEFBMFTUJFOFO DPOGSFDVFODJB VOBWPMBUJMJEBESFMBUJWB "#DPOTUBOUF  FTUBOEP "#EFàOJEBDPNP 





1BSBTJTUFNBTCJOBSJPT 



ZMBWPMBUJMJEBESFMBUJWBFT 



B

"MEFTQFKBSZ"EFMBFDVBDJÓO  SFTVMUB 



www.FreeLibros.me

C

 %FTUJMBDJÓOJOTUBOUÃOFBCJOBSJB



$VBOEPFTWÃMJEBMBMFZEF3BPVMU MBWPMBUJMJEBESFMBUJWBTFQVFEFEFUFSNJOBSDPNP 





5BNCJÊOTFQVFEFBKVTUBSMBWPMBUJMJEBESFMBUJWB BMPTEBUPTFYQFSJNFOUBMFT "MSFTPMWFSTJNVMUÃOFBNFOUFMBTFDVBDJPOFT  Z 

TFPCUJFOF 





RVFFTVOBFDVBDJÓODVBESÃUJDBRVFTFSFTVFMWFDPOGBDJMJEBE&TPTFQVFEFIBDFSDÓNPEBNFOUFDPO VOBIPKBEFDÃMDVMP

 1SPDFEJNJFOUPEFTPMVDJÓOTJNVMUÃOFB

4JMBWBSJBCMFFTQFDJàDBEBFTMBUFNQFSBUVSBEFMBBMJNFOUBDJÓOBMUBNCPS 5' FTOFDFTBSJPSFTPMWFS FOGPSNBTJNVMUÃOFBMPTCBMBODFTEFNBTBZFOFSHÎB ZMBTFDVBDJPOFTEFFRVJMJCSJP&OFMCBMBODFEF FOFSHÎB FDVBDJÓO 

TFQVFEFWFSQPSRVÊTVDFEFBTÎ4FQVFEFDBMDVMBSMBFOUBMQÎBEFBMJNFOUB DJÓO I' QFSPMBTFOUBMQÎBTEFWBQPSZMÎRVJEP )WZI- EFQFOEFOEF5UBNC ZZY RVFTFEFTDPOPDFO 1PSFMMPOPFTQPTJCMFUFOFSVOBTPMVDJÓOTFDVFODJBM 4FQPESÎBOFTDSJCJSMBTFDVBDJPOFT  BMB  ZSFTPMWFSTJNVMUÃOFBNFOUFTJFUFFDVBDJPOFT DPOTJFUFJODÓHOJUBTZ Y - 7 )W I-Z5UBNC&TPFTQPTJCMFQFSPCBTUBOUFEJGÎDJM FOFTQFDJBMQPSRVF MBTFDVBDJPOFT 

  ZDPOGSFDVFODJBMB  TPOOPMJOFBMFTFOUPODFTTFSFDVSSFBVOQSPDF EJNJFOUPEFQSVFCBPFSSPS PEFUBOUFPT&TUFNÊUPEPDPOTJTUFFOBEJWJOBSFMWBMPSEFVOBEFMBT WBSJBCMFT DBMDVMBSMBTEFNÃTWBSJBCMFTZDPNQSPCBSFMWBMPSBEJWJOBEPEFMBWBSJBCMFUFOUBUJWB1BSB VOTJTUFNBCJOBSJPTFQVFEFTFMFDDJPOBSDVBMRVJFSBEFWBSJBTWBSJBCMFTUFOUBUJWBT DPNPZ Y 5UBNC  7'P-'1PSFKFNQMP TJTFTFMFDDJPOBMBUFNQFSBUVSBEFMUBNCPS 5UBNC DPNPWBSJBCMFUFOUBUJWB  FMQSPDFEJNJFOUPEFDÃMDVMPFT   $BMDVMBSI' 5' [    "EJWJOBSPQSPQPOFSFMWBMPSEF5UBNC   $BMDVMBSYZZDPOMBTFDVBDJPOFTEFFRVJMJCSJP  Z 

PHSÃàDBNFOUF VTBOEPVOEJBHSB NBEFUFNQFSBUVSBDPNQPTJDJÓO    $BMDVMBS-Z7 SFTPMWJFOEPMBTFDVBDJPOFTEFCBMBODFEFNBTB  P 

PDBMDVMBS-7DPO MBàHVSBZVTBSFMCBMBODFHFOFSBMEFNBTB FDVBDJÓO     $BMDVMBSI- 5UBNC Y Z)W 5UBNC Z DPOMBTFDVBDJPOFT  P B Z 

PCJFODPOFMEJBHSB NBEFFOUBMQÎBDPNQPTJDJÓO   $PNQSPCBDJÓOy4FTBUJTGBDFMBFDVBDJÓOEFCBMBODFEFFOFSHÎB  4JTFTBUJTGBDF UFSNJOB NPTTJOP IBZRVFSFHSFTBSBMQBTP -PTQSPDFEJNJFOUPTTPOQBSFDJEPTQBSBPUSBTWBSJBCMFTUFOUBUJWBT 1BSBMBEFTUJMBDJÓOJOTUBOUÃOFBCJOBSJB FMQSPDFEJNJFOUPTJNVMUÃOFPTFQVFEFMMFWBSBDBCPFO VOEJBHSBNBEFFOUBMQÎBDPNQPTJDJÓO1SJNFSPTFDBMDVMBMBFOUBMQÎBEFBMJNFOUBDJÓO I' DPOMBFDVB DJÓO  PMBFDVBDJÓO C BDPOUJOVBDJÓOTFHSBàDBFMQVOUPEFBMJNFOUBDJÓODPNPTFNVFTUSB FOMBàHVSB WFBFMQSPCMFNB" &OFMUBNCPSEFEFTUJMBDJÓO MBBMJNFOUBDJÓOTFTFQBSBFO

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOJOTUBOUÃOFB

P = Ptamb

Línea de unión

Alimentación

'*(63" $¦-$6-0%&%&45*-"$*¶/ */45"/5¦/&"#*/"3*"&/&-%*"(3"." %&&/5"-1±"$0.104*$*¶/ MÎRVJEPZWBQPSFOFRVJMJCSJP&OUPODFT MBJTPUFSNBRVFQBTBQPSFMQVOUPEFBMJNFOUBDJÓO RVFEFCF TFSMBEF5UBNC JOEJDBMPTWBMPSFTDPSSFDUPTEFYZZ-BTUBTBTEFáVKP-Z7TFQVFEFODBMDVMBSDPOMPT CBMBODFTEFNBTB FDVBDJPOFT  Z 

PDPOVOCBMBODFEFNBTBHSÃàDP 1BSBEFUFSNJOBSMBJTPUFSNBRVFQBTBQPSFMQVOUPEFBMJNFOUBDJÓOTFSFRVJFSFVOQSPDFEJNJFO UPEFQSVFCBZFSSPS4FQSPQPOFVOBZ PVOBY

TFUSB[BMBJTPUFSNBZTFDPNQSVFCBTJQBTBQPSFM QVOUPEFBMJNFOUBDJÓO4JOPQBTB TFEFCFSFQFUJSDPOVOBOVFWBZ PY  4FQVFEFPCUFOFSVOBTPMVDJÓOHSÃàDBQBSBMPTCBMBODFTEFNBTBZMBTFDVBDJPOFTEFFRVJMJCSJP QBSBMBàHVSB4FTVTUJUVZFMBFDVBDJÓO 

EFCBMBODFHFOFSBM FOMBFDVBDJÓOEFCBMBODFEF NBTBQBSBFMDPNQPOFOUFNÃTWPMÃUJM FDVBDJÓO 





&TUBFDVBDJÓOTFPSEFOBQBSBEFTQFKBS-7 





%FBDVFSEPDPOMBHFPNFUSÎBCÃTJDB  Z¢[ FTQSPQPSDJPOBMBMBEJTUBODJB FV Z [¢Y FTQSP QPSDJPOBMBMBEJTUBODJB FL &OUPODFT 





-BFDVBDJÓO  TFMMBNBSFHMBEFMBQBMBODBPSFHMBEFMCSB[PEFQBMBODB QPSRVFTFMMFHBBM NJTNPSFTVMUBEPDVBOEPTFPCUJFOFVOCBMBODFEFCSB[PTEFQBMBODBFOVOTVCFZCBKB"TÎ TJTF JHVBMBOMPTCSB[PTEFNPNFOUPFOFMTVCFZCBKBEFMBàHVSB TFPCUJFOF 

PCJFO 

RVFEBFMNJTNPSFTVMUBEPRVFMBFDVBDJÓO  &MTVCFZCBKBFTVOFKFNQMPBEFDVBEPQBSBSF DPSEBSMBSFHMBEFMBQBMBODB

www.FreeLibros.me

 &RVJMJCSJPWBQPSMÎRVJEPDPOWBSJPTDPNQPOFOUFT



­TUBUBNCJÊOTFQVFEFBQMJDBSBEJBHSBNBTEFFOUBMQÎBDPNQPTJDJÓOZBEJBHSBNBTUFSOBSJPT QBSBFYUSBDDJÓO EPOEFUJFOFWBSJPTPUSPTVTPT WFBFMDBQÎUVMP 

'*(63" *-6453"$*¶/%&-"3&(-"%&-"1"-"/$"  &26*-*#3*07"103-±26*%0$0/7"3*04$0.10/&/5&4

4JIBZNÃTEFEPTDPNQPOFOUFTTFSFRVJFSFVOQSPDFEJNJFOUPBOBMÎUJDP-BDPOàHVSBDJÓOCÃTJDBEFM FRVJQPFTMBNJTNBRVFMBEFMBàHVSB -BTFDVBDJPOFTRVFTFVTBOTPOMBTEFCBMBODFTEFNBTBZFOFSHÎB ZSFMBDJPOFTFTUFRVJPNÊUSJ DBT UPEBTEFFRVJMJCSJP-PTCBMBODFTEFNBTBZFOFSHÎBTPONVZQBSFDJEPTBMPTRVFTFVTBOFOFM DBTPCJOBSJP QFSPMBTFDVBDJPOFTEFFRVJMJCSJPTFTVFMFOFTDSJCJSFOGVODJÓOEFWBMPSFT,-BGPSNB EFFRVJMJCSJPFT 

ZJ,JYJ



,J,J 5UBNC QUBNC UPEBTMBTYJ 



EPOEFFOHFOFSBM 

-BTFDVBDJPOFT  Z  TFFTDSJCFOQBSBDBEBDPNQPOFOUF&OHFOFSBM MPTWBMPSFTEF,EF QFOEFOEFMBUFNQFSBUVSB MBQSFTJÓOZMBDPNQPTJDJÓO&TPTWBMPSFTOPJEFBMFTEF,MPTEFTDSJCFO DPOEFUBMMF4NJUI  Z8BMBT 

ZUBNCJÊOFOMJCSPTEFUFYUPEFUFSNPEJOÃNJDBZFOMBT SFGFSFODJBTEFMBUBCMB 1PSGPSUVOB MPTWBMPSFTEF,TPOBQSPYJNBEBNFOUFJOEFQFOEJFOUFTEFMBDPNQPTJDJÓO&OUPODFT 

,, 5 Q   BQSPYJNBEP 



1BSBIJESPDBSCVSPTMJHFSPT MPTWBMPSFTBQSPYJNBEPTEF,TFQVFEFOEFUFSNJOBSFOMPTOPNPHSBNBT QSFQBSBEPTQPS%F1SJFTUFS­TUPTTFNVFTUSBOFOMBTàHVSBTZQBSBEJTUJOUPTJOUFSWBMPTEF UFNQFSBUVSB4JTFEFTDPOPDFOMBUFNQFSBUVSBZPMBQSFTJÓOEFMBNF[DMBFOFRVJMJCSJP TFSFRVJFSF VONÊUPEPEFUBOUFPT-BTHSÃàDBTEF%F1SJFTUFSQBSBPUSBTVOJEBEFTEFUFNQFSBUVSBZQSFTJÓOTF QSFTFOUBOFO1FSSZZ(SFFO 

1FSSZFUBM  Z4NJUIZ7BO/FTT  -BTHSÃàDBTEF %F1SJFTUFSGVFSPOBKVTUBEBTBMBTJHVJFOUFFDVBDJÓO .D8JMMJBNT   

MO,B55 B5 5 B5 BQMOQ BQ Q BQ Q



0CTFSWFRVFFOMBFDVBDJÓO  5FTUÃFOž3ZQFOQTJB-BTDPOTUBOUFTB5 B5 B5 BQ BQZBQ TFFODVFOUSBOFOMBUBCMB-BÙMUJNBDPMVNOBJOEJDBMPTFSSPSFTNFEJPTFOMPTWBMPSFTEF, FO DPNQBSBDJÓODPOMPTWBMPSFTPCUFOJEPTFOMBTDBSUBTEF%F1SJFTUFS&TUBFDVBDJÓOFTWÃMJEBEFTEF ¢ž$ P3 IBTUBž$ ž3

ZQBSBQSFTJPOFTEFL1B QTJB BL1B  QTJB 4JTFDPOPDFO,ZQ TFQVFEFEFTQFKBS5EFMBFDVBDJÓO  -BWFOUBKBPCWJBEFDPOUBSDPO VOBFDVBDJÓO FODPNQBSBDJÓODPOMBTHSÃàDBT FTRVFTFQVFEFQSPHSBNBSFOVOBDPNQVUBEPSBP

www.FreeLibros.me

TEMPERATURA, °C

N-HEXANO N-HEPTANO ISOPENTANO N-PENTANO ISOBUTANO N-BUTANO

PROPILENO PROPANO

ETANO

ETILENO METANO

N-OCTANO N-NONANO

$BQÎUVMP  %FTUJMBDJÓOJOTUBOUÃOFB

PRESIÓN, k Pa



'*(63" (3¦'*$".0%*'*$"%"%&%&13*&45&3 &/6/*%"%&44* "#"+"45&.1&3"563"4 %#%"%:#63+03 $)&.&/(130(3  "#3*-%&$01:3*()5 "*$)&4& 3&130%6$&$0/"6503*;"$*¶/%&".&3*$"/*/45*565&0'$)&.*$"-&/(*/&&34  DBMDVMBEPSB-BFDVBDJÓO  TFQVFEFTJNQMJàDBSQBSBUPEPTMPTDPNQPOFOUFT FYDFQUPQBSBFM OPDUBOPZOEFDBOP WFBMBFDVBDJÓO B

 -PTWBMPSFT,TFVTBOKVOUPDPOMBTFDVBDJPOFTFTUFRVJPNÊUSJDBT RVFFTUBCMFDFORVFMBTGSBD DJPOFTNPMBSFTFOMBTGBTFTMÎRVJEBZWBQPSEFCFOTVNBS 





EPOEF$FTMBDBOUJEBEEFDPNQPOFOUFT 4JTÓMPIBZQSFTFOUFVODPNQPOFOUF FOUPODFTZZY&TUPJNQMJDBRVF,JZY &TUP QFSNJUF DPOUBS DPO VOB GPSNB TFODJMMB QBSB EFUFSNJOBS MB UFNQFSBUVSB EF FCVMMJDJÓO EF VO DPNQVFTUPQVSPBDVBMRVJFSQSFTJÓO1PSFKFNQMP TJTFRVJFSFDBMDVMBSFMQVOUPEFFCVMMJDJÓOEFM JTPCVUBOPBQL1B TFQPOFMBSFHMBFOQZFOEFMBFTDBMBEFMJTPCVUBOPFOMBàHVSB &OUPODFTTFMFFRVF5¢ž$ RVFFTFMQVOUPEFFCVMMJDJÓO5BNCJÊOTFQVFEFEFTQFKBS5EF MBFDVBDJÓO 

DPOWBMPSFTEFMBUBCMB%FFTBGPSNBTFMMFHBB5ž3 P¢ž$

www.FreeLibros.me

N-DECANO

N-HEXANO

N-HEPTANO N-OCTANO N-NONANO

ISOPENTANO N-PENTANO

ISOBUTANO N-BUTANO

PROPILENO PROPANO

ETILENO ETANO



N-NONANO

N-HEPTANO N-OCTANO

N-HEXANO

ISOPENTANO N-PENTANO

ISOBUTANO N-BUTANO

PROPILENO PROPANO

ETANO

ETILENO

METANO

N-DECANO

TEMPERATURA, °C

PRESIÓN, k Pa

METANO

 &RVJMJCSJPWBQPSMÎRVJEPDPOWBSJPTDPNQPOFOUFT

'*(63" (3¦'*$".0%*'*$"%"%&%&13*&45&31"3""-5"45&.1&3"563"4 %#%"%:#63+03 $)&.&/(130(3  "#3*-%&$01:3*()5 "*$)& 4&3&130%6$&$0/"6503*;"$*¶/%&".&3*$"/*/45*565&0'$)&.*$"-&/(*/&&34 

-BMFZEF3BPVMUHPCJFSOBMPTTJTUFNBTJEFBMFTZFTUBCMFDFRVFMBQSFTJÓOQBSDJBMEFVODPNQP OFOUFFTJHVBMBTVQSFTJÓOEFWBQPSNVMUJQMJDBEBQPSTVGSBDDJÓONPMBSFOFMMÎRVJEP&TEFDJS 

Q"Y" 17 "

B

EPOEFMBQSFTJÓOEFWBQPS 17 EFQFOEFEFMBUFNQFSBUVSB%FBDVFSEPDPOMBMFZEF%BMUPOEFMBT QSFTJPOFTQBSDJBMFT 

Z"Q"Q

C

Z" 17 "Y"Q

D

&TUBTFDVBDJPOFTTFDPNCJOBOQBSBMMFHBSB 

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOJOTUBOUÃOFB

5"#-" $0/45"/5&41"3""+645&"7"-03&4,.&%*"/5&-"&$6"$*¶/  $PNQVFTUP

 B5

 B5

 B5

 BQ

 BQ

 BQ

&SSPS NFEJP

.FUBOP &UJMFOP &UBOP 1SPQJMFOP 1SPQBOP

−   −   −   −   −  

    

− − − − −

    

    

    

*TPCVUBOP OCVUBOP *TPQFOUBOP OQFOUBOP OIFYBOP

−   −   −   −   −  

    

    

− − − − −

    

    

    

OIFQUBOP OPDUBOP OOPOBOP OEFDBOP

−    −   

 −  −

   

− − − −

   

   

   

/PUB5FTUÃFO°3ZQFOQTJB 'VFOUF.D8JMMJBNT 

$PNQBSBOEPMBTFDVBDJPOFT D Z 

FMWBMPSEF,FOMBMFZEF3BPVMUFT 

," 17 "Q



&TUBFDVBDJÓOFTÙUJMQPSRVFIBZEJTQPOJCMFTUBCMBTEFQSFTJPOFTEFWBQPS QPSFKFNQMP #PVCMJLFU BM  1FSSZZ(SFFO   $POGSFDVFODJBMBQSFTJÓOEFWBQPSTFDPSSFMBDJPOBDPOMBFDVBDJÓO EF"OUPJOF 

MO 17 "−# 5 $ 



EPOEF" #Z$TPODPOTUBOUFTQBSBDBEBDPNQVFTUPQVSP&TBTDPOTUBOUFTTFUBCVMBOFOWBSJBTGVFO UFTEFEBUPT #PVCMJLFUBM :BXTFUBM  -BTFDVBDJPOFTCBTBEBTFOMBMFZEF3BPVMUTFEF CFOVTBSDPOHSBODVJEBEP QPSRVFMBTEFTWJBDJPOFTSFTQFDUPBFTBMFZTPOFYUSFNBEBNFOUFDPNVOFT -PTDPNQPSUBNJFOUPTOPJEFBMFTFOMBGBTFMÎRVJEBQVFEFOUFOFSTFFODVFOUBDPOVODPFàDJFOUF EFBDUJWJEBEFOGBTFMÎRVJEB  J&OUPODFT MBFDVBDJÓO  TFUSBOTGPSNBFO 

," " 17" QUPUBM



&MDPFàDJFOUFEFBDUJWJEBEEFQFOEFEFMBUFNQFSBUVSB MBQSFTJÓOZMBDPODFOUSBDJÓO)BZFYDFMFOUFT QSPDFEJNJFOUPT EF DPSSFMBDJÓO QBSB EFUFSNJOBS DPFàDJFOUFT EF BDUJWJEBE  DPNP MPT EF .BSHVMFT  7BO-BBS 8JMTPO /35-Z6/*26"$ 1PMJOHFUBM 1SBVTOJU[FUBM 4BOEMFS  5FTUFSZ.PEFMM 7BO/FTTZ"CCPUU  8BMBT  1BSBVOBHSBOWBSJFEBEEFNF[DMBT  MPTDPFàDJFOUFTEFFTBTFDVBDJPOFTTFIBOUBCVMBEPKVOUPDPOMPTEBUPTFYQFSJNFOUBMFT WFBMBUBCMB

www.FreeLibros.me

 &RVJMJCSJPWBQPSMÎRVJEPDPOWBSJPTDPNQPOFOUFT



 $VBOEPOPTFEJTQPOFEFEBUPTCJOBSJPT TFQVFEFOVTBSDPFàDJFOUFTEFEJMVDJÓOJOàOJUB UBCMB $BSMTPO 4DIBE -B[[BSPOJFUBM  PCJFOFMNÊUPEPEFDPOUSJCVDJÓOEFHSVQP EF6/*'"$ 'SFEFOTMVOEFUBM 1SBVTOJU[FUBM  QBSBEFUFSNJOBSMPTEBUPTRVFGBMUFO .VDIPTTJNVMBEPSFTEFEFTUJMBDJÓOVTBOMBTFDVBDJPOFT  Z 

DPOVOBFDVBDJÓOBEFDVBEB QBSBFMDPFàDJFOUFEFBDUJWJEBE"VORVFTBMFEFMBMDBODFEFFTUFMJCSPVOBEFTDSJQDJÓOEFUBMMBEB

5"#-" (6±"4"1309*."%"41"3"4&-&$$*0/"3.­50%04%&$¦-$6-0%&7"-03&4%&, 4JTUFNBTRVÎNJDPT

"MDPIPMFTFIJESPDBSCVSPTEFCBKP1.  "MDPIPMFTFIJESPDBSCVSPTEF1.NBZPS  4JTUFNBTDPOQVFOUFTEFIJESÓHFOP  &YUSBDDJÓOMÎRVJEPMÎRVJEP  "HVBDPNPTFHVOEBGBTFMÎRVJEB  $PNQPOFOUFTEFVOBGBNJMJBIPNÓMPHB  4JTUFNBBCBKBQSFTJÓODPOGBTFWBQPSBTPDJBOUF

8JMTPO /35.BSHVMFT /35-6/*26"$ /356/*26"$ )BZEFO0$POOFMM

4JTUFNBTEFIJESPDBSCVSPTZBDFJUFTMJHFSPT

4JTUFNBTEFHBTOBUVSBMDPOHBTEVMDFZBHSJP 4JTUFNBTDSJPHÊOJDPT  .F[DMBTEFSFGJOFSÎBDPOQQTJB  )JESPUSBUBEPSFTZSFGPSNBEPSFT  4JTUFNBTQBSBGÎOJDPTTJNQMFT  $PNQPOFOUFTQFTBEPTDPO1FC/ž' "SPNÃUJDPT DFSDBEFMBSFHJÓODSÎUJDB  )

43,13 43,13 43,13 (SBZTPO4USFBE 43,13 #, 1343,

#BTBEPTFOQPMBSJEBEFJEFBMJEBE

OPQPMBSOPQPMBSJEFBMZOPJEFBM OPQPMBSEÊCJMNFOUFQPMBS JEFBM OPQPMBSEÊCJMNFOUFQPMBS OPJEFBM OPQPMBSGVFSUFNFOUFQPMBS JEFBM OPQPMBSGVFSUFNFOUFQPMBS OPJEFBM EÊCJMNFOUFQPMBSEÊCJMNFOUFQPMBS JEFBM EÊCJMNFOUFQPMBSEÊCJMNFOUFQPMBS OPJEFBM EÊCJMNFOUFQPMBSGVFSUFNFOUFQPMBS JEFBM EÊCJMNFOUFQPMBSGVFSUFNFOUFQPMBS OPJEFBM GVFSUFNFOUFQPMBSGVFSUFNFOUFQPMBS JEFBM GVFSUFNFOUFQPMBSGVFSUFNFOUFQPMBS OPJEFBM BDVPTPGVFSUFNFOUFQPMBS 

DVBMRVJFSNPEFMPDPODPFGJDJFOUFEFBDUJWJEBE DVBMRVJFSNPEFMPDPODPFGJDJFOUFEFBDUJWJEBE 6/*26"$ 6/*26"$ 8JMTPO /356/*26"$ /356/*26"$ 6/*26"$ /*/(6/"3&$0.&/%"$*¶/ 6/*26"$

1BSBTJTUFNBTRVÎNJDPTZEFIJESPDBSCVSPTZBDFJUFTMJHFSPT DPSUFTÎBEFM%S8JMMJBN8BMUFST#BTBEPFOTVHFSFODJBTEFQPMBSJEBEZFTUBCJMJEBE EF(FTTFUBM  WÊBTFMBUBCMB  $MBWF/35-NPEFMPOPBMFBUPSJPEFEPTMÎRVJEPT43,NPEFMPEF4PBWF3FEMJDI,XPOH131FOH3PCJOTPO#,,EF#SBVO QBSBQFUSÓMFP

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOJOTUBOUÃOFB

EFFTPTNÊUPEPT FOMBUBCMBTFQSFTFOUBVOBHVÎBQBSBTFMFDDJPOBSDPSSFMBDJPOFTEFFRVJMJCSJPT WBQPSMÎRVJEPQBSBVTBSMPTFOTJNVMBDJPOFTFODPNQVUBEPSB

 %&45*-"$*¶/*/45"/5¦/&"%&7"3*04$0.10/&/5&4

4FSFTVFMWFOMBTFDVBDJPOFT  Z  KVOUPDPOMBTFDVBDJPOFTFTUFRVJPNÊUSJDBT 

FMCB MBODFHFOFSBMEFNBTB FDVBDJÓO 

MPTCBMBODFTEFNBTBEFMPTDPNQPOFOUFT 

'[J-YJ 7ZJ



ZFMCBMBODFEFFOFSHÎB FDVBDJÓO  -BFDVBDJÓO  FTNVZQBSFDJEBBMBEFMCBMBODFEFNBTB EFNF[DMBTCJOBSJBT FDVBDJÓO   $POGSFDVFODJBTFFTQFDJàDBSÃOMBUBTBEFáVKPEFBMJNFOUBDJÓO ' ZMBTGSBDDJPOFTNPM[JFOMB BMJNFOUBDJÓO QBSB$¢DPNQPOFOUFT4JUBNCJÊOTFFTQFDJàDBOQUBNCZ5UBNC PVOBDPNQPTJDJÓOEF MÎRVJEPPEFWBQPS TFQPESÃVTBSFOUPODFTVOQSPDFEJNJFOUPTFDVFODJBM&TUPFT TFSFTVFMWFOTJNVM UÃOFBNFOUFMBTFDVBDJPOFTEFCBMBODFTEFNBTB MBTFTUFRVJPNÊUSJDBTZMBTEFFRVJMJCSJP ZEFTQVÊT TFSFTVFMWFOMPTCBMBODFTEFFOFSHÎB 7FBNPTMPRVFRVJFSFEFDJSFTUP4VQPOHBNPTRVFIBZDPNQPOFOUFT $ &OUPODFTTFEF CFOEFUFSNJOBS, Y VOB-ZVOB7 PTFB WBSJBCMFT1BSBIBDFSMPTFEFCFOSFTPMWFSFDVBDJP OFT TJNVMUÃOFBNFOUF­TUBFTMBTPMVDJÓOTFDVFODJBM NÃTTJNQMF QBSBVOQSPCMFNBSFMBUJWBNFOUFTJNQMF y$ÓNPIBDFVOPQBSBSFTPMWFSFDVBDJPOFTTJNVMUÃOFBT &OHFOFSBM MBTSFMBDJPOFTQBSBMPT WBMPSFT,QPESÎBOTFSGVODJPOFTOPMJOFBMFTEFMBDPNQPTJDJÓO4JOFNCBSHP OPTMJNJUBSFNPTBTP MVDJPOFTJEFBMFT QBSBMBTRVFFTWÃMJEBMBFDVBDJÓO  Z 

,J,J 5UBNC QUBNC

$PNPTFDPOPDFO5UBNCZQUBNC MBT,JTFQVFEFODBMDVMBSDPOGBDJMJEBE 2VFEBO FOUPODFT TÓMP  FDVBDJPOFT MJOFBMFT RVÊ SFTPMWFSFOGPSNBTJNVMUÃOFB&TPFTQPTJCMFQFSPTPONÃTTJNQMFTMPTQSPDFEJNJFOUPTQPSUBOUFPT 1BSB TJNQMJàDBS FM QSPDFEJNJFOUP EF TPMVDJÓO  QSJNFSP VTBSFNPT FM FRVJMJCSJP  ZJ  ,JYJ QBSB FMJNJOBSZJEFMBFDVBDJÓO   

'[J-YJ 7,JYJ    J $

%FTQFKBOEPYJSFTVMUB 

4JEFMBFDVBDJÓO  EFTQFKBNPT--='−7ZMBTVTUJUVJNPTFOMBÙMUJNBFDVBDJÓO SFTVMUB 



www.FreeLibros.me



 %FTUJMBDJÓOJOTUBOUÃOFBEFWBSJPTDPNQPOFOUFT



&OUPODFT TJTFEFUFSNJOBMBJODÓHOJUB7 TFQVFEFOEFUFSNJOBSUPEBTMBTYJ&TDPNÙOEJWJEJSBM OVNFSBEPSZFMEFOPNJOBEPSEFMBFDVBDJÓO  FOUSFMBUBTBEFBMJNFOUBDJÓO' ZUSBCBKBSFO GVODJÓOEFMBWBSJBCMF7'&OUPODFT BMPSEFOBSMBFDVBDJÓOMMFHBNPTB 





-BSB[ÓOQBSBVTBS7' MBGSBDDJÓOFWBQPSBEB FTRVFFTUÃBDPUBEBFOUSFZFOUPEPTMPTQSPCMF NBTQPTJCMFT$PNPZJ,JYJ SFTVMUB 





6OBWF[EFUFSNJOBEP7' TFDBMDVMBOYJZZJGÃDJMNFOUF DPOMBTFDVBDJPOFT  Z   y$ÓNPTFQPESÎBEFEVDJSVOBFDVBDJÓORVFQFSNJUJFSBDBMDVMBS7' 1BSB DPOUFTUBS MP BOUFSJPS  WFBNPT QSJNFSP DVÃMFT FDVBDJPOFT OP TF IBO VTBEP 4PO MBT EPT FDVBDJPOFTFTUFRVJPNÊUSJDBT ° YJZ° ZJ4JTVTUJUVJNPTMBTFDVBDJPOFT  Z  FO FTBTFDVBDJPOFT MMFHBSFNPTB 









Z 

$VBMRVJFSBEFFTBTFDVBDJPOFTTFQVFEFVTBSQBSBEFTQFKBS7'4JFMJNJOBNPTMBTGSBDDJPOFT UFO ESFNPTQPMJOPNJPTEFPSEFO$"TÎ TJ$FTNBZPSRVF TFEFCFVTBSVOQSPDFEJNJFOUPEFUBOUFPT  P VOB UÊDOJDB QBSB DBMDVMBS SBÎDFT  QBSB PCUFOFS 7' "VORVF MBT FDVBDJPOFT   Z   TPO WÃMJEBT OPUJFOFOCVFOBTQSPQJFEBEFTEFDPOWFSHFODJB&TUPFT TJTFFTDPHFVOWBMPSJODPSSFDUPEF 7' RVJ[ÃFMWBMPSTJHVJFOUFEF7'RVFTFFTDPKBOPTFBNFKPS 1PS GPSUVOB FT GÃDJM EFEVDJS VOB FDVBDJÓO RVF TÎ UJFOF CVFOBT QSPQJFEBEFT EF DPOWFSHFODJB 1BSBFMMPTFSFTUBMBFDVBDJÓO  EFMB  





3FTUBOEPMBTTVNBTUÊSNJOPBUÊSNJOP SFTVMUB 



www.FreeLibros.me





$BQÎUVMP  %FTUJMBDJÓOJOTUBOUÃOFB

­TUB FT MB MMBNBEB FDVBDJÓO EF 3BDIGPSE3JDF Z UJFOF FYDFMFOUFT QSPQJFEBEFT EF DPOWFSHFODJB 5BNCJÊOTFQVFEFNPEJàDBSQBSBTJTUFNBTEFEFTUJMBDJÓOJOTUBOUÃOFBDPOUSFTGBTFT MÎRVJEPMÎRVJ EPWBQPS  $IJFO   :BRVFMBTDPNQPTJDJPOFTEFMBBMJNFOUBDJÓO [J FTUÃOFTQFDJàDBEBT ZMBT,JTFQVFEFODBMDVMBS DVBOEPMPTEBUPTTPO5UBNCZQUBNC MBÙOJDBWBSJBCMFFOMBFDVBDJÓO  FT7' MBGSBDDJÓOFWBQP SBEB&TUBFDVBDJÓOTFQVFEFSFTPMWFSDPOEJTUJOUPTQSPDFEJNJFOUPTEFDPOWFSHFODJBPEFDÃMDVMP EFSBÎDFT&MQSPDFEJNJFOUPEFDPOWFSHFODJBEF/FXUPODPOWFSHFDPOSBQJEF[:BRVFG 7' EFMB FDVBDJÓO  FTVOBGVODJÓOEF7'RVFEFCFUFOFSVODFSP MBFDVBDJÓOQBSBFMQSPDFEJNJFOUPEF DPOWFSHFODJBEF/FXUPOFT 





EPOEFGLFTFMWBMPSEFMBGVODJÓOQBSBFMUBOUFPL ZEGLE 7' FTFMWBMPSEFMBEFSJWBEBEFMBGVO DJÓOQBSBFMUBOUFPL4FEFCFUFOFSFODVFOUBRVFGL JHVBMBDFSP BTÎRVFTFJHVBMBGL =ZTF EFTQFKB° 7'  





&TUBFDVBDJÓOQSPQPSDJPOBMBNFKPSFTUJNBDJÓOEFMBGSBDDJÓOFWBQPSBEB4JOFNCBSHP QBSBVTBSMB TFOFDFTJUBOFDVBDJPOFTUBOUPQBSBMBGVODJÓODPNPQBSBMBEFSJWBEB1BSBGLVTBSFNPTMBFDVBDJÓO EF3BDIGPSE3JDF   &OUPODFT MBEFSJWBEBFT 





4VTUJUVZFOEPMBTFDVBDJPOFT  Z  FOMB  ZEFTQFKBOEP 7' L TFPCUJFOF 





-BFDVBDJÓO  QSPQPSDJPOBVOBCVFOBFTUJNBDJÓOQBSBFMTJHVJFOUFUBOUFP6OBWF[DBMDVMBEP 7' L  TFQVFEFEFUFSNJOBSFMWBMPSEFMBGVODJÓOEF3BDIGPSE3JDF4JTFBDFSDBMPTVàDJFOUFBDFSP  TFUFSNJOBFMDÃMDVMPFODBTPDPOUSBSJP TFSFQJUFMBDPOWFSHFODJBEF/FXUPOQBSBFMTJHVJFOUFUBOUFP -PTQSPDFEJNJFOUPTEFDPOWFSHFODJBEF/FXUPOOPTJFNQSFDPOWFSHFO6OBWFOUBKBEFVTBSMB FDVBDJÓOEF3BDIGPSE3JDFDPOFMQSPDFEJNJFOUPEFDPOWFSHFODJBEF/FXUPOFTRVFTJFNQSFIBZ VOBDPOWFSHFODJBSÃQJEB&TUPTFJMVTUSBFOFMFKFNQMP 6OBWF[DBMDVMBEBMBSFMBDJÓO7' TFDBMDVMBOYZZJDPOMBTFDVBDJPOFT  Z  -Z7TF EFUFSNJOBODPOFMCBMBODFHFOFSBMEFNBTB FDVBDJÓO  "IPSBTFQVFEFODBMDVMBSMBTFOUBMQÎBT I-Z)W1BSBTPMVDJPOFTJEFBMFT MBTFOUBMQÎBTTFQVFEFOEFUFSNJOBSDPOMBTVNBEFMBTFOUBMQÎBTEF MPTDPNQPOFOUFTQVSPT NVMUJQMJDBEBTQPSMBTGSBDDJPOFTNPMBSFTDPSSFTQPOEJFOUFT 



www.FreeLibros.me



 %FTUJMBDJÓOJOTUBOUÃOFBEFWBSJPTDPNQPOFOUFT









° ° EPOEF)WJZI-JTPOFOUBMQÎBTEFMPTDPNQPOFOUFTQVSPT4JMBTTPMVDJPOFTOPTPOJEFBMFT TFSFRVJFSF DPOPDFSMPTDBMPSFTEFNF[DMB&OUPODFTTFEFTQFKBI'EFMCBMBODFEFFOFSHÎB FDVBDJÓO 

ZTF EFUFSNJOB5' 4JTFFTQFDJàDBO7'ZQUBNC EFCFSÃDBMDVMBSTF5UBNC&TPTFIBDFQSPQPOJFOEPVOWBMPSEF5UBNC  DBMDVMBOEP,J ZDPNQSPCBOEPDPOMBFDVBDJÓOEF3BDIGPSE3JDF   6OBHSÃàDBEFG 7' DPO USB5UBNCBZVEBBTFMFDDJPOBSFMWBMPSEFMBUFNQFSBUVSBQBSBFMTJHVJFOUFUBOUFP5BNCJÊOTFQVFEF VTBSVOQSPDFEJNJFOUPBQSPYJNBEPEFDPOWFSHFODJB QBSFDJEPBMRVFTFFNQMFBQBSBDÃMDVMPTEF QVOUPEFCVSCVKBZQVOUPEFSPDÎP WFBMBTFDDJÓO -BOVFWB,SFGTFQVFEFDBMDVMBSDPO 





EPOEFFMGBDUPSEFBNPSUJHVBNJFOUPFTE° &OBMHVOPTDBTPTTFQVFEFUFOFSVOBTPCSFDPSSFD DJÓO BNFOPTRVFFMUBOUFPJOJDJBMTFBDFSRVFBMSFTVMUBEPDPSSFDUP&MDÃMDVMPDVBOEP7'=EB DPNPSFTVMUBEPMBUFNQFSBUVSBEFMQVOUPEFCVSCVKB DVBOEPFMMÎRVJEPDPNJFO[BBIFSWJS ZDVBOEP 7'=TFPCUJFOFMBUFNQFSBUVSBEFMQVOUPEFSPDÎP FMWBQPSTFDPNJFO[BBDPOEFOTBS  &+&.1-0 &WBQPSBDJÓOJOTUBOUÃOFBEFWBSJPTDPNQPOFOUFT 6OBDÃNBSBEFFWBQPSBDJÓOJOTUBOUÃOFBPQFSBBž$ZL1BQBSBTFQBSBSLHNPMI EFVOBBMJNFOUBDJÓORVFDPOUJFOFNPMEFQSPQBOP NPMEFOCVUBOP NPM EF OQFOUBOP Z  NPM EF OIFYBOP %FUFSNJOF MBT DPNQPTJDJPOFT Z MPT áVKPT EF MPT QSPEVDUPT 4PMVDJÓO " %FGJOB$BMDVMFZJ YJ 7Z-QBSBMBDÃNBSBEFFWBQPSBDJÓOJOTUBOUÃOFBFOFRVJMJCSJP RVFTFNVFTUSBFOFMEJBHSBNB

T t amb p tamb

# &YQMPSF$PNP5UBNCZQUBNCTPOEBUPT FOUPODFTTFQVFEFVTBSVOBTPMVDJÓOTFDVFODJBM 6TBSFNPTMBFDVBDJÓOEF3BDIGPSE3JDFQBSBEFTQFKBS7'ZBDPOUJOVBDJÓODBMDVMBS YJ ZJ -Z7 $ 1MBOFF$BMDVMF,JDPOMBTHSÃàDBTEF%F1SJFTUFS PDPOMBFDVBDJÓO  6TFDPOWFS HFODJBEF/FXUPODPOMBFDVBDJÓO 

EF3BDIGPSE3JDF QBSBMMFHBSBMWBMPSDPSSFDUP

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOJOTUBOUÃOFB

EF7'6OBWF[FODPOUSBEB7' DBMDVMFYJDPOMBFDVBDJÓO  ZZJDPOMBFDVBDJÓO  $BMDVMF7DPO7'Z-EFMCBMBODFHFOFSBMEFNBTB FDVBDJÓO   % )ÃHBMP%FBDVFSEPDPOMBHSÃàDBEF%F1SJFTUFS àHVSB

Bž$ZL1B TF EFUFSNJOBOMPTTJHVJFOUFTWBMPSFT          $ÃMDVMPEFG 7' DPOMBFDVBDJÓOEF3BDIGPSE3JDF 



%JSFNPTRVF7' DPNPQSJNFSBUFOUBUJWB FTPJMVTUSBSÃMBDPOWFSHFODJBQBSBVO QSJNFSUBOUFPDPOSFTVMUBEPEFàDJFOUF 



$PNPG  FTQPTJUJWB TFSFRVJFSFVOWBMPSNBZPSEF7'0CTFSWFRVFDBNCJBTÓMPVO WBMPSFOFMEFOPNJOBEPSEFDBEBUÊSNJOP%FFTFNPEPQPESFNPTQSFQBSBSMBFDVBDJÓOEF UBMNPEPRVFDBNCJFTÓMP7'&OUPODFT G 7' FTJHVBMB



"TÎUPEPTMPTDÃMDVMPTTJHVJFOUFTTFSÃONÃTTFODJMMPT -BEFSJWBEBEFMBFDVBDJÓOEF3BDIGPSE3JDF FDVBDJÓO33 TFQVFEFDBMDVMBSQBSBFTUF QSJNFSUBOUFP



%FBDVFSEPDPOMBFDVBDJÓO 

FMTJHVJFOUFUBOUFPTFSÃ 7'   "MDBMDVMBSFMWBMPSEFMBFDVBDJÓOEF33 SFTVMUBRVFG  4JHVFTJFOEP QPTJUJWPZ7'FTUPEBWÎBEFNBTJBEPCBKB

www.FreeLibros.me

 %FTUJMBDJÓOJOTUBOUÃOFBEFWBSJPTDPNQPOFOUFT



4FHVOEPUBOUFP DPOMPRVFTFMMFHBB 7'   ZMBFDVBDJÓOEF3BDIGPSE3JDFFTG  &TPTFBDFSDBNÃT QFSP7'TJHVFTJFOEP EFNBTJBEPCBKB$POUJOVBSMBDPOWFSHFODJB 5FSDFSUBOUFP

DPOMBRVFSFTVMUB 7'   $BMDVMBNPTG   RVFFTNVZDFSDBOPZRVFEBEFOUSPEFMBFYBDUJUVEEFMBT DBSUBTEF%F1SJFTUFS1PSDPOTJHVJFOUF 7' "IPSBDBMDVMBSFNPTYJDPOMBFDVBDJÓO 

ZZJDPO,JYJ

$PNP'Z7' 7'LHNPMIS Z-'¢7¢LH NPMIS & $PNQSVFCF1PEFNPTDPNQSPCBS° ZJZ° YJ 

-BTDVBMFTUJFOFOMBTVàDJFOUFBQSPYJNBDJÓO/PTPOQFSGFDUPTQPSRVF7'OPFSBFYBDUB &OFTFODJBTFPCUJFOFFMNJTNPSFTVMUBEPTJTFVTBMBFDVBDJÓO  QBSBEFUFSNJOBSMPT WBMPSFT EF , /PUB 1BSFDFSÃ NÃT FYBDUB MB FDVBDJÓO   QPSRVF VOP QVFEF PCUFOFS NVDIPTEÎHJUPTTJOFNCBSHP DPNPFTVOBKVTUFBMBTHSÃàDBTEF%F1SJFTUFS OPQVFEFTFS NÃTFYBDUB ' (FOFSBMJDF$PNPMBFDVBDJÓOEF3BDIGPSE3JDFFTDBTJMJOFBM DPOMBSVUJOBEF/FXUPO TFPCUJFOFVOBDPOWFSHFODJBSÃQJEB0CTFSWFRVFMBDPOWFSHFODJBGVFNPOÓUPOBZOP PTDJMÓ4FQPESÎBPCUFOFSVOBDPOWFSHFODJBNÃTSÃQJEBDPOVONFKPSWBMPSJOJDJBMFTUJ NBEPEF7'&TUBDMBTFEFQSPCMFNBTEFQSVFCBZFSSPSFTGÃDJMEFQSPHSBNBSFOVOB IPKBEFDÃMDVMP 4JMBTWBSJBCMFTFTQFDJàDBEBTTPO' [J QUBNC ZDVBMRVJFSDPNQPOFOUFEFYPZ TFQVFEFTFHVJS VOQSPDFEJNJFOUPTFDVFODJBMEFDPOWFSHFODJBDPOMBFDVBDJÓO  P  QBSBSFMBDJPOBSDPOMB

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOJOTUBOUÃOFB

DPNQPTJDJÓOFTQFDJàDBEB FMDPNQPOFOUFEFSFGFSFODJB DPO,SFGP7'&TPTFQVFEFIBDFSEFEPT NBOFSBT-BQSJNFSBFTBEJWJOBS5UBNCZVTBSMBFDVBDJÓO  PMB  QBSBEFTQFKBS7'BDPOUJ OVBDJÓOTFWFSJàDB5UBNCDPOMBFDVBDJÓOEF3BDIGPSE3JDF4JMBFDVBDJÓOEF3BDIGPSE3JDFOPFTTB UJTGBDUPSJB TFTFMFDDJPOBVOBOVFWBUFNQFSBUVSBDPOMBFDVBDJÓO  ZTFSFQJUFFMQSPDFEJNJFOUP &OFMTFHVOEPNÊUPEP TFQSPQPOF7'ZTFDBMDVMB,SFGDPOMBFDVBDJÓO  P  "DPOUJOVB DJÓOTFEFUFSNJOBMBUFNQFSBUVSBEFMUBNCPSDPOFTUB,SFG%FOVFWPTFDPNQSVFCBDPOMBFDVBDJÓO EF3BDIGPSE3JDFTJOPTFTBUJTGBDF TFTFMFDDJPOBVOBOVFWB7'ZTFDPOUJOÙBFMQSPDFTP

 $0/7&3(&/$*"4*.6-5¦/&"$0/7"3*04$0.10/&/5&4

4JTFFTQFDJàDBOMBUBTBEFBMJNFOUBDJÓO' MBDPNQPTJDJÓOEFMBBMJNFOUBDJÓOGPSNBEBQPS $m  WBMPSFTEF[J MBQSFTJÓOEFMUBNCPSEFEFTUJMBDJÓOQUBNCZMBUFNQFSBUVSBEFBMJNFOUBDJÓO5' FMMÎRVJ EPDBMJFOUFTFFWBQPSBSÃDVBOEPCBKFTVQSFTJÓO&TUBFWBQPSBDJÓOJOTUBOUÃOFBPGMBTIFPFOGSÎBBM MÎRVJEP UPNBOEPTVFOFSHÎBQBSBFWBQPSBSBMHPEFÊMNJTNP-B5UBNCRVFSFTVMUBTFEFTDPOPDFQPS MPUBOUP EFCFNPTVTBSVOQSPDFEJNJFOUPEFTPMVDJÓOTJNVMUÃOFB1SJNFSP TFFTDPHFVOBQSFTJÓOEF FOUSBEBUBMRVFMBBMJNFOUBDJÓOTFBMÎRVJEB&OUPODFTTFQVFEFDBMDVMBSMBFOUBMQÎBEFBMJNFOUBDJÓO FOMBNJTNBGPSNBDPOMBTFDVBDJPOFT  Z   





"VORVFMPTCBMBODFTEFNBTBZFOFSHÎB MBTFDVBDJPOFTEFFRVJMJCSJPZMBTFDVBDJPOFTFTUFRVJPNÊ USJDBTQPESÎBOSFTPMWFSTFTJNVMUÃOFBNFOUF PUSBWF[FTNÃTGÃDJMVTBSVOQSPDFEJNJFOUPEFQSVFCBZ FSSPS&TUFQSPCMFNBFTBIPSBVOPEFEPCMFUBOUFP -BQSJNFSBQSFHVOUBQBSBQSFQBSBSVOQSPDFEJNJFOUPEFQSVFCBZFSSPSFTy$VÃMFTTPOMBTWBSJB CMFTUFOUBUJWBTQPTJCMFTZDVÃMFTTFEFCFSÃOVTBS "RVÎQSJNFSPFTDPHFSFNPT5UBNCQPSRVFTFSFRVJFSF ° ° DBMDVMBSUPEBTMBT,J )WJZI-J ZUBNCJÊOQPSRVFFTEJGÎDJMEFEFTQFKBS-BTFHVOEBWBSJBCMFQBSBUFO UBUJWBFT7'QPSRVFQPEFNPTVTBSFMNÊUPEPEF3BDIGPSE3JDFDPODPOWFSHFODJBOFXUPOJBOB -BTFHVOEBQSFHVOUBFTy4FEFCFIBDFSDPOWFSHFSMBTEPTWBSJBCMFTFOGPSNBTJNVMUÃOFB FTUP FT DBNCJBSBMNJTNPUJFNQP5UBNCZ7' PTFEFCFIBDFSDPOWFSHFODJBTFDVFODJBM "NCBTUÊDOJ DBTGVODJPOBO QFSPTÓMPTJTFBQMJDBOCJFO-BDPOWFSHFODJBTFDVFODJBMUJFOEFBTFSNÃTFTUBCMF4J VTBNPTDPOWFSHFODJBTFDVFODJBM VOBUFSDFSBQSFHVOUBFTy$VÃMWBSJBCMFTFEFCFIBDFSDPOWFSHFS QSJNFSP 7'P5UBNC 1BSBDPOUFTUBSOFDFTJUBNPTUFOFSFODVFOUBFMTJTUFNBRVÎNJDPRVFFTUFNPT TFQBSBOEP4JMBNF[DMBIJFSWFFOUSFBNQMJPTMÎNJUFT FTUPFT TJFMQVOUPEFSPDÎPZFMQVOUPEFCVS CVKBTFTUÃONVZBMFKBEPTFOUSFTÎ EJHBNPT FOUSFBž$PNÃT

FOUPODFTVODBNCJPQFRVFÒP FO5UBNCOPQVFEFUFOFSHSBOFGFDUPTPCSF7'&OFTUFDBTP EFCFNPTIBDFSDPOWFSHFS7'QSJNFSP "DPOUJOVBDJÓO DVBOEPTFDBNCJB5UBNC OPTBDFSDBSFNPTBMSFTVMUBEPDPSSFDUPQBSB7'1BSBUFOFS VOBTFQBSBDJÓOJNQPSUBOUFFOVOTJTUFNBEFEFTUJMBDJÓOJOTUBOUÃOFB MBTWPMBUJMJEBEFTEFCFOTFSNVZ EJGFSFOUFTFTFMDBTPEFMBFWBQPSBDJÓOJOTUBOUÃOFB&MQSPDFEJNJFOUPEFFCVMMJDJÓOFTUSFDIBQBSBMB EFTUJMBDJÓOTFWFFOMBàHVSB &M QSPDFEJNJFOUP QBSB BMJNFOUBDJPOFT DPO QVOUPT EF FCVMMJDJÓO TFQBSBEPT TF NVFTUSB FO MB àHVSB/PUFRVFFMCBMBODFEFFOFSHÎBTFVTBBMÙMUJNP­TUFFTFMQSPDFEJNJFOUPVTVBMQPSRVF TFEJTQPOFEFWBMPSFTFYBDUPTEFYJZZJQBSBDBMDVMBSFOUBMQÎBTFOFMCBMBODFEFFOFSHÎB -BDVBSUBQSFHVOUBFTy$ÓNPIBDFSMPTQBTPTJOEJWJEVBMFTEFDPOWFSHFODJB 1BSBMBFDVBDJÓOEF 3BDIGPSE3JDF MBJOUFSQPMBDJÓOMJOFBMPMBDPOWFSHFODJBEF/FXUPOTFSÃOTBUJTGBDUPSJBT4FQVFEFO

www.FreeLibros.me

  $POWFSHFODJBTJNVMUÃOFBDPOWBSJPTDPNQPOFOUFT



Ingresar condiciones especificadas y datos de equilibrio Estimar Ttamb

Calcular Ki (Ttamb, ptamb)

Estimar V/F Resolver Ec. Rachford-Rice (2-42)

¿Es f(V/F) = 0



Calcular xi, yi, L, V, H y h

Estimar Ttamb

¿Se satisface el balance de energía?



Finalizar

'*(63" %*"(3"."%&'-6+01"3"6/""-*.&/5"$*¶/26& )*&37&&/53&".1-*047"-03&4%&5&.1&3"563"

FNQMFBSWBSJPTNÊUPEPTQBSBFTUJNBSMBTJHVJFOUFUFNQFSBUVSBEFMUBNCPSEFEFTUJMBDJÓOVOPEFMPT NÃTSÃQJEPTZTFODJMMPTFTVTBSVOQSPDFEJNJFOUPEFDPOWFSHFODJBEF/FXUPO1BSBIBDFSMP TFSFBDP NPEBFMCBMBODFEFFOFSHÎB FDVBDJÓO FOMBGPSNBGVODJPOBM 

&L 5UBNC 7)W -I-−'I'−2

www.FreeLibros.me





$BQÎUVMP  %FTUJMBDJÓOJOTUBOUÃOFB

&MTVCÎOEJDFLTFSFàFSFEFOVFWPBMOÙNFSPEFUBOUFP$VBOEP&LFTDFSP FMQSPCMFNBFTUÃ SFTVFMUP&OFMQSPDFEJNJFOUPEF/FXUPOTFFTUJNB&L  5UBNC DPOMBEFSJWBEB 





EPOEF° 5UBNCFTFMDBNCJPEF5UBNCEFVOUBOUFPBMTJHVJFOUF 

° 5UBNC5L −5L

 

ZE&LE5UBNCFTMBWBSJBDJÓOEF&LBNFEJEBRVFDBNCJBMBUFNQFSBUVSB$PNPMPTEPTÙMUJNPTUÊSNJ OPTFOMBFDVBDJÓO  OPEFQFOEFOEF5UBNC FTUBEFSJWBEBTFQVFEFDBMDVMBSDPO 





FOEPOEFTFIBVTBEPMBEFàOJDJÓOEFDBQBDJEBEDBMPSÎàDB"MEFEVDJSMBFDVBDJÓO  IJDJNPT RVFE7E5ZE-E5GVFSBODFSP QPSRVFTFFTUÃVTBOEPVOBSVUJOBTFDVFODJBMEFDPOWFSHFODJB ZOP TFRVJFSFWBSJBS7P-FOFTUFDJDMP&OFMTJHVJFOUFUBOUFPTFRVJFSFTBUJTGBDFSFMCBMBODFEFFOFSHÎB &OUPODFT IBDFNPTRVF&L ZTFQVFEFEFTQFKBS° 5UBNCEFMBFDVBDJÓO   





&OFTUBFDVBDJÓOTFTVTUJUVZFMBFYQSFTJÓOEF° 5UBNCZTFEFTQFKB5UBNCL EFFTFNPEPTFPCUJFOFMB NFKPSFTUJNBDJÓOEFMBUFNQFSBUVSB QBSBMBTJHVJFOUFUFOUBUJWB 





&OFTUBFDVBDJÓO &LFTFMWBMPSOVNÊSJDPDBMDVMBEPEFMBGVODJÓOEFCBMBODFEFFOFSHÎBDPOMBFDVB DJÓO  E&LE5UBNCFTFMWBMPSOVNÊSJDPEFMBEFSJWBEBDBMDVMBEPDPOMBFDVBDJÓO   &MQSPDFEJNJFOUPIBDPOWFSHJEPDVBOEP 

]° 5UBNC] 2 & f$A $ 9 o;



m > 2

f &&A $ Km9o; f &A $ Kf





1BSBFTUBDPMVNOBTFEFTBSSPMMBSPOMBTFDVBDJPOFTEFBMJNFOUBDJÓO4JOFNCBSHP MBTFDVBDJPOFT  ZEFMB  BMB  TPOWÃMJEBTQBSBDVBMRVJFSDPOàHVSBDJÓOEFDPMVNOB TJHFOFSBMJ[B NPTMBTEFàOJDJPOFTEFGZR&OHFOFSBM q5  f5 

L abajo de la alimentación 2 L arriba de la alimentación tasa de flujo de alimentación Varriba de la alimentación 2 Vabajo de la alimentación tasa de flujo de alimentación



B



C

&+&.1-0 $ÃMDVMPTEFMBMÎOFBEFBMJNFOUBDJÓO $BMDVMBSMBQFOEJFOUFEFMBMÎOFBEFBMJNFOUBDJÓOQBSBMPTDBTPTTJHVJFOUFT B  6OBBMJNFOUBDJÓOEFEPTGBTFT DPOFOGPSNBEFWBQPS BMBTDPOEJDJPOFTEFMB DPMVNOB

www.FreeLibros.me

  -ÎOFBEFBMJNFOUBDJÓO



4PMVDJÓO-BQFOEJFOUFFTR R−

EPOEFR -BCBKPEFMBBMJNFOUBDJÓO−-BSSJCBEFMBBMJNFOUBDJÓO ' TF QPESÎBOIBCFSVTBEPPUSBTFDVBDJPOFT 1BSBVOBBMJNFOUBDJÓOFOEPTGBTFTMBTJUVBDJÓOFT MBTJHVJFOUF

m - - -'$PNPEFMBBMJNFOUBDJÓOFTWBQPS FTMÎRVJEPZ-'' &OUPODFT f2

A−A A %#';− A %#'; 2 2 2 %#' ; ; ;

1FOEJFOUF

f %#' & 2 2− f−& %#' − & )

-PRVFDPODVFSEBDPOMBàHVSB C  6OBBMJNFOUBDJÓOEFWBQPSTPCSFDBMFOUBEP EPOEFNPMEFMÎRVJEPTFFWBQPSBFOMB FUBQBEFBMJNFOUBDJÓO QPSDBEBNPMFTEFBMJNFOUBDJÓORVFFOUSBO 4PMVDJÓO"IPSBMBTJUVBDJÓOFTMBRVFSFQSFTFOUBMBTJHVJFOUFàHVSB

$VBOEPFOUSBMBBMJNFOUBDJÓO BMHPEFMÎRVJEPEFCFIFSWJSQBSBFOGSJBSMB"TÎ 

m - -−DBOUJEBEFWBQPSBEB W

ZMBDBOUJEBEFWBQPSBEBFTW  ' "TÎ A− A f2 2 ;

A−

& & ;− A ; . . & 2− 2− ; ; .

f 1FOEJFOUF 2 f− & 

& & − & . . 2 2 &%  &% & − − −& . . −

www.FreeLibros.me





$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

RVFDPODVFSEBDPOMBàHVSB D  6OBBMJNFOUBDJÓOMÎRVJEBTVCFOGSJBEBž'-BDBQBDJEBEDBMPSÎàDBQSPNFEJPEFMMÎ RVJEPFT#UVMCNPMž' Z  #UVMCNPM 4PMVDJÓO"RVÎ MBBMJNFOUBDJÓOEFCFDPOEFOTBSBMHPEFWBQPS&OUPODFT MBTJUVBDJÓOTF QVFEFSFQSFTFOUBSDPNPTJHVF

m Z- - ' D EPOEFDFTMBDBOUJEBEDPOEFOTBEB $PNPMBDPMVNOBFTUÃBJTMBEB MBGVFOUFEFFOFSHÎBQBSBDBMFOUBSMBBMJNFOUBDJÓOIBTUB TVQVOUPEFFCVMMJDJÓOFTFMWBQPSDPOEFOTBOUF 

;8E ΔI2Xλ 

B

EPOEF 551&C−5'ž' FOUPODFT 

X2

2

XE ΔI ; λ

C

(%(*  ;2%#%,; &*!%%%

f2 A− A 2 A ; %#%,;− A 2&#%, ; ;

1FOEJFOUF

f &#%, 2 2&*#'. f− & &#%,− &

&TUP DPODVFSEB DPO MB àHVSB  /P PCTUBOUF MB HSBO DBOUJEBE EF TVCFOGSJBNJFOUP  MB MÎOFBEFBMJNFOUBDJÓOTFBQSPYJNBCBTUBOUFBMBWFSUJDBMZMPTSFTVMUBEPTTFSÃOQBSFDJEPTB MPTEFVOMÎRVJEPTBUVSBEP4JFMEBUPFT5'FOMVHBSEF 5 TFEFCFFTUJNBS51&C&TPTFIBDF DPOVOBHSÃàDBEFUFNQFSBUVSBDPNQPTJDJÓO àHVSB

EFFOUBMQÎBDPNQPTJDJÓO àHVSB 

PCJFODPOVODÃMDVMPEFQVOUPEFCVSCVKB TFDDJÓO  E  6OBNF[DMBEFFUBOPMZBHVB GPSNBEBQPSNPMEFFUBOPM TFBMJNFOUBBž$-B QSFTJÓOFTLHDN 4PMVDJÓO"IPSBQPEFNPTBQMJDBSMBFDVBDJÓO   fs

=− ]; =− ]

www.FreeLibros.me

  .ÊUPEPDPNQMFUPEF.D$BCF5IJFMF



-PTEBUPTEFFOUBMQÎBTFUPNBOEFMBàHVSB1BSBVTBSFTBàHVSBEFCFNPTQBTBS UFOFSMPTWBMPSFTEFDPNQPTJDJÓOFOGSBDDJÓOFOQFTP-BGSBDDJÓONPMFTGSBDDJÓOFO QFTP&OUPODFT EFMBàHVSB ] ; %#+(!)%°82'%`XVa$`\

&MWBQPS SFQSFTFOUBEPQPS) ZFMMÎRVJEP SFQSFTFOUBEPQPSI FTUBSÃOFOFRVJMJCSJPFOMB FUBQBEFBMJNFOUBDJÓO4FEFTDPOPDFOMBTDPODFOUSBDJPOFTEFMBFUBQBEFBMJNFOUBDJÓO"M DPNQBSBSMPTMVHBSFTEFFUBQBEFBMJNFOUBDJÓOFOMBTàHVSBT" #Z$ TFWFRVFMBT DPODFOUSBDJPOFTEFMÎRVJEPZWBQPS FOMBFUBQBEFBMJNFOUBDJÓO QVFEFOTFSNVZEJGFSFOUFT ZFOHFOFSBMOPTPOJHVBMFTBMBDPODFOUSBDJÓO[EFMBBMJNFOUBDJÓO PBMBTDPODFOUSBDJPOFT Z*ZY* àHVSB EFMQVOUPEFJOUFSTFDDJÓOEFMBMÎOFBEFPQFSBDJÓO4JOFNCBSHP DPNP FTWÃMJEPFMEFSSBNFNPMBMDPOTUBOUF )ZI FOVOJEBEFTNPMBMFT TFSÃODPOTUBOUFT1PEF NPTDBMDVMBSUPEBTMBTFOUBMQÎBTDPOVOBGSBDDJÓOFOQFTPEF DPOWFSUJSMBTBFOUBMQÎBT QPSLHNPMZFTUJNBSR%FMBàHVSB )  7BQ4BU  I  -ÎR4BU  LDBMLHZ fs

=EB− ] ; EB =EB− ]EB

$PNPUPEPTMPTQFTPTNPMFDVMBSFTFTUÃOBMBNJTNBDPODFOUSBDJÓO TFTJNQMJàDBOZEFT BQBSFDFO fs

=− ] ; (.*− '% 2 2&#&(+ =− ] (.*− +*

1FOEJFOUF

f &#&(+ s 2-#(* f− & %#&(+

&TUPDPODVFSEBDPOMBàHVSB"QFTBSEFRVFFMTVCFOGSJBNJFOUPFTDPOTJEFSBCMF MB MÎOFBEFBMJNFOUBDJÓOUJFOFVOBQFOEJFOUFBMUB/PUFRVFOPTFVTÓMBUBTBEFBMJNFOUBDJÓO QBSBDBMDVMBSROJMBQFOEJFOUF

 .­50%0$0.1-&50%&.D$"#&5)*&-&

"IPSBFTUBNPTMJTUPTQBSBBSNBSMBTQJF[BTZSFTPMWFSVOQSPCMFNBEFEJTFÒPEFEFTUJMBDJÓODPOFM NÊUPEPEF.D$BCF5IJFMF-PIBSFNPTFOFMTJHVJFOUFFKFNQMP &+&.1-0 .ÊUPEPEF.D$BCF5IJFMF 6OB DPMVNOB EF EFTUJMBDJÓO DPO VO DPOEFOTBEPS UPUBM Z VO WBQPSJ[BEPS QBSDJBM TFQBSB VOBNF[DMBEFFUBOPMBHVB-BBMJNFOUBDJÓOFTLHNPMIBž'ZDPOUJFOFEFFUB OPM4FEFTFBRVFFMEFTUJMBEPDPOUFOHBNPMEFFUBOPMZMPTGPOEPTNPMEFFUBOPM -BSFMBDJÓOEFSFáVKPFYUFSOPFT&MSFáVKPSFHSFTBDPNPMÎRVJEPTBUVSBEPZTFQVFEF TVQPOFSRVFEFSSBNFNPMBMDPOTUBOUF$BMDVMFFMMVHBSÓQUJNPEFMQMBUPEFBMJNFOUBDJÓOZ OÙNFSPEFFUBQBTEFFRVJMJCSJPOFDFTBSJBT-BQSFTJÓOFTBUN

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

4PMVDJÓO " %FGJOB&MFTRVFNBEFMBDPMVNOBFTFMTJHVJFOUF

Líquido saturado

Etapa óptima de alimentación

%FUFSNJOFFMMVHBSÓQUJNPEFMQMBUPEFBMJNFOUBDJÓOZMBDBOUJEBEUPUBMEFFUBQBTEFFRVJ MJCSJP # &YQMPSF-PTEBUPTEFFRVJMJCSJPBBUNTFFODVFOUSBOFOMBàHVSB1BSBFTUJNBSR  TFSÃÙUJMVOEJBHSBNBFOUBMQÎBDPNQPTJDJÓOBBUNÊTUFTFFODVFOUSBFOPUSBTGVFOUFT QPSFKFNQMP #SPXOFUBM  P'PVTUFUBM  1ÃH

PTFQVFEFPCUFOFSVOB CVFOBFTUJNBDJÓOEFREFMBàHVSB BVOBQFTBSEFMBEJGFSFODJBEFQSFTJÓO&OFM FKFNQMPEFNPTUSBNPTRVFFTWÃMJEPTVQPOFSEFSSBNFNPMBMDPOTUBOUF QPSMPRVF QPEFNPTBQMJDBSFMNÊUPEPEF.D$BCF5IJFMF $ 1MBOFF%FUFSNJOFRDPOMBFDVBDJÓO  ZFMEJBHSBNBEFFOUBMQÎBDPNQPTJDJÓOBBUN 5SBDFMBHSÃàDBEFMBMÎOFBEFBMJNFOUBDJÓO$BMDVMF-7(SBàRVFMBMÎOFBEFPQFSBDJÓO TVQFSJPSZBDPOUJOVBDJÓOMBMÎOFBEFPQFSBDJÓOJOGFSJPS ZFTDBMPOFMBTFUBQBT % )ÃHBMP -ÎOFB EF BMJNFOUBDJÓO 1BSB EFUFSNJOBS R  QSJNFSP TF DPOWJFSUF MB DPODFO USBDJÓOEFMBBMJNFOUBDJÓO NPMBS FOFOQFTPEFFUBOPMFOQFTP4F NVFTUSBOEPTDÃMDVMPTFOEJTUJOUBTVOJEBEFT DPOEBUPTEJGFSFOUFT $ÃMDVMPFYBDUP %BUPTBQBUN EF#SPXOFUBM  

$ÃMDVMPBQSPYJNBEP QLHDN

VTBOEPMBàHVSB

I'#UVMC ž'  )#UVMC WBQPSTBU  I#UVMC MÎRVJEPTBU 

I'LDBMLH ž$

)LDBMLH WBQPSTBU

ILDBMLH MÎRVJEPTBU

fs

--%− '* 2&#&( --%− &'*

fs

)-*− &* 2&#&( )-*− ,%

7FNPTRVFMBTEJGFSFODJBTEFQSFTJÓODBVTBOQFRVFÒBTEJGFSFODJBTFOMPTEJBHSBNBT QPS MPRVFFMWBMPSEFROPDBNCJB/PUFRVF DPNPFOFMFKFNQMPE MPTUÊSNJOPTDPOQFTP NPMFDVMBSEFTBQBSFDFO&OUPODFT

www.FreeLibros.me

  .ÊUPEPDPNQMFUPEF.D$BCF5IJFMF



1FOEJFOUFEFMBMÎOFBEFBMJNFOUBDJÓO

f s-#, f− &

-BMÎOFBEFBMJNFOUBDJÓOJOUFSTFDBBMBMÎOFBZYBMBDPODFOUSBDJÓOEFBMJNFOUBDJÓO[ &TUBMÎOFBTFHSBàDBFOMBàHVSB -ÎOFBEFPQFSBDJÓOTVQFSJPS A A m &− m K K 9



n2



1FOEJFOUF

*$( A A $9 2 2 2*$K  & A $9  & *$( 

0SEFOBEBBMPSJHFO 2&− A m 9 2($-%#-2%#( K

4PMVDJÓOBMUFSOBUJWB-BJOUFSTFDDJÓOEFMBMÎOFBTVQFSJPSEFPQFSBDJÓOZMBMJOFBZY SF TPMWFSTJNVMUÃOFBNFOUFMBTFDVBDJPOFTEFMBMÎOFBTVQFSJPSEFPQFSBDJÓOZMBMJOFBZY

 FTUÃFOZYY%-BMÎOFBTVQFSJPSEFPQFSBDJÓOFTUÃFOMBàHVSB

Línea de alimentación Alimentación Línea superior de operación

Línea inferior de operación

'*(63" 40-6$*¶/1"3"&-&+&.1-0

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

-ÎOFBJOGFSJPSEFPQFSBDJÓO n2 A m−  A − &m 7 K K

4BCFNPTRVFMBMÎOFBJOGFSJPSEFPQFSBDJÓODSV[BBMBTVQFSJPSFOMBMÎOFBEFBMJNFOUBDJÓO mm ÊTUF FT VO QVOUP 1PESÎBNPT DBMDVMBS - 7  DPO MPT CBMBODFT EF NBTB P DPO MB FDVBDJÓO 

 QFSP FT NÃT GÃDJM EFUFSNJOBS PUSP QVOUP -B JOUFSTFDDJÓO EF MB MÎOFB JOGFSJPS EF PQFSBDJÓODPOMBMÎOFBZYFTUÃFOZYY# WÊBFMQSPCMFNB$ "TÎTFPCUJFOFVO TFHVOEPQVOUP -BMÎOFBEFBMJNFOUBDJÓO MBMÎOFBTVQFSJPSEFPQFSBDJÓOZMBMÎOFBJOGFSJPSEFPQFSBDJÓO TFWFOFOMBàHVSB"MMÎTFFTDBMPOBSPOMBTFUBQBTEFBCBKPIBDJBBSSJCB ÊTUBFTVOB FMFDDJÓOBSCJUSBSJB -BFUBQBÓQUJNBEFBMJNFOUBDJÓOFTMBTFHVOEBBSSJCBEFMWBQPSJ[BEPS QBSDJBM4FSFRVJFSFOFUBQBTEFFRVJMJCSJP NÃTVOWBQPSJ[BEPSQBSDJBM & 7FSJGJRVF$POUBNPTDPOVOBWFSJàDBDJÓOJODPSQPSBEBFOMBMÎOFBEFPQFSBDJÓOTVQF SJPS QPSRVFTFDBMDVMBOVOBQFOEJFOUFZEPTQVOUPT-BMÎOFBEFPQFSBDJÓOJOGFSJPSTF mm QVFEF DPNQSPCBS DBMDVMBOEP - 7  DPO CBMBODFT EF NBTB Z DPNQBSBOEP DPO MB QFO mm EJFOUF -BT DBOUJEBEFT SFTVMUBO SB[POBCMFT QPSRVF -7    - 7    Z R   &O MB àHVSB MBDBVTBEFFSSPSNÃTQSPCBCMFZMBNÃTEJGÎDJMEFWFSJàDBSTPOMPTEBUPTEF FRVJMJCSJP ' (FOFSBMJDF 4J FM EJBHSBNB EF .D$BCF5IJFMF TF USB[B DPO DVJEBEP SFTVMUB CBTUBOUF FYBDUP /PUF RVF OP IBZ OFDFTJEBE EF USB[BS QBSUFT EFM EJBHSBNB EF FRVJMJCSJP RVF TFBONBZPSFTRVFY%PNFOPSFTRVFY#1BSBBVNFOUBSMBFYBDUJUVETFQVFEFOBNQMJà DBSQBSUFTEFMEJBHSBNB &OFTUFFKFNQMPOPUVWJNPTRVFVTBSCBMBODFTFYUFSOPT NJFOUSBTRVFTÎMPIJDJNPTFOFMFKFN QMP&TUPTFEFCFBRVFVTBNPTMBMÎOFBEFBMJNFOUBDJÓODPNPBVYJMJBSQBSBEFUFSNJOBSMBMÎOFB JOGFSJPSEFPQFSBDJÓO-PTQVOUPTEFJOUFSTFDDJÓODPOZYTPOÙUJMFT QFSPDVBOEPDBNCJBMBDPOà HVSBDJÓOEFMBDPMVNOB QVFEFDBNCJBSTVVCJDBDJÓO

 1&3'*-&41"3"%&45*-"$*¶/#*/"3*"

&OFTFODJB MBàHVSBNVFTUSBMBTPMVDJÓODPNQMFUBEFMFKFNQMPTJOFNCBSHP FTÙUJMHSBàDBS DPNQPTJDJPOFT UFNQFSBUVSBTZáVKPTRVFTBMFOEFDBEBFUBQB TFMMBNBOQFSGJMFT &OMBàHVSB TFQVFEFOEFUFSNJOBSDPOGBDJMJEBEMBTGSBDDJPOFTNPMBSFTEFFUBOPMFOFMMÎRVJEPZFMWBQPSRVF TBMFOEFDBEBFUBQB&OUPODFT Y8−Y&ZZ8−Z&-BUFNQFSBUVSBEFDBEBFUBQBTFQVFEFEF UFSNJOBSDPOEBUPTEFFRVJMJCSJP àHVSB QPSRVFMBTFUBQBTTPOEFFRVJMJCSJP$PNPTVQVTJNPT EFSSBNFNPMBMDPOTUBOUF MBTUBTBTEFáVKPEFMÎRVJEPZWBQPSTFSÃODPOTUBOUFTFOMBTTFDDJPOFTEF FOSJRVFDJNJFOUPZBHPUBNJFOUP ZDPOFMWBMPSDBMDVMBEPEFR FTQPTJCMFEFUFSNJOBSMPTDBNCJPTFO MBTUBTBTEFáVKPFOMBFUBQBEFBMJNFOUBDJÓO -PTQFSàMFTTFWFOFOMBàHVSB$PNPFSBEFFTQFSBSTF MBDPODFOUSBDJÓOEFBHVBFOMBT DPSSJFOUFTEFMÎRVJEPZWBQPSEFDSFDFFOGPSNBNPOÓUPOBBMTVCJSQPSMBDPMVNOB NJFOUSBTRVF BVNFOUBMBDPODFOUSBDJÓOEFFUBOPM$PNPMBTFUBQBTTPOEJTDSFUBT MPTQFSàMFTOPTPODVSWBTVOJ GPSNFT$PNQBSFMBTàHVSBTZ0CTFSWFDVBOEPTFBDFSDBOMBMÎOFBEFPQFSBDJÓOZMBDVSWB EFFRVJMJCSJP$VBOEPDBTJTFUPDBOFTBTEPTMÎOFBT TFUJFOFFMMMBNBEPQVOUPEFFTUSJDDJÓO QJODI QPJOU &OÊM MPTQFSàMFTEFDPNQPTJDJÓOZUFNQFSBUVSBTFWVFMWFODBTJIPSJ[POUBMFTZIBCSÃNVZ

www.FreeLibros.me

  1FSGJMFTQBSBEFTUJMBDJÓOCJOBSJB



Fracción mol que sale de la etapa

Temperatura de la etapa, °C

Flujos, kg mol/h, salen de la etapa

Ubicación de la etapa

'*(63" 1&3'*-&41"3"&-&+&.1-0 QPDPDBNCJPFOMBDPNQPTJDJÓO EFVOBBPUSBFUBQB-BVCJDBDJÓOEFVOQVOUPEFFTUSJDDJÓOFOFM JOUFSJPSEFMBDPMVNOBEFQFOEFEFMTJTUFNBZEFMBTDPOEJDJPOFTEFPQFSBDJÓO &OFTUBDPMVNOBEFFUBOPMBHVB MBUFNQFSBUVSBEFDSFDFSÃQJEBNFOUFFOMPTQSJNFSPTDPOUBD UPTTPCSFFMWBQPSJ[BEPS QFSPFTDBTJDPOTUBOUFFOMBTÙMUJNBTPDIPFUBQBT&TUPTVDFEFQSJODJQBM NFOUFEFCJEPBMBGPSNBEFMEJBHSBNBUFNQFSBUVSBDPNQPTJDJÓOQBSBMBNF[DMBFUBOPMBHVB WFB MBàHVSB  $PNPTVQVTJNPTEFSSBNFNPMBMDPOTUBOUF MPTQFSàMFTEFáVKPTPOQMBOPTFODBEBTFDDJÓOEF m m MBDPMVNOB$PNPTFFTQFSBCB - 7 Z7- FTVOBCVFOBWFSJàDBDJÓO $PNPMBFUBQBFTMBEF BMJNFOUBDJÓO -FTUÃFOMBTFDDJÓOEFBHPUBNJFOUP NJFOUSBTRVF7FTUÃFOMBEFFOSJRVFDJNJFOUP TJOPMFRVFEBDMBSPFTUP USBDFVOEJBHSBNBEFMBFUBQBEFBMJNFOUBDJÓO "MJNFOUBDJPOFTDPOEJ GFSFOUFTDBMJEBEFTUFOESÃOEJGFSFOUFTDBNCJPTFOMBFUBQBEFBMJNFOUBDJÓO"MQBTBSEFMBTFDDJÓO EF BHPUBNJFOUP B MB EF FOSJRVFDJNJFOUP  MBT UBTBT EF áVKP EF MÎRVJEP Z WBQPS QVFEFO BVNFOUBS  EJTNJOVJSPOPDBNCJBS

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

-BàHVSBJMVTUSBMBWFOUBKBQSJODJQBMEFMPTEJBHSBNBTEF.D$BCF5IJFMF1FSNJUFOWJTVBMJ [BSMBTFQBSBDJÓO"OUFTEFRVFTFEJGVOEJFSBFMVTPEFMBTDPNQVUBEPSFTEJHJUBMFT TFVTBCBOHSBOEFT EJBHSBNBT RVFBWFDFTDVCSÎBOVOBQBSFE EF.D$BCF5IJFMFQBSBEJTFÒBSDPMVNOBTEFEFTUJMBDJÓO &TUPT EJBHSBNBT OP QVFEFO DPNQFUJS DPO MB WFMPDJEBE Z FYBDUJUVE EF MPT TJNVMBEPSFT EF QSPDFTP WFBFMBQÊOEJDFEFFTUFDBQÎUVMP P FOFMDBTPEFTFQBSBDJPOFTCJOBSJBT DPOMBTIPKBTEFDÃMDVMP 4JOFNCBSHP MPTEJBHSBNBTEF.D$BCF5IJFMFTJHVFOQFSNJUJFOEPWJTVBMJ[BSZFOUFOEFSNFKPSMB TFQBSBDJÓO ,JTUFS  &OFMDBTPJEFBM TFVTBSÎBOMPTEJBHSBNBTEF.D$BCF5IJFMFKVOUPDPOMPT SFTVMUBEPTEFTJNVMBEPSFTEFQSPDFTP UBOUPQBSBBOÃMJTJTDPNPQBSBMPDBMJ[BDJÓOEFGBMMBT  $"-&/5".*&/50$0/7"103%*3&$50

"IPSBDPOUBNPTDPOUPEBTMBTIFSSBNJFOUBTOFDFTBSJBTQBSBSFTPMWFSDVBMRVJFSQSPCMFNBEFEFTUJ MBDJÓOCJOBSJB DPOFMQSPDFEJNJFOUPHSÃàDPEF.D$BCF5IJFMF7FSFNPT DPNPVOFKFNQMPFTQFDÎ àDP MBTFQBSBDJÓOEFNFUBOPMZBHVBFOVOBDPMVNOBEFEFTUJMBDJÓOFOFUBQBT &+&.1-0 "OÃMJTJTEF.D$BCF5IJFMFEFDBMFOUBNJFOUPDPOWBQPSEJSFDUP -BBMJNFOUBDJÓOBVOBDPMVNOBEFEFTUJMBDJÓODPOUJFOFNPMEFNFUBOPMZNPM EFBHVB ZFOUSBDPNPNF[DMBFOEPTGBTFTRVFTFFWBQPSBJOTUBOUÃOFBNFOUFEFNPEPRVF 7''-BUBTBEFáVKPEFBMJNFOUBDJÓOFTLHNPMI-BDPMVNOBFTUÃCJFOBJTMBEBZ UJFOFVODPOEFOTBEPSUPUBM&MSFáVKPSFHSFTBBMBDPMVNOBDPNPMÎRVJEPTBUVSBEP4FVTB VOBSFMBDJÓOEFSFáVKPFYUFSOP-%4FEFTFBRVFMBDPODFOUSBDJÓOEFMNFUBOPMFOFM EFTUJMBEPTFBNPMZRVFMBDPODFOUSBDJÓOFOMPTGPOEPTTFBNPM&OMVHBSEFVTBSVO WBQPSJ[BEPS FOFMGPOEPEFMBDPMVNOBTFCVSCVKFBEJSFDUBNFOUFWBQPSTBUVSBEPBBUN B FTUPTFMFMMBNBWBQPSEJSFDUPPWBQPSBCJFSUP -BQSFTJÓOEFMBDPMVNOBFTBUN$BMDVMBS MBDBOUJEBEEFFUBQBTEFFRVJMJCSJPZFMMVHBSÓQUJNPEFMQMBUPEFBMJNFOUBDJÓO 4PMVDJÓO " %FGJOB"ZVEBUSB[BSVOFTRVFNBEFMBQBSBUP FOFTQFDJBMQPSRVFTFFTUÃVTBOEPVO OVFWPUJQPEFEFTUJMBDJÓO&TUFEJBHSBNBTFWFFOMBàHVSB4FEFTFBEFUFSNJOBSFM MVHBSÓQUJNPEFMQMBUPEFBMJNFOUBDJÓO /' ZMBDBOUJEBEUPUBMEFFUBQBTEFFRVJMJCSJP  / OFDFTBSJBTQBSBMBTFQBSBDJÓO1PESÎBNPTDBMDVMBS2D % #ZFMáVKPEFWBQPS 4  QFSPOPTFTPMJDJUBSPO4VQPOESFNPTRVFMBDPMVNOBFTBEJBCÃUJDB QPSRVFFTUÃCJFO BJTMBEB # &YQMPSF-PQSJNFSPRVFOFDFTJUBNPTTPOEBUPTEFFRVJMJCSJP1PSGPSUVOBTFDPOTJ HVFODPOGBDJMJEBE WFBMBUBCMBEFMQSPCMFNB%  &OTFHVOEPMVHBSOPTHVTUBSÎBTVQPOFSEFSSBNFNPMBMDPOTUBOUF QBSBQPEFSVTBSFMQSPDF EJNJFOUPEF.D$BCF5IJFMFFOFMBOÃMJTJT6OBGPSNBGÃDJMEFDPNQSPCBSFTUBTVQPTJDJÓO FTDPNQBSBSMPTDBMPSFTMBUFOUFTEFFWBQPSBDJÓOQPSNPM )JNNFMCMBV   )WBQNFUBOPM FOTV1FC LDBMHNPM )WBQBHVB FOTV1FC LDBMHNPM &TUPTWBMPSFTOPTPOJHVBMFTEFIFDIP FMDBMPSMBUFOUFEFMBHVBFTNBZPSRVFFMEFM NFUBOPM&OUPODFT FTUSJDUBNFOUFOPFTWÃMJEPTVQPOFSEFSSBNFNPMBMDPOTUBOUFTJOFN CBSHP SFTPMWFSFNPTFTUFQSPCMFNBTVQPOJÊOEPMPZWFSJàDBSFNPTOVFTUSPTSFTVMUBEPTDPO VOTJNVMBEPSEFQSPDFTPT

www.FreeLibros.me

  $BMFOUBNJFOUPDPOWBQPSEJSFDUP



LO líquido saturado

(aislado)

Etapa óptima de alimentación

Vapor de agua saturado puro Líquido saturado

'*(63" %&45*-"$*¶/$0/$"-&/5".*&/501037"103%*3&$50

6OWJTUB[PBMBàHVSBNVFTUSBRVFMBDPOàHVSBDJÓOFOFMGPOEPEFMBDPMVNOBFT EJTUJOUBRVFDVBOEPFYJTUFVOWBQPSJ[BEPS1PSFMMPEFCFNPTFTQFSBSRVFMBTFDVBDJPOFTEF PQFSBDJÓOEFMBQBSUFJOGFSJPSTFBOEJGFSFOUFTEFMBTRVFEFEVKJNPTBOUFT $ 1MBOFF6TBSFNPTVOBOÃMJTJTEF.D$BCF5IJFMF5SB[BSFNPTMPTEBUPTEFFRVJMJCSJP FOVOBHSÃàDBZY -ÎOFBTVQFSJPSEFPQFSBDJÓO-PTCBMBODFTEFNBTBFOMBTFDDJÓOEFSFDUJàDBDJÓO WFBMB àHVSB TPO K_ & 2A_ 9 n_ &K_ & 2A_ m_ 9m9

4VQPOHBEFSSBNFNPMBMDPOTUBOUFZEFTQFKBSZK  

n_ & 2A $ Km_ &− A $ Km9

1FOEJFOUF-7 PSEFOBEBBMPSJHFO Y  −-7 Y% 

*OUFSTFDDJÓOZYFOY% $PNPFMSFáVKPSFHSFTBDPNPMÎRVJEPTBUVSBEP

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

A $ K2

A% A %$9 2 A % 9 A % $9 &

)BZTVàDJFOUFJOGPSNBDJÓOQBSBHSBàDBSMBMÎOFBTVQFSJPSEFPQFSBDJÓO -ÎOFBEFBMJNFOUBDJÓO n2



f m f− &

1FOEJFOUF 

o &− f

o f

PSEFOBEBBMPSJHFO Y  − & f − & f

*OUFSTFDDJÓOZY[ f2



;  K; A−A K K − K ; 2 2 − 2&− ; ; ; ; ; ;

6OBWF[TVTUJUVJEPTMPTWBMPSFT TFQVFEFHSBàDBSMBMÎOFBEFBMJNFOUBDJÓO -ÎOFBJOGFSJPSEFPQFSBDJÓO-PTCBMBODFTEFNBTBTPO K 72 A H Kn 7m 7 2 Am HnH  QBSBNFUBOPM

4FEFTQFKBZ n2A$ K m H$K nh − 7$Km7

4JNQMJàDBDJPOFT$PNPFMWBQPSFTEFBHVBQVSB ZT OPDPOUJFOFNFUBOPM $PNPFM WBQPSFTTBUVSBEP 47Z#- EFSSBNFNPMBMDPOTUBOUF &OUPODFT 

n2 A$ Km− A$Km7 



0CTFSWFRVFFTUBFDVBDJÓOFTEJTUJOUBBMBFDVBDJÓOEFPQFSBDJÓOQBSBMBTFDDJÓOJOGFSJPS  mm DVBOEPTFUSBUBEFVOWBQPSJ[BEPS1FOEJFOUF- 7  EFTDPOPDJEB

PSEFOBEBBMPSJHFO mm − - 7 Y# EFTDPOPDJEB

n2m2

− A $ Km 7 &− A $ K

EFTDPOPDJEB



6OQVOUPRVFTFDPOPDFFTFMDSVDFEFMBMÎOFBTVQFSJPSEFPQFSBDJÓODPOMBMÎOFBEFBMJ NFOUBDJÓO5PEBWÎBOFDFTJUBNPTVOTFHVOEPQVOUP RVFFTFOMBBCTDJTBBMPSJHFO$VBOEP TFIBDFRVFZ FOUPODFTYY# FTUPTFEFKBDPNPQSPCMFNB$  % )ÃHBMP-PTEBUPTEFFRVJMJCSJPTFHSBàDBOFOMBàHVSB -ÎOFBTVQFSJPSEFPQFSBDJÓO A $ K2

A $9 2($)2 QFOEJFOUF & A $9

www.FreeLibros.me

  $BMFOUBNJFOUPDPOWBQPSEJSFDUP

Op. Sup.



Línea inferior de operación

'*(63" 40-6$*¶/1"3"&-&+&.1-0 

ZYY% PSEFOBEBBMPSJHFO −-7 Y% -BHSÃàDBEFFTUBSFDUBTFWFFOMBàHVSB -ÎOFBEFBMJNFOUBDJÓO1FOEJFOUFR R−  − − *OUFSTFDDJÓOFOZY[4FNVFTUSBFOMBàHVSB -ÎOFBJOGFSJPSEFPQFSBDJÓO&TUBMÎOFBTFQVFEFHSBàDBSDPOEPTQVOUPTFMDSVDFDPOMB MÎOFBTVQFSJPSEFPQFSBDJÓODPOMBMÎOFBEFBMJNFOUBDJÓOZ BCTDJTBBMPSJHFO Z Y# &TUFQVOUPUBNCJÊOTFWFFOMBàHVSB 4FFTDBMBOMBTFUBQBTDPNFO[BOEPEFTEFBSSJCB&MWBMPSYFTUÃFOFRVJMJCSJPDPOZFOY% "MUSB[BSVOBIPSJ[POUBMIBTUBMBDVSWBEFFRVJMJCSJPTFPCUJFOFFMWBMPSY-PTWBMPSFTZZ YTFSFMBDJPOBODPOMBMÎOFBEFPQFSBDJÓO"ZDPOTUBOUF MÎOFBIPSJ[POUBM

TFWBIBTUBMB DVSWBEFFRVJMJCSJPQBSBMMFHBSBY$POUJOVBSFTUFQSPDFEJNJFOUPEFFUBQBQPSFUBQB -BFUBQBÓQUJNBEFBMJNFOUBDJÓOTFEFUFSNJOBDPNPFOMBàHVSB"-BBMJNFOUBDJÓO ÓQUJNBFOMBàHVSBFTUÃFOMBFUBQBP QPSRVFDBTVBMNFOUFYFTUÃFOFMQVOUPEF JOUFSTFDDJÓO EF MBT MÎOFBT EF BMJNFOUBDJÓO Z EF PQFSBDJÓO  $PNP MB BMJNFOUBDJÓO DPOTUB EFEPTGBTFT FOFTUFDBTPVTBSFNPTMBFUBQBDPNPMBÓQUJNBEFBMJNFOUBDJÓO/ÙNFSPEF FUBQBT$JODPFTNÃTRVFTVàDJFOUF1PEFNPTDBMDVMBSVOBDBOUJEBEGSBDDJPOBSJBEFFUBQBT 'SBDD

EJTUBODJBEFMBMÎOFBEFPQFSBDJÓOBMQSPEVDUP EJTUBODJBEFMBMÎOFBEFPQFSBDJÓOBMBDVSWBEFFRVJMJCSJP

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

&OMBàHVSB ;gVX2

m 7 − m) %#%-− %#(%* 2 2%#. m * − m) %#%+− %#(%*

/FDFTJUBNPT DPOUBDUPT & 7FSJGJRVF4FQVFEFIBDFSVOBTFSJFEFQSVFCBTEFDPOTJTUFODJBJOUFSOB-BEFFRVJMJ CSJPEFCFTFSVOBDVSWBVOJGPSNF$POFTPTFWFTJIBZQVOUPTNBMHSBàDBEPT-7 mm EFOPTFSBTÎ OPIBCSÎBQSPEVDUPEFTUJMBEP Z- 7  TJOP OPIBCSÎBQSPEVDUPFO MPTGPOEPT -BQFOEJFOUFEFMBMÎOFBEFPQFSBDJÓOUJFOFMBEJSFDDJÓODPSSFDUBQBSBVOB BMJNFOUBDJÓOFOEPTGBTFT4FSÎBBDPOTFKBCMFIBDFSVOBQSVFCBàOBMEFMBIJQÓUFTJTEF EFSSBNFNPMBMDPOTUBOUF QPSRVFMPTDBMPSFTMBUFOUFTWBSÎBOFO &TUFQSPCMFNBGVFSFTVFMUPUBNCJÊODPOFMTJNVMBEPSEFQSPDFTPT"TQFO1MVT WFBFM QSPCMFNB(ZFMBQÊOEJDFEFMDBQÎUVMP &O"TQFO1MVTOPTFTVQPOFEFSSBNFNPMBM DPOTUBOUFZDPOVOBDPSSFMBDJÓOBEFDVBEBQBSBFMFRVJMJCSJPWBQPSMÎRVJEP TFVTÓFMNP EFMPOPBMFBUPSJPDPOEPTMÎRVJEPT TFEFCFUFOFSNBZPSFYBDUJUVERVFDPOFMEJBHSBNBEF .D$BCF5IJFMF RVFTVQPOFEFSSBNFNPMBMDPOTUBOUF$POFUBQBTEFFRVJMJCSJPZMBBMJ NFOUBDJÓOFOMBFUBQB FMMVHBSÓQUJNP

Y%ZY# RVFOPDVNQMFODPO MBTFTQFDJàDBDJPOFT$POFUBQBTEFFRVJMJCSJPZMBBMJNFOUBDJÓOFOMBFUBQB MBÓQUJNB

 Y%ZY# VOQPDPNFKPSRVFMPRVFQJEFOMBTFTQFDJàDBDJPOFT-BTEJGFSFO DJBTFOUSFMPTSFTVMUBEPTDPOFMEJBHSBNB.D$BCF5IJFMFZDPOMBTJNVMBDJÓOEFQSPDFTP TFEFCFOBMFSSPSDPNFUJEPBMTVQPOFSEFSSBNFNPMBMDPOTUBOUFZ FONFOPSHSBEP BEJGF SFODJBTFOFMFRVJMJCSJP/PUFMBVUJMJEBEEFMEJBHSBNBEF.D$BCF5IJFMF QPSRVFQSFTFOUB WJTVBMNFOUFFMFGFDUPEFVTBSDBMFOUBNJFOUPDPOWBQPSWJWP ' (FOFSBMJDF/PUFRVFOPTJFNQSFFTÙUJMMBMÎOFBZY/PNFNPSJDFMPTMVHBSFTEFMPT QVOUPT"QSFOEBBEFEVDJSRVÊFTMPRVFTFOFDFTJUB&MDPOEFOTBEPSUPUBMOPDBNCJB MBTDPNQPTJDJPOFTZOPDVFOUBDPNPFUBQBEFFRVJMJCSJP&MDPOEFOTBEPSUPUBMBQBSFDF FOMBàHVSBDPNPVOTPMPQVOUPFOZYY%.FEJUFQPSRVÊFTPFTWÃMJEP&O HFOFSBM UPEBTMBTFOUSBEBTBMBDPMVNOBQVFEFODBNCJBSMBTUBTBTEFáVKPZ QPSMP UBOUP MBTQFOEJFOUFTEFOUSPEFMBDPMVNOB&MPCKFUPEFMBMÎOFBEFBMJNFOUBDJÓOFT BZVEBSBEFUFSNJOBSFTUFFGFDUP-BDPSSJFOUFEFSFáVKPZFMWBQPSWJWPUBNCJÊOTPO FOUSBEBTBMBDPMVNOB4JOPTPODPSSJFOUFTTBUVSBEBT MBTUBTBTEFáVKPTFDBMDVMBOFO GPSNBEJTUJOUBFTUPTFEFTDSJCJSÃEFTQVÊT /PUFRVFFMWBQPSWJWPTFQVFEFDPOTJEFSBSDPNPVOBBMJNFOUBDJÓODPOR -BCBKP−-BSSJCB  m m 4 #−- 4"TÎ #- -BQFOEJFOUFEFFTUBMÎOFBEFBMJNFOUBDJÓOFTR R−   ZDSV[BMBSFDUBZYFOZY[ MPRVFRVJFSFEFDJSRVFMBMÎOFBEFBMJNFOUBDJÓOQBSB FMWBQPSTBUVSBEPFTFMFKFY -VEXJH  JOEJDBRVFTFVTFVOQMBUPQBSBTVTUJUVJSFMWBQPSJ[BEPS ZEFBVOP ZRVJ[ÃNÃT QMBUPT QBSBDPNQFOTBSMBEJMVDJÓODPOBHVBTJOFNCBSHP DPNPMPTWBQPSJ[BEPSFTTVFMFOTFSNVDIP NÃTDPTUPTPTRVFMPTQMBUPT WFBFMDBQÎUVMP

FTUBQSÃDUJDBSFTVMUBFDPOÓNJDB&MDBMFOUBNJFOUP DPOWBQPSEJSFDUPQVFEFVTBSTFBVODVBOEPFMBHVBOPTFBVOPEFMPTDPNQPOFOUFTPSJHJOBMFT  130$&%*.*&/50(&/&3"-%&"/¦-*4*4.D$"#&5)*&-&

&MFKFNQMPDPOWBQPSWJWPFTVODBTPFTQFDÎàDP$POWJFOFFOUPODFTHFOFSBMJ[BSFMQSPDFEJNJFOUP EFBOÃMJTJT6OBTFDDJÓOEFMBDPMVNOBFTFMTFHNFOUPEFFUBQBTFOUSFEPTDPSSJFOUFTEFFOUSBEBPEF TBMJEB"TÎ FOMBàHVSBIBZEPTTFDDJPOFTTVQFSJPSFJOGFSJPS-BàHVSBJMVTUSBVOBDPMVNOB

www.FreeLibros.me

  1SPDFEJNJFOUPHFOFSBMEFBOÃMJTJT.D$BCF5IJFMF



Corriente lateral

'*(63" $0-6./"%&%&45*-"$*¶/ $0/$6"5304&$$*0/&4 DPODVBUSPFUBQBT-BFDVBDJÓOEFPQFSBDJÓOEFDBEBTFDDJÓOTFQVFEFEFEVDJSEFGPSNBJOEFQFO EJFOUF &OUPODFT  FM USVDP MMBNÊNPTMP BTÎ  FT DPOTJEFSBS B DBEB TFDDJÓO DPNP VO TVCQSPCMFNB JOEFQFOEJFOUF QFSPDPOFDUBEPBMPTEFNÃTTVCQSPCMFNBTQPSNFEJPEFMBTMÎOFBTEFBMJNFOUBDJÓO RVFUBNCJÊOTPOJOEFQFOEJFOUFT  6OBMHPSJUNPQBSBDVBMRVJFSQSPCMFNBFTFMTJHVJFOUF   5SBDFVOBàHVSBEFMBDPMVNOBFJEFOUJàRVFUPEBTMBTWBSJBCMFTDPOPDJEBT QPSFKFNQMP DPNP MBàHVSB 7FSJàDBSTJFTWÃMJEPFMEFSSBNFNPMBMDPOTUBOUF   1BSBDBEBTFDDJÓO B 5SBDFVOBFOWPMWFOUFEFCBMBODFEFNBTB4FRVJFSFRVFFTUBFOWPMWFOUFDPSUFMBTDPSSJFOUFT EFTDPOPDJEBT EF MÎRVJEP Z WBQPS FO MB TFDDJÓO  Z MBT DPSSJFOUFT DPOPDJEBT BMJNFOUBDJPOFT  QSPEVDUPTFTQFDJàDBEPTPTBMJEBTMBUFSBMFTFTQFDJàDBEBT .JFOUSBTNFOPTDPSSJFOUFTIBZB MPT CBMBODFTEFNBTBTFSÃONÃTTJNQMFT&TUFQBTPFTJNQPSUBOUFQPSRVFEFUFSNJOBMBGBDJMJEBE EFMPTQBTPTTJHVJFOUFT C &TDSJCBMPTCBMBODFTEFNBTBHFOFSBMZEFMDPNQPOFOUFNÃTWPMÃUJM D %FEV[DBMBFDVBDJÓOEFPQFSBDJÓO E 4JNQMJàRVF F $BMDVMFUPEBTMBTQFOEJFOUFT PSEFOBEBTBMPSJHFOFJOUFSTFDDJPOFT   'PSNVMFFDVBDJPOFTEFMBTMÎOFBTEFBMJNFOUBDJÓO$BMDVMFR QFOEJFOUFTFJOUFSTFDDJPOFTDPO ZY   1BSBMBTMÎOFBTEFPQFSBDJÓOZBMJNFOUBDJÓO B (SBàRVFUPEBTMBTMÎOFBTEFPQFSBDJÓOZBMJNFOUBDJÓORVFTFQVFEB C 4JOPFTQPTJCMFHSBàDBSUPEBTMBTMÎOFBTEFPQFSBDJÓO FTDBMFMBTFUBQBT TJTFFTQFDJàDBFM MVHBSEFMBFUBQBPEFDVBMRVJFSBMJNFOUBDJÓOPTBMJEBMBUFSBM D 4JFTOFDFTBSJP IBHBCBMBODFTFYUFSOPTEFNBTBZFOFSHÎB WFBFMFKFNQMP 6TFMPTWBMP SFTEF%Z#FOFMQBTP

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

  $VBOEPIBZBHSBàDBEPUPEBTMBTMÎOFBTEFPQFSBDJÓO FTDBMFMBTFUBQBT EFUFSNJOFMPTMVHBSFT EFQMBUPÓQUJNPEFBMJNFOUBDJÓOZMBDBOUJEBEUPUBMEFFUBQBT4JMPEFTFB DBMDVMFVOOÙNFSP GSBDDJPOBSJPEFFUBQB &OFMFKFNQMPBOUFSJPSOPTFJMVTUSBSPOUPEPTFTUPTQBTPTHFOFSBMFT QFSPFOFMFKFNQMPRVF TJHVFTÎTFJODMVJSÃO &TUFBMHPSJUNPEFTPMVDJÓOEFQSPCMFNBTEFCFVTBSTFDPNPHVÎB OPDPNPQSPHSBNBEFDPNQV UBEPSBRVFEFCBTFHVJSTFDPOFYBDUJUVE-BHSBOWBSJFEBEEFDPOàHVSBDJPOFTQPTJCMFTEFMBTDPMVN OBTEFEFTUJMBDJÓOQFSNJUJSÃBERVJSJSQSÃDUJDBFOFMVTPEFMNÊUPEPEF.D$BCF5IJFMF &+&.1-0 %FTUJMBDJÓODPOEPTBMJNFOUBDJPOFT 4FEFTFBTFQBSBSFUBOPMEFBHVBFOVOBDPMVNOBEFEFTUJMBDJÓODPOVODPOEFOTBEPSUPUBM ZVOWBQPSJ[BEPSQBSDJBM-BBMJNFOUBDJÓOFTLHNPMIEFVOBDPSSJFOUFRVFFTWBQPS TBUVSBEPZDPOUJFOFNPMEFFUBOPM BEFNÃTTFBMJNFOUBOLHNPMIEFVOBDPSSJFOUF  DPONPMEFFUBOPM-BBMJNFOUBDJÓOFTVOMÎRVJEPTVCFOGSJBEP6OBNPMEFWBQPS EFCFDPOEFOTBSTFEFOUSPEFMBDPMVNOBQBSBDBMFOUBSNPMFTEFMBBMJNFOUBDJÓOIBTUB TVQVOUPEFFCVMMJDJÓO4FEFTFBRVFFMQSPEVDUPEFGPOEPTUFOHBNPMEFFUBOPMZFM EFTUJMBEPNPMEFFUBOPM-BSFMBDJÓOEFSFáVKPFYUFSOPFT-%&MSFáVKPFTVO MÎRVJEPTBUVSBEP-BQSFTJÓOFOMBDPMVNOBFTL1BZMBDPMVNOBFTUÃCJFOBJTMBEB %FUFSNJOFMPTMVHBSFTÓQUJNPTEFBMJNFOUBDJÓO JEFOUJàDBEPTDPNPFUBQBTBSSJCBEFMWB QPSJ[BEPS ZMBDBOUJEBEUPUBMEFFUBQBTEFFRVJMJCSJPOFDFTBSJBT

Líquido saturado

La alimentación condensa 1 mol de vapor/4 moles Alim.

Alimentaciones óptimas

Vapor saturado

'*(63" $0-6./"%& %&45*-"$*¶/$0/%04"-*.&/5"$*0/&4  1"3"&-&+&.1-0

www.FreeLibros.me

  1SPDFEJNJFOUPHFOFSBMEFBOÃMJTJT.D$BCF5IJFMF



4PMVDJÓO " %FGJOB5BNCJÊOBRVÎBZVEBSÃVOFTRVFNBWFBMBàHVSB$PNPMBTEPTDPSSJFO UFTEFBMJNFOUBDJÓOZBFTUÃOQBSDJBMNFOUFTFQBSBEBT UJFOFTFOUJEPJOUSPEVDJSMBTQPS TFQBSBEPQBSBNBOUFOFSMBEJGFSFODJBEFDPODFOUSBDJPOFTRVFZBFYJTUF)FNPTIFDIP VOBIJQÓUFTJTJOIFSFOUFFOMBàHVSB-BBMJNFOUBDJÓO DPONBZPSGSBDDJÓONPM EFFUBOPMEFCFFOUSBSBMBDPMVNOBFOVOMVHBSNÃTBMUPRVFMBBMJNFOUBDJÓO&TUB IJQÓUFTJTTFDPNQSPCBSÃBMDBMDVMBSMPTMVHBSFTÓQUJNPTEFMPTQMBUPTEFBMJNFOUBDJÓO  QFSPBGFDUBSÃMBGPSNBEFIBDFSMPTDÃMDVMPTQSFMJNJOBSFT$PNPTFQJEJFSPOMPTMVHB SFTEFMPTQMBUPTEFBMJNFOUBDJÓODPNPQMBUPTTPCSFFMWBQPSJ[BEPS MBTFUBQBTTFIBO OVNFSBEPEFBCBKPIBDJBBSSJCB # &YQMPSF&TPCWJPRVFTFSFRVJFSFOEBUPTEFFRVJMJCSJP&TUÃOEJTQPOJCMFTFOMBàHVSB :BIFNPTDPNQSPCBEP FOFMFKFNQMP RVFFMEFSSBNFNPMBMDPOTUBOUFFTVOB IJQÓUFTJTSB[POBCMF6OWJTUB[PBMBàHVSBJOEJDBRVFMBTFDDJÓOTVQFSJPSFTJHVBMB MBTTFDDJPOFTTVQFSJPSFTRVFIFNPTVTBEPBOUFT5BNCJÊOMBTFDDJÓOJOGFSJPSFTGBNJMJBS -POVFWPEFFTUFQSPCMFNBFTMBQBSUFJOUFSNFEJB)BZEPTMÎOFBTEFBMJNFOUBDJÓOZUSFT MÎOFBTEFPQFSBDJÓO $ 1MBOFF.BOFKBSFNPTMBTEPTMÎOFBTEFBMJNFOUBDJÓO MBMÎOFBTVQFSJPSEFPQFSBDJÓO MB MÎOFBJOGFSJPSEFPQFSBDJÓOZMBMÎOFBJOUFSNFEJBEFPQFSBDJÓO"RVÎUBNCJÊOIBSFNPT MPTDÃMDVMPTOVNÊSJDPTTJNQMFT "MJNFOUBDJPOFT n2

f^ o^ m− f^ − & f ^ − &

"MJNFOUBDJÓO7BQPSTBUVSBEP R QFOEJFOUF PSEFOBEBBMPSJHFO[ R−   JOUFSTFDDJÓODPOZY[ "MJNFOUBDJÓO f' 2

AVWV_d − AVgg^WV ;'

-BFUBQBEFMBBMJNFOUBDJÓOTFWFFTRVFNÃUJDBNFOUFFOMBTJHVJFOUFàHVSB

&OUPODFT -BCBKPEFMBBMJNFOUBDJÓO- - ' D $BOUJEBEDPOEFOTBEBD  ' f' 2

A ;' X− A ;' &$);' 2*$) 2 ;' ;'

EZcY^ZciZ2

f' *$) 2 2* f ' − & *$)− &

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

*OUFSTFDDJÓOZY[ -ÎOFBTVQFSJPSEFPQFSBDJÓO1PEFNPTEFEVDJSMBFDVBDJÓOEFPQFSBDJÓOTVQFSJPS n2

A A m &− m K K 9

&TMBMÎOFBTVQFSJPSEFPQFSBDJÓOBDPTUVNCSBEB$POSFáVKPEFMÎRVJEPTBUVSBEP MBQFO EJFOUFFT A A A $9 2 2 2&$' K  A 9 A $9 &

*OUFSTFDDJÓOZYY% -ÎOFBJOGFSJPSEFPQFSBDJÓO1PEFNPTEFEVDJSMBFDVBDJÓOEFPQFSBDJÓOJOGFSJPS n2 A m −  A − &m 7 K K

mm &TMBMÎOFBJOGFSJPSEFPQFSBDJÓOBDPTUVNCSBEB-BQFOEJFOUF- 7TFEFTDPOPDF -BJOUFSTFDDJÓOZYFTUÃFOZYY#0USPQVOUPFTMBJOUFSTFDDJÓOEFMBMÎOFB EFBMJNFOUBDJÓO'DPOMBMÎOFBJOUFSNFEJBEFPQFSBDJÓO TJFTRVFTFQVFEFEFUFSNJOBSFTB MÎOFB -ÎOFBJOUFSNFEJBEFPQFSBDJÓO1BSBEFEVDJSVOBFDVBDJÓOEFPQFSBDJÓOQBSBMBTFDDJÓOJO UFSNFEJBQPEFNPTGPSNVMBSVOCBMBODFEFNBTBFOUPSOPBMBQBSUFTVQFSJPSPBMGPOEPEF MBDPMVNOB-BTFDVBDJPOFTRVFSFTVMUBOTFWFSÃOEJGFSFOUFT QFSPTFSÃOFRVJWBMFOUFT&O GPSNBBSCJUSBSJBVTBSFNPTMBFOWPMWFOUFEFCBMBODFEFNBTBFOUPSOPBMBQBSUFTVQFSJPS EFMBDPMVNOB DPNPNVFTUSBMBàHVSB-PTCBMBODFTEFNBTBTPO ;' K′ 2A′ 9 ;'o' K′ n2A′ m 9m9  .7$

%FFTUBFDVBDJÓOTFEFTQFKBZQBSBEFTBSSPMMBSMBFDVBDJÓOEFPQFSBDJÓOJOUFSNFEJB 

n2

A′ m K′

9m 9 − ;' o '  K′



6OQVOUPDPOPDJEPFTFMEFJOUFSTFDDJÓOEFMBMÎOFBEFBMJNFOUBDJÓO'DPOMBMÎOFB TVQFSJPSEFPQFSBDJÓO4FOFDFTJUBVOTFHVOEPQVOUP1PEFNPTQSPCBSDPOPSEFOBEBBM PSJHFO 9m 9 − ;' o' K′

QFSPTFEFTDPOPDF -BJOUFSTFDDJÓOEFMBMÎOFBEFPQFSBDJÓOJOUFSNFEJBDPOMBMÎOFBZYTFEFUFSNJOB IBDJFOEPRVFZYFOMBFDVBDJÓO 

ZEFTQFKBOEP m2n2

9m 9 − ;' o ' K′ − A′

www.FreeLibros.me

  1SPDFEJNJFOUPHFOFSBMEFBOÃMJTJT.D$BCF5IJFMF



%FMBFDVBDJÓOHFOFSBMEFCBMBODF 7 −- %−' "TÎ m2n2



9m 9 − ;' m '  9− ;'



&TUFQVOUPTFEFTDPOPDF QFSPTFQVFEFDBMDVMBSVOBWF[RVFTFDPOP[DB% -BQFOEJFOUF- 7 TFEFTDPOPDF QFSPTFQVFEFDBMDVMBSDPOMPTDÃMDVMPTEFMBFUBQB EFBMJNFOUBDJÓO%FMBEFàOJDJÓOEFR A′ 2;'f' A 





EPOEF- -% %6OBWF[EFUFSNJOBEB% TFQVFEFODBMDVMBS-ZEFTQVÊT- &OUPODFT  FMCBMBODFEFNBTBSFTVMUB 7 -  %−' ZTFQVFEFDBMDVMBSMBQFOEJFOUF- 7  -BDPODMVTJÓOEFFTUPTDÃMDVMPTFTRVFTFEFCFDBMDVMBS%1BSBIBDFSMP OFDFTJUBNPT CBMBODFTEFNBTBFYUFSOPT 

;& ;'29 7 

B



;&o& ;'o' 29m9 7m7  .7$ 

C

&TUBTEPTFDVBDJPOFTUJFOFOEPTJODÓHOJUBT %Z# RVFTFQVFEFOEFTQFKBS-BQSJNFSB FDVBDJÓOTFPSEFOBFOMBGPSNB#' '−%&OUPODFTTFTVTUJUVZFFOFMCBMBODFEFNBTB EFMDPNQPOFOUFNÃTWPMÃUJM ;&o& ;'o' 29m9 ;& ;'m7 −9m7

ZTFEFTQFKB% 

92

;&o& ;'o' − ;& ;'m7  m9 − m7



% )ÃHBMP%FJONFEJBUPTFQVFEFOHSBàDBSMBTEPTMÎOFBTEFBMJNFOUBDJÓOZMBMÎOFBTV QFSJPSEFPQFSBDJÓOFOVOEJBHSBNBZY&TUPTFWFFOMBàHVSB"OUFTEFHSBàDBS MBMÎOFBJOUFSNFEJBEFPQFSBDJÓOIBZRVFDBMDVMBS%DPOMBFDVBDJÓO   92

'%%%#( (%%%#)− *%%%#%' %#,'− %#%'

2')'#.`\bda$]

&OUPODFTTFQVFEFEFUFSNJOBSMBJOUFSTFDDJÓOEFZYDPOMBMÎOFBJOUFSNFEJBEFPQFSB DJÓO DPOMBFDVBDJÓO 

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

n 2m 2

2

9m 9 − ;' m ' 9 − ;'

')'#.%#,'− (%%%#) 2−%#.+ ')'#.− (%%

4FQPESÎBVTBSFTUFQVOUPEFJOUFSTFDDJÓO QFSPTBMFEFMBHSÃàDBFOMBàHVSB&OMVHBS EFVTBSVOBIPKBEFQBQFMNÃTHSBOEF DBMDVMBSFNPTMBQFOEJFOUF- 7  A′ 2;' f ' A2;' f ' 

A 9 9

-       LHNPMI 7 -  %−' −LHNPMI - 7  "IPSBTFHSBàDBMBMÎOFBEFPQFSBDJÓOJOUFSNFEJBDPNPFOMBàHVSB DPOMBJOUFS TFDDJÓOEFMBMÎOFBEFBMJNFOUBDJÓOZMBMÎOFBTVQFSJPSEFPQFSBDJÓO DPOQFOEJFOUF &OUPODFT MBMÎOFBJOGFSJPSEFPQFSBDJÓOWBEFZYY#IBTUBMBJOUFSTFDDJÓOEFMBMÎOFB JOUFSNFEJBEFPQFSBDJÓODPOMBMÎOFBEFBMJNFOUBDJÓO WFBMBàHVSB  $PNPTFEFTFBRVFMPTMVHBSFTEFMBTBMJNFOUBDJPOFTTFJOEJRVFODPNPFUBQBTBSSJCB EFMWBQPSJ[BEPS FTDBMPOBSFNPTMBTFUBQBTEFBCBKPIBDJBBSSJCBDPNFO[BOEPDPOFMWBQP SJ[BEPSQBSDJBMDPNPQSJNFSDPOUBDUPEFFRVJMJCSJP-BFUBQBÓQUJNBEFBMJNFOUBDJÓOQBSB MBBMJNFOUBDJÓOFTMBQSJNFSB NJFOUSBTRVFMBFUBQBÓQUJNBEFMBBMJNFOUBDJÓOFTMB TFHVOEBFUBQBFUBQBT VOWBQPSJ[BEPSQBSDJBMTPONÃTRVFTVàDJFOUFT

'*(63" 40-6$*¶/1"3"&-&+&.1-0

www.FreeLibros.me

  0USBTTJUVBDJPOFTFOMBTDPMVNOBTEFEFTUJMBDJÓO

'SBDDJÓO 



Y%−WBMPSEFFRVJMJCSJPEFPQFSBDJÓO WBMPSEFFRVJMJCSJP−WBMPSEFFRVJMJCSJPEFPQFSBDJÓO  'SBDD



m 9 − n* 2&$' n+ − n*

/FDFTJUBNPT˜FUBQBT WBQPSJ[BEPSQBSDJBM & 7FSJGJRVF5PEBTMBTDPNQSPCBDJPOFTEFDPOTJTUFODJBJOUFSOBUJFOFOTFOUJEP/PUFRVF - 7 QVFEFTFSNBZPSPNFOPSRVF$PNPMPTDBMPSFTMBUFOUFTEFFWBQPSBDJÓOTF QBSFDFO FTQSPCBCMFRVFFMEFSSBNFNPMBMDPOTUBOUFTFBVOBCVFOBIJQÓUFTJT/VFTUSB IJQÓUFTJTJOJDJBM EFRVFMBBMJNFOUBDJÓOFOUSBBMBDPMVNOBFOVOMVHBSNÃTBMUPRVF MBBMJNFOUBDJÓO SFTVMUÓWÃMJEBEFBDVFSEPDPOFMEJBHSBNBEF.D$BCF5IJFMF1P m m ESÎBNPTUBNCJÊODBMDVMBS- Z7 ZDPNQSPCBSRVFMBQFOEJFOUFEFMBMÎOFBJOGFSJPSEF PQFSBDJÓOFTDPSSFDUB ' (FOFSBMJDF&MNÊUPEPEFJOTFSUBSFMCBMBODFHFOFSBMEFNBTBQBSBTJNQMJàDBSMBEFUFS NJOBDJÓOEFMBMÎOFBZYDPOMBMÎOFBJOUFSNFEJBEFPQFSBDJÓO QBSBEFEVDJSMBFDVB DJÓO 

TFQVFEFVTBSFOPUSPTDBTPT&MNÊUPEPQBSBDBMDVMBS- 7 UBNCJÊOTF QVFEFHFOFSBMJ[BSBPUSBTTJUVBDJPOFT&TUPFT QPEFNPTDBMDVMBS% P#

EFUFSNJOBS MBUBTBEFáVKPFOMBTFDDJÓOTVQFSJPS PJOGFSJPS ZVTBSMBTDPOEJDJPOFTEFMBBMJNFO UBDJÓOQBSBDBMDVMBSáVKPTFOMBTFDDJÓORVFTFRVJFSB$PNPFTDBMPOBNPTMBTFUBQBT EFBCBKPIBDJBBSSJCB MBFUBQBGSBDDJPOBSJBTFDBMDVMBDPOMBEJGFSFODJBFOUSFWBMPSFTZ FTUPFT EJTUBODJBTWFSUJDBMFT FOMBFDVBDJÓO  &OMPTQSPCMFNBTJOEVTUSJBMFTTF VTBOSFMBDJPOFTEFSFáVKPNFOPSFT ZFMOÙNFSPEFFUBQBTFTNBZPS&OFTUFFKFNQMP TFVTÓVOBSFMBDJÓOEFSFáVKPSFMBUJWBNFOUFHSBOEFQBSBNBOUFOFSTFODJMMBMBHSÃàDB  053"44*56"$*0/&4&/-"4$0-6./"4%&%&45*-"$*¶/

$POGSFDVFODJBTFVTBOEJWFSTBTNPEJàDBDJPOFTEFMBTDPMVNOBTCÃTJDBT&OFTUBTFDDJÓOEFTDSJCJSF NPTFOGPSNBCSFWFMPTBTQFDUPTÙOJDPTEFBMHVOBTEFFMMBT4VQPOESFNPTEFSSBNFNPMBMDPOTUBOUF /PQSFTFOUBSFNPTFKFNQMPTEFUBMMBEPT QFSPTFEFKBSÃODPNPQSPCMFNBTEFUBSFB 4.9.1

Condensadores parciales

6ODPOEFOTBEPSQBSDJBMDPOEFOTBTÓMPVOBQBSUFEFMBDPSSJFOUFEFWBQPSZMBSFHSFTBFOGPSNBEF SFáVKP&TUFQSPEVDUPEFTUJMBEPTFTFQBSBDPNPWBQPS DPNPFOMBàHVSB4JTFEFTFBUFOFSVO EFTUJMBEPWBQPS VODPOEFOTBEPSQBSDJBMTFSÃNVZBEFDVBEP&MDPOEFOTBEPSQBSDJBMGVODJPOBDPNP VODPOUBDUPEFFRVJMJCSJP 4JTFIBDFVOCBMBODFEFNBTBDPOFMDPNQPOFOUFNÃTWPMÃUJM VTBOEPMBFOWPMWFOUFEFCBMBODF EFMBàHVSB TFPCUJFOF 7Z-Y %Z% "MFMJNJOBS%ZEFTQFKBSZ SFTVMUBMBFDVBDJÓOEFPQFSBDJÓO 

n2

A A m &− n  K K 9

www.FreeLibros.me





$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

Vapor destilado

Línea Sup. de Op.

Línea y = x

yCMV xCMV

'*(63" $0/%&/4"%031"3$*"-" &/70-7&/5&%&#"-"/$& # -±/&" 461&3*03%&01&3"$*¶/ ­TUBFT FOFTFODJB MBNJTNBFDVBDJÓORVFMBEFMBMÎOFBTVQFSJPSEFPQFSBDJÓODPOVODPOEFOTB EPSUPUBM FYDFQUPRVFZ%TVTUJUVZFBY%-BMÎOFBEFPQFSBDJÓOTVQFSJPSDPSUBSÃBMBMÎOFBZYFO ZYZ%-BMÎOFBTVQFSJPSEFPQFSBDJÓOTFNVFTUSBFOMBàHVSB-BEJGFSFODJBQSJODJQBM FOUSF FTUF DBTP Z FM EF VO DPOEFOTBEPS UPUBM FT RVF FM DPOEFOTBEPS QBSDJBM TJSWF DPNP QSJNFS DPOUBDUPEFFRVJMJCSJP 4.9.2

Vaporizadores totales

&O VO WBQPSJ[BEPS UPUBM TF FWBQPSB UPEB MB DPSSJFOUF RVF MF MMFHB &OUPODFT  MB DPNQPTJDJÓO EFM WBQPSFTJHVBMBMBDPNQPTJDJÓOEFMMÎRVJEP-BFDVBDJÓOEFCBMBODFEFNBTBZMBEFMBMÎOFBJOGFSJPS EFPQFSBDJÓO DPOVOWBQPSJ[BEPSUPUBM TPOFYBDUBNFOUFJHVBMFTBMBTEFVOWBQPSJ[BEPSQBSDJBM -BÙOJDBEJGFSFODJBFTRVFVOWBQPSJ[BEPSQBSDJBMFTVODPOUBDUPEFFRVJMJCSJPZBTÎTFDPOTJEFSBFO FMEJBHSBNBEF.D$BCF5IJFMF&MWBQPSJ[BEPSUPUBMOPFTVODPOUBDUPEFFRVJMJCSJPZBQBSFDFFOFM EJBHSBNBEF.D$BCF5IJFMFDPNPVOQVOUPZYY# "MHVOPTUJQPTEFWBQPSJ[BEPSFTQBSDJBMFTQVFEFOGVODJPOBSNÃTPNFOPTDPNPVODPOUBDUPEF FRVJMJCSJP&OFTPTDBTPTTFSFRVJFSFDPOPDFSMPTEFUBMMFTFYBDUPTEFMBDPOTUSVDDJÓOEFMWBQPSJ[BEPS 4.9.3

Corrientes laterales o líneas de salida

4JTFSFRVJFSFVOQSPEVDUPEFDPNQPTJDJÓOJOUFSNFEJB TFQVFEFTBDBSVOBDPSSJFOUFMBUFSBMEF WBQPSPMÎRVJEP&TUPTFTVFMFIBDFSDPOGSFDVFODJBFOMBTSFàOFSÎBTQFUSPMFSBT ZTFJMVTUSBFOMB àHVSB " QBSB VOB DPSSJFOUF MBUFSBM MÎRVJEB 4F EFCFO FTQFDJàDBS USFT WBSJBCMFT BEJDJPOBMFT DPNPUBTBEFáVKP4 UJQPEFTBMJEBMBUFSBM MÎRVJEPPWBQPS ZVCJDBDJÓOPDPNQPTJDJÓOY4PZ4 -BFDVBDJÓOEFPQFSBDJÓOQBSBMBTFDDJÓOJOUFSNFEJBTFQVFEFEFEVDJSDPOCBMBODFTEFNBTBFO UPSOPBMBQBSUFTVQFSJPSPJOGFSJPSEFMBDPMVNOB1BSBFMDBTPEFMBàHVSB" MBFDVBDJÓOEF PQFSBDJÓOJOUFSNFEJBFT 

n2

A m K

9m 9  Hmh  K

www.FreeLibros.me



  0USBTTJUVBDJPOFTFOMBTDPMVNOBTEFEFTUJMBDJÓO



'*(63" 7"103*;"%03505"- -BJOUFSTFDDJÓODPOZYFT 

m2n2

9m 9 Hm h  9 H



TJTFDPOPDFO4 Y4 %ZY% FTFQVOUPTFQVFEFHSBàDBS-BEFEVDDJÓOEFMBTFDVBDJPOFT  Z  TFEFKBDPNPQSPCMFNB$

Superior YCMV Intermedia

Inferior 51/3 contactos Equil. xCMV

'*(63" 4"-*%"-"5&3"-" $0-6./"# %*"(3"."%&.$$"#&5)*&-&

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

4FQVFEFEFUFSNJOBSVOTFHVOEPQVOUPEPOEFTFSFUJSBMBDPSSJFOUFMBUFSBM6OBTBMJEBEFMÎ RVJEP TBUVSBEP FRVJWBMF B VOB BMJNFOUBDJÓO OFHBUJWB EF DPODFOUSBDJÓO Y4 1PS UBOUP EFCF IBCFS VOBMÎOFBWFSUJDBMEFBMJNFOUBDJÓOFOYY4-BTMÎOFBTEFPQFSBDJÓOTVQFSJPSFJOUFSNFEJBEFCFO DSV[BSTFFOFTUBMÎOFBEFBMJNFOUBDJÓO -PT DÃMDVMPT DPO DPSSJFOUFT MBUFSBMFT UJFOFO VOB EJGFSFODJB RVF MPT BQBSUB EF MPT DÃMDVMPT EF BMJNFOUBDJPOFT-BFUBQBEFCFDPJODJEJSFYBDUBNFOUFFOFMQVOUPEFJOUFSTFDDJÓOEFMBTEPTMÎOFBT EFPQFSBDJÓO&TUPTFWFFOMBàHVSB#$PNPMBDPSSJFOUFMBUFSBMEFMÎRVJEPTFSFUJSBEFMQMBUP  TFEFCFDVNQMJSY4Y4JMBVCJDBDJÓOEFMBFUBQBFTEBUP Y4TFQVFEFEFUFSNJOBSFTDBMPOBOEPMB DBOUJEBEOFDFTBSJBEFFUBQBT 1BSBVOBTBMJEBMÎRVJEB VOCBMBODFEFMÎRVJEPFT 

--  4



.JFOUSBTRVFMBTUBTBTEFáVKPEFWBQPSOPDBNCJBO 77 "TÎ MBQFOEJFOUF- 7 EFMBMÎOFBJOUFS NFEJBEFPQFSBDJÓOTFQVFEFEFUFSNJOBS TJTFDPOPDFO-Z7"TVWF[ -Z7TFQVFEFOEFUFSNJOBS DPO-%Z% Z%TFQVFEFFODPOUSBSDPOCBMBODFTFYUFSOPT VOBWF[DPOPDJEBY4 1BSBVOBDPSSJFOUFMBUFSBMEFWBQPS MBMÎOFBEFBMJNFOUBDJÓOFTIPSJ[POUBMFOZZ46OCBMBODF EFMBTUBTBTEFáVKPEFWBQPSFT 

7 7 47



NJFOUSBTRVFMBTUBTBTEFáVKPEFMÎRVJEPTOPDBNCJBO5BNCJÊOBRVÎ - 7 TFQVFEFDBMDVMBSTJTF DPOPDFO-Z7 4JTFEFTFBUFOFSVOWBMPSFTQFDJàDBEPEFY4 PEFZ4

FMQSPCMFNBFTEFUBOUFPT-BMÎOFBTVQF SJPSEFPQFSBDJÓOTFBKVTUB TFDBNCJB-% IBTUBRVFVOBFUBQBUFSNJOFFYBDUBNFOUFFOY4PZ4 4FQVFEFOEFTDSJCJSMPTDÃMDVMPTQBSBDPSSJFOUFTMBUFSBMFTBCBKPEFMBBMJNFOUBDJÓOVTBOEPCBTFT TJNJMBSFT WFBFMQSPCMFNB$  4.9.4

Vaporizadores intermedios y condensadores intermedios

0USBNPEJàDBDJÓORVFTFVTBFOPDBTJPOFTFTUFOFSVOWBQPSJ[BEPSJOUFSNFEJP PVODPOEFOTBEPS JOUFSNFEJP$POFMWBQPSJ[BEPSJOUFSNFEJPTFTBDBVOBDPSSJFOUFMÎRVJEBMBUFSBMEFMBDPMVNOB TF FWBQPSBZFMWBQPSTFSFHSFTBBMBDPMVNOB$POFMDPOEFOTBEPSJOUFSNFEJPTFTBDBVOBDPSSJFOUF MBUFSBMEFWBQPS TFDPOEFOTBZTFSFHSFTBBMBDPMVNOB-BàHVSB"JMVTUSBVOWBQPSJ[BEPSJO UFSNFEJP $POVOCBMBODFEFFOFSHÎBFOUPSOPBMBDPMVNOBNPTUSBSÃRVF23TJOWBQPSJ[BEPSJOUFSNFEJP FTJHVBMB23 2DPOFMWBQPSJ[BEPSJOUFSNFEJP RVFEBOEPDPOTUBOUFT' [ R Y% Y# Q -% &O UPODFT MBFOFSHÎBSFRVFSJEBOPDBNCJBMPRVFDBNCJBFTMBUFNQFSBUVSBBMBRVFTFSFRVJFSF$PNP Y4Y# MBUFNQFSBUVSBEFMWBQPSJ[BEPSJOUFSNFEJPFTNFOPSRVFMBEFMWBQPSJ[BEPSJOGFSJPSZTF QVFEFVTBSVOBGVFOUFEFDBMPSNFOPTDPTUPTB WFSJàRVFFTUPDPOEBUPTEFFRVJMJCSJP  $PNPMBDPMVNOBEFMBàHVSB"UJFOFDVBUSPTFDDJPOFT IBCSÃDVBUSPMÎOFBTEFPQFSBDJÓO &TUPTFWFFOFMEJBHSBNBEF.D$BCF5IJFMFEFMBàHVSB#4FEFCFFTQFDJàDBSRVFTFSFUJSFFM MÎRVJEPDPOVOBUBTBEFáVKP4 ZBTFBDPOMBDPODFOUSBDJÓOFTQFDJàDBEBY4PFOEFUFSNJOBEPQMBUP&M WBQPSTBUVSBEPUJFOFMBDPODFOUSBDJÓOZ4Y4&OUPODFT IBZVOBMÎOFBIPSJ[POUBMEFBMJNFOUBDJÓOFO Z44JFMMVHBSÓQUJNPQBSBMBFOUSBEBEFWBQPSFTUÃJONFEJBUBNFOUFBCBKPEFMBFUBQBEFEPOEFTFTBDB FMMÎRVJEP FTUBSÃQSFTFOUFMBMÎOFB- 7 QFSPOPTFIBCSÃOFTDBMPOBEPFUBQBTFOFMMB DPNPTFWFFO MBàHVSB# FMMVHBSÓQUJNPQBSBBMJNFOUBSFMWBQPSQVFEFFTUBSWBSJBTFUBQBTBCBKPEFEPOEFTF TBDBFMMÎRVJEP &MUSB[PEFMBTEPTMÎOFBTJOUFSNFEJBTEFPQFSBDJÓOTFEFKBDPNPQSPCMFNB$6TF MBTFOWPMWFOUFTEFCBMBODFEFNBTBRVFNVFTUSBMBàHVSB"

www.FreeLibros.me

  0USBTTJUVBDJPOFTFOMBTDPMVNOBTEFEFTUJMBDJÓO



yCMV

Inferior xCMV

'*(63" 7"103*;"%03*/5&3.&%*0" &/70-7&/5&4%&#"-"/$&  # %*"(3"."%&.$$"#&5)*&-&

-PTDPOEFOTBEPSFTJOJDJBMFTTPOÙUJMFT QPSRVFFMSFGSJHFSBOUFQVFEFFTUBSBNBZPSUFNQFSBUV SB7FBFMQSPCMFNB$ 4.9.5

Columnas de agotamiento y enriquecimiento

)BTUBBIPSBIFNPTEFTDSJUPDPMVNOBTEFEFTUJMBDJÓODPNQMFUBDPOEPTTFDDJPOFT DVBOEPNFOPT 5BNCJÊOTFVTBODPOGSFDVFODJBDPMVNOBTDPOTÓMPVOBTFDDJÓOEFBHPUBNJFOUP PTÓMPVOBTFDDJÓO EFFOSJRVFDJNJFOUP­TUBTTFNVFTUSBOFOMBTàHVSBT"Z#$VBOEPTFVTBTÓMPVOBTFDDJÓOEF BHPUBNJFOUP MBBMJNFOUBDJÓOEFCFTFSVOMÎRVJEPTVCFOGSJBEPPTBUVSBEP/PTFVTBSFáVKP4FQVF EFPCUFOFSVOQSPEVDUPEFGPOEPTNVZQVSP QFSPFMWBQPSEFTUJMBEPOPTFSÃQVSP&OMBDPMVNOB EFFOSJRVFDJNJFOUPPSFDUJàDBDJÓO QPSPUSBQBSUF MBBMJNFOUBDJÓOFTVOWBQPSTPCSFDBMFOUBEPPVO WBQPSTBUVSBEP ZFMEFTUJMBEPQVFEFTFSNVZQVSP QFSPMPTGPOEPTOPTFSÃONVZQVSPT-BTDPMVN OBTEFBHPUBNJFOUPZMBTEFFOSJRVFDJNJFOUPTFVTBODVBOEPOPTFOFDFTJUBVOEFTUJMBEPNVZQVSP PGPOEPTNVZQVSPT SFTQFDUJWBNFOUF &MBOÃMJTJTEFMBTDPMVNOBTEFBHPUBNJFOUPZEFFOSJRVFDJNJFOUPFTTJNJMBS"OBMJ[BSFNPTBRVÎ MBDPMVNOBEFBHPUBNJFOUPZEFKBSFNPTFMBOÃMJTJTEFMBDPMVNOBEFFOSJRVFDJNJFOUPDPNPQSPCMF NBEFUBSFB QSPCMFNB$ 4FQVFEFDPODFCJSRVFMBDPMVNOBEFBHPUBNJFOUPRVFNVFTUSBMB àHVSB"FTVOBDPMVNOBEFEFTUJMBDJÓODPNQMFUB DPOUBTBEFáVKPEFMÎRVJEPJHVBMBDFSPFOMB TFDDJÓOEFFOSJRVFDJNJFOUP&OUPODFT MBMÎOFBTVQFSJPSEFPQFSBDJÓOFTZZ%-BMÎOFBEFPQFSB DJÓOJOGFSJPSTFQVFEFEFEVDJSZSFTVMUB mm mm Z - 7 Y− - 7− Y# RVFFTMBFDVBDJÓOOPSNBMQBSBPQFSBDJÓOJOGFSJPSDPOVOWBQPSJ[BEPSQBSDJBM-BTMÎOFBTEFPQF SBDJÓOTVQFSJPSFJOGFSJPSTFDSV[BOFOMBMÎOFBEFBMJNFOUBDJÓO4JMBTWBSJBCMFTFTQFDJàDBEBTTPO

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

Línea de alimentación

yCMV

xCMV

'*(63" $0-6./"4%&"(05".*&/50:&/3*26&$*.*&/50 " "(05".*&/50 # &/3*26&$*.*&/50 $ %*"(3"."%& .$$"#&5)*&-&1"3"-"$0-6./"%&"(05".*&/50 ' R [ Q Y#ZZ% TFQVFEFHSBàDBSMBMÎOFBEFBMJNFOUBDJÓO ZFOUPODFTTFQVFEFPCUFOFSMBMÎOFB JOGFSJPSEFPQFSBDJÓODPOTVJOUFSTFDDJÓOFOZYY#ZTVJOUFSTFDDJÓODPOMBMÎOFBEFBMJNFOUBDJÓO FOZ% TFEFKBMBEFNPTUSBDJÓODPNPQSPCMFNB$ 4JTFFTQFDJàDBMBFOUSBEBEFWBQPSBMGPOEP  m 7 # FOUPODFTOPTFFTQFDJàDBZ% QFSPTFQVFEFEFTQFKBS&OMBàHVSB$TFWFVOEJBHSBNBEF .D$BCF5IJFMFQBSBVOBDPMVNOBEFBHPUBNJFOUP  $0/%*$*0/&4-±.*5&%&01&3"$*¶/

4JFNQSFFTÙUJMSFWJTBSMBTDPOEJDJPOFTMÎNJUF1BSBMBEFTUJMBDJÓO EPTDPOEJDJPOFTMÎNJUFTPOSFáVKP UPUBMZSFáVKPNÎOJNP&OFMSFáVKPUPUBM UPEPFMWBQPSEFTUJMBEPSFHSFTBBMBDPMVNOBDPNPSFáV KPZUPEPFMMÎRVJEPEFGPOEPTSFHSFTBDPNPWBQPSBMQMBUPJOGFSJPS&OUPODFT MBTUBTBTEFáVKPEF EFTUJMBEPZGPOEPTTPODFSP&OFMFTUBEPFTUBCMF MBUBTBEFBMJNFOUBDJÓOUBNCJÊOEFCFTFSDFSP&M

www.FreeLibros.me

  $POEJDJPOFTMÎNJUFEFPQFSBDJÓO



SFáVKPUPUBMTFVTBFOFMBSSBORVFEFMBTDPMVNOBT QBSBNBOUFOFSGVODJPOBOEPMBDPMVNOBDVBOEP TFEFUJFOFPUSBQBSUFEFMBQMBOUB ZUBNCJÊOQBSBEFUFSNJOBSMBFàDJFODJBEFMBDPMVNOB &MBOÃMJTJTDPOSFáVKPUPUBMFTTFODJMMP$PNPUPEPFMWBQPSTFWBBSFáVKP -7Z-7 m m mm 5BNCJÊO- 7 Z- 7 &OUPODFT MBTEPTMÎOFBTEFPQFSBDJÓOTFDPOWJFSUFOFOMBMÎOFBZY &TUP TF NVFTUSB FO MB àHVSB # &M SFáVKP UPUBM SFQSFTFOUB MB TFQBSBDJÓO NÃYJNB RVF QVFEF PCUFOFSTFDPOEFUFSNJOBEBDBOUJEBEEFFUBQBTQFSPDFSPDBQBDJEBE5BNCJÊO DPOFMSFáVKPUPUBM TFPCUJFOFMBDBOUJEBENÎOJNBEFFUBQBTQBSBEFUFSNJOBEBTFQBSBDJÓO"VORVFFTTJNQMF FMSFáVKP UPUBMQVFEFDBVTBSQSPCMFNBTEFTFHVSJEBE-BTGVHBTDFSDBEFMBQBSUFTVQFSJPSEFMBDPMVNOBQVF EFODBVTBSDPODFOUSBDJPOFTEFNBUFSJBMFTDPOBMUPQVOUPEFFCVMMJDJÓO DPOVOBVNFOUPDPSSFTQPO EJFOUFEFUFNQFSBUVSB&TPQVFEFDBVTBSQPMJNFSJ[BDJÓO JODFOEJPTPFYQMPTJPOFT ,JTUFS   &OUPODFT FTJNQPSUBOUFWJHJMBSMBUFNQFSBUVSBFOMBQBSUFTVQFSJPSEFMBDPMVNOB ZEFCFTPOBSVOB BMBSNBTJTVCFEFNBTJBEPFTBUFNQFSBUVSB &MSFáVKPNÎOJNP  -% NÎO TFEFàOFDPNPMBSFMBDJÓOEFSFáVKPFYUFSOPDPOMBRVFBQFOBTTF QVFEFPCUFOFSMBTFQBSBDJÓORVFTFEFTFBDPOVOBDBOUJEBEJOàOJUBEFFUBQBT&TPCWJPRVFOPFT VOBDPOEJDJÓOSFBM QFSPFTVODPODFQUPIJQPUÊUJDPÙUJM1BSBUFOFSVOBDBOUJEBEJOàOJUBEFFUBQBT  MBTMÎOFBTEFPQFSBDJÓOZEFFRVJMJCSJPTFEFCFOUPDBS&OHFOFSBM FTPQVFEFTVDFEFSFOMBBMJNFOUB DJÓOPFOVOQVOUPUBOHFOUFBMBDVSWBEFFRVJMJCSJP&TUPTEPTQVOUPTTFWFOFOMBTàHVSBT"Z #&MQVOUPEPOEFMBMÎOFBEFPQFSBDJÓOUPDBBMBDVSWBEFFRVJMJCSJPTFMMBNBQVOUPEFFTUSJDDJÓO QJODIQPJOU &OFMQVOUPEFFTUSJDDJÓOOPDBNCJBOMBTDPODFOUSBDJPOFTEFMÎRVJEPZWBQPSEFVOB BPUSBFUBQB&TPTFNVFTUSBFOMBàHVSB$ QBSBVOBFTUSJDDJÓOFOMBFUBQBEFBMJNFOUBDJÓO 4JTFBVNFOUBMJHFSBNFOUFMBSFMBDJÓOEFSFáVKPTFQVFEFBMDBO[BSMBTFQBSBDJÓOEFTFBEBDPOVOB DBOUJEBEàOJUBEFFUBQBT 1BSB TJTUFNBT CJOBSJPT  MB SFMBDJÓO EF SFáVKP NÎOJNP TF EFUFSNJOB DPO GBDJMJEBE 4F USB[B MB MÎOFBTVQFSJPSEFPQFSBDJÓOIBTUBVOQVOUPEFFTUSJDDJÓO DPNPFOMBàHVSB"PMB#&O UPODFT  -7 NÎOFTJHVBMBMBQFOEJFOUFEFMBMÎOFBTVQFSJPSEFPQFSBDJÓO RVFOPQVFEFVTBSTFFO VOBDPMVNOBSFBM QPSRVFTFOFDFTJUBSÎBVOBDBOUJEBEJOàOJUBEFFUBQBT

Z 



A A A$Kb†c  2  2  9 b†c K−A b†c &−A$Kb†c

yCMV Línea y = x

xCMV

'*(63" 3&'-6+0505"-" $0-6./" # %*"(3"."%&.$$"#&5)*&-&

www.FreeLibros.me





$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

Estricción Estricción

yCMV

yCMV

xCMV

xCMV

Conc. en la etapa

Vaporizador

Alimentación

Condensador

Ubicación en la etapa

'*(63" 3&'-6+0.±/*.0" &453*$$*¶/&/-"&5"1"%&"-*.&/5"$*¶/  # &453*$$*¶/5"/(&/5& $ 1&3'*-%&$0/$&/53"$*¶/1"3"-%  -% .±/ /PUFRVFMBSFMBDJÓOEFSFáVKPNÎOJNPEFQFOEFEFY% [ZR ZQVFEFEFQFOEFSEFY#&MDÃMDVMPEFM SFáVKPNÎOJNPQVFEFTFSNÃTDPNQMJDBEPDVBOEPIBZEPTBMJNFOUBDJPOFTPVOBDPSSJFOUFMBUFSBM &TPTFFYQMPSBFOMPTQSPCMFNBTEFUBSFB -BSFMBDJÓOEFSFáVKPNÎOJNPTFVTBOPSNBMNFOUFQBSBFTQFDJàDBSMBTDPOEJDJPOFTEFPQFSB DJÓO1PSFKFNQMP TFQVFEFFTQFDJàDBSRVFMBSFMBDJÓOEFSFáVKPTFB-% -% NÎO&MSFáVKP NÎOJNPVTBSÎBMBDBOUJEBENÎOJNBEFMÎRVJEPSFáVKBEP ZQPSUBOUP MBDBOUJEBENÎOJNBEFDBMPSFO FMWBQPSJ[BEPS QFSP UBNCJÊOMBDBOUJEBENÃYJNB JOàOJUB EFFUBQBT ZVOEJÃNFUSPNÃYJNP JOà OJUP QBSBEFUFSNJOBEBTFQBSBDJÓO&TPCWJPRVFMBTNFKPSFTDPOEJDJPOFTEFPQFSBDJÓOFTUÃOFOUSF FMSFáVKPNÎOJNPZFMSFáVKPUPUBM$PNPSFHMBBQSPYJNBEB MBSFMBDJÓOÓQUJNBEFSFáVKPFYUFSOP FTUÃFOUSFZQPS -% NÎO WFBNÃTEFUBMMFTFOFMDBQÎUVMP  mm 5BNCJÊOTFQVFEFEFàOJSVOB- 7 NÃYJNB ZFODPOTFDVFODJBVOBSFMBDJÓONÎOJNBEFWBQPSBM m GPOEP 7 #-PTQVOUPTEFFTUSJDDJÓOTFWFSÃOJHVBMRVFFOMBàHVSB"P#&OFMQSPCMFNB $TFFYBNJOBFTUBTJUVBDJÓO

www.FreeLibros.me

  &GJDJFODJBT



 &'*$*&/$*"4

)BTUBBIPSBTJFNQSFIFNPTTVQVFTUPRVFMBTFUBQBTTPOEFFRVJMJCSJP4FQVFEFODPOTUSVJSFUBQBT RVFFTUÊONVZDFSDBEFMFRVJMJCSJP QFSPTÓMPTFVTBOQBSBàOFTFTQFDJBMFT DPNPMBEFUFSNJOBDJÓO EFDPODFOUSBDJPOFTEFFRVJMJCSJP1BSBDPNQBSBSFMGVODJPOBNJFOUPEFVOBFUBQBSFBMZVOBEFFRVJ MJCSJP VTBNPTVOBNFEJEBEFMBFàDJFODJB 4FIBOEFàOJEPNVDIBTEPTEFVTPDPNÙOTPOMBFàDJFODJBHFOFSBMZMBFàDJFODJBEF.VSQISFF -BFàDJFODJBHFOFSBM &P TFEFàOFDPNPMBDBOUJEBEEFFUBQBTEFFRVJMJCSJPOFDFTBSJBQBSBMBTFQB SBDJÓO EJWJEJEBFOUSFMBDBOUJEBESFBMEFFUBQBTSFRVFSJEBT



:d 2

CZfj^a CgZVa





&OMBDBOUJEBEEFFUBQBTSFBMPMBEFFRVJMJCSJPOPTFJODMVZFODPOEFOTBEPSFTQBSDJBMFTOJWBQPSJ[B EPSFTQBSDJBMFT QPSRVFOPUFOESÃOMBNJTNBFàDJFODJBRVFMBTFUBQBTFOMBDPMVNOB &OMBFàDJFODJBHFOFSBMTFBHSVQBUPEPMPRVFTVDFEFFOMBTDPMVNOBTy$VÃMFTWBSJBCMFTBGFDUBO MBFàDJFODJBEFMBDPMVNOB -BTQSPQJFEBEFTIJESPEJOÃNJDBTEFáVKP DPNPWJTDPTJEBEZUBTBEF áVKPEFHBT BGFDUBSÎBOBMSÊHJNFOEFáVKP-BWFMPDJEBEEFUSBOTGFSFODJBEFNBTBFTUÃJOáVJEBQPS MBEJGVTJWJEBE ZBTVWF[BGFDUBMBFàDJFODJB-BFàDJFODJBHFOFSBMTVFMFTFSNFOPSBNFEJEBRVFMB TFQBSBDJÓOTFBNÃTGÃDJM "#BVNFOUB 5BNCJÊOFMUBNBÒPEFMBDPMVNOBQVFEFUFOFSTVFGFDUP &OFMDBQÎUVMPTFEFTDSJCJSÃODPSSFMBDJPOFTQBSBEFUFSNJOBSMBFàDJFODJBHFOFSBM1PSBIPSB TV QPOESFNPTRVFMBFàDJFODJBHFOFSBMTFEFUFSNJOBDPOMBFYQFSJFODJBEFPQFSBDJÓOFODPMVNOBTEF EFTUJMBDJÓOTJNJMBSFT -BFàDJFODJBHFOFSBMUJFOFMBWFOUBKBEFTFSGÃDJMEFVTBS QFSPMBEFTWFOUBKBEFTFSNVZEJGÎDJM EFDBMDVMBSBQBSUJSEFMPTQSJNFSPTQSJODJQJPT4FEFàOFOFàDJFODJBTEFFUBQB QBSBDBEBFUBQB RVF QVFEFOWBSJBSEFVOBBPUSB-BTFàDJFODJBTEFFUBQBTPONÃTGÃDJMFTEFFTUJNBSDPOMPTQSJNFSPT QSJODJQJPT PEFDPSSFMBDJPOBSDPOMPTEBUPTEFPQFSBDJÓO-BTFàDJFODJBTEFFUBQBEFVTPNÃTDP NÙO QBSBEFTUJMBDJÓOCJOBSJB TPOMBTFàDJFODJBTEF.VSQISFFEFWBQPSZMÎRVJEP .VSQISFF   -BFàDJFODJBEFWBQPSEF.VSQISFFTFEFàOFDPNP



&.7

DBNCJPSFBMEFDPODFOUSBDJÓOEFMWBQPS DBNCJPEFDPODFOUSBDJÓOEFWBQPSQBSBFUBQBFOFRVJMJCSJP





.VSQISFFQPTUVMÓRVFFMWBQPSFOUSFMBTFUBQBTFTUÃCJFONF[DMBEP RVFFMMÎRVJEPFOMBTCBKBOUFT FTUÃCJFONF[DMBEP ZRVFFMMÎRVJEPFOFMQMBUPFTUÃCJFONF[DMBEPZUJFOFMBNJTNBDPNQPTJDJÓORVF MBEFMMÎRVJEPFOMBCBKBOUFRVFTBMFEFMQMBUP1BSBMBOPNFODMBUVSBRVFNVFTUSBMBàHVSB" MB FàDJFODJBEFWBQPS.VSQISFFFT 

:BK 2

n_ − n_

&

n _ − n_

&





EPOEFZ KFTMBGSBDDJÓONPMEFWBQPSFOFRVJMJCSJPDPOMBGSBDDJÓONPMEFMMÎRVJEPSFBM YK 6OB WF[ DPOPDJEB MB FàDJFODJB EF WBQPS .VSQISFF QBSB DBEB FUBQB  TFSÃ GÃDJM VTBSMB FO VO EJBHSBNBEF.D$BCF5IJFMF EFIFDIP .VSQISFFBKVTUÓTVUSBCBKPQBSBVTBSFMSFDJÊOEFTBSSPMMBEP

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

curva de pseudo-equilibrio

yj * en equilibrio con xj xj * en equilibrio con yj

yCMV

xCMV

'*(63" &'*$*&/$*"%&.631)3&&" /0.&/$-"563"%&-"&5"1"  # %*"(3"."%&.$$"#&5)*&-&1"3"&.7

EJBHSBNBEF.D$BCF5IJFMF &MEFOPNJOBEPSFOMBFDVBDJÓO  SFQSFTFOUBMBEJTUBODJBWFSUJDBM EFMBMÎOFBEFPQFSBDJÓOBMBDPODFOUSBDJÓOSFBMEFMBTBMJEB"TÎ MBFàDJFODJBEFWBQPS.VSQISFF FTMBDBOUJEBEGSBDDJPOBSJBEFMBEJTUBODJBWFSUJDBMUPUBMEFTEFMBMÎOFBEFPQFSBDJÓO4JFTDBMPOBNPT MBTFUBQBTEFBCBKPIBDJBBSSJCB MMFHBSFNPTBMSFTVMUBEPEFMBàHVSB#0CTFSWFRVFFMWBQPSJ [BEPSQBSDJBMTFDPOTJEFSBQPSTFQBSBEP QPSRVFUFOESÃVOBFàDJFODJBEJGFSFOUFBMBEFMSFTUPEFMB DPMVNOB 5BNCJÊOTFQVFEFVTBSMBFàDJFODJBEF.VSQISFFDPNPSFMBDJÓOEFMBTEJTUBODJBTRVFTFWFO FOMBàHVSB#4JMBTFàDJFODJBTEF.VSQISFFTPOFYBDUBT MPTMVHBSFTJEFOUJàDBEPTQPSMPTOÙ NFSPTEFFUBQBSFQSFTFOUBOMBTDPNQPTJDJPOFTSFBMFTEFWBQPSZMÎRVJEPRVFTBMFOEFVOBFUBQB &TPTQVOUPTTFQVFEFOVOJSZGPSNBSVOBDVSWBEFQTFVEPFRVJMJCSJPÊTUBEFQFOEFEFMBTMÎOFBTEF PQFSBDJÓORVFTFVTFO QPSMPRVFEFCFUSB[BSTFQBSBDBEBDPOKVOUPOVFWPEFMÎOFBTEFPQFSBDJÓO -BàHVSB#OPTQFSNJUFEFUFSNJOBSFMQMBUPÓQUJNPSFBMEFBMJNFOUBDJÓO ZMBDBOUJEBEUPUBM SFBMEFFUBQBT 6OBFàDJFODJBMÎRVJEBEF.VSQISFFTFQVFEFEFàOJSDPNP 

:BA 2

m _ − m _−& m _ − m _−&





RVFFTFMDBNCJPSFBMEFGSBDDJÓONPMEJWJEJEPFOUSFFMDBNCJPFOVOBFUBQBEFFRVJMJCSJP-BFà DJFODJBMÎRVJEBEF.VSQISFFFTTJNJMBSBMBEFWBQPS QFSPVTBEJTUBODJBTIPSJ[POUBMFT/PUFRVF &.- &.7 1BSBNF[DMBTCJOBSJBT MBTFàDJFODJBTEF.VSQISFFTPOJHVBMFT ZBTFBRVFTFFTDSJCBOQBSBFM DPNQPOFOUFNÃTWPMÃUJMPFMNFOPTWPMÃUJM1BSBNF[DMBTDPOWBSJPTDPNQPOFOUFT QVFEFOTFSEJGF SFOUFTQBSBMPTEJGFSFOUFTDPNQPOFOUFT ZIBTUBQVFEFOTFSOFHBUJWBT

www.FreeLibros.me

  1SPCMFNBTEFTJNVMBDJÓO



 130#-&."4%&4*.6-"$*¶/

&OVOQSPCMFNBEFTJNVMBDJÓO ZBTFIBDPOTUSVJEPMBDPMVNOBZTFEFTFBDPOPDFSDVÃOUBTFQBSBDJÓO TFQVFEFBMDBO[BS$PNPTFWFFOMBTUBCMBTZ TFDPOPDFOMBDBOUJEBESFBMEFFUBQBT MVHBS SFBMEFBMJNFOUBDJÓO EJÃNFUSPEFMBDPMVNOBZMPTUJQPTZUBNBÒPTEFWBQPSJ[BEPSZDPOEFOTBEPS &MJOHFOJFSPIBDFFMDÃMDVMPEFUBMMBEPEFFUBQBQPSFUBQB FMDÃMDVMPEFUBMMBEPEFMEJÃNFUSP ZQPS ÙMUJNPWFSJàDBRVFMBPQFSBDJÓOTFBQPTJCMF &O GPSNB FTQFDÎàDB  WFBNPT FM DBTP FO FM RVF MBT WBSJBCMFT DPOPDJEBT TPO '  [  R  Y%  5SFáVKP MÎRVJEPTBUVSBEP

Q 2DPM /SFBM /BMJN SFBM EJÃNFUSP -% MBFàDJFODJBHFOFSBM&PZFMEFSSBNF NPMBMDPOTUBOUF&TUBDPMVNOBTFJMVTUSBFOMBàHVSB"4FEFCFEFUFSNJOBSMBDPNQPTJDJÓOEF MBTDPMBT Y# $PNFO[BSFNPTEFEVDJFOEPMBTFDVBDJPOFTEFPQFSBDJÓOTVQFSJPSFJOGFSJPS4POMBTDPOPDJEBT GPSNBT n2

A A m &− m K K 9

Z n2 A m −  A − &m 7 K K

5BNQPDPDBNCJBMBFDVBDJÓOEFMBMÎOFBEFBMJNFOUBDJÓO n2

f f− & 

o;

m

&− f

$PNPFMSFáVKPFTMÎRVJEPTBUVSBEPZTFDPOPDFMBSFMBDJÓOEFSFáVKPFYUFSOP -% DBMDVMBSFNPT -7ZHSBàDBSFNPTMBMÎOFBEFPQFSBDJÓOTVQFSJPS àHVSB# 5BNCJÊOTFQVFEFHSBàDBSMBMÎOFB EFBMJNFOUBDJÓO-BJOUFSTFDDJÓOEFMBMÎOFBTVQFSJPSEFPQFSBDJÓODPOMBMÎOFBEFBMJNFOUBDJÓOEF àOFVOQVOUPFOMBMÎOFBEFPQFSBDJÓOJOGFSJPS%FTBGPSUVOBEBNFOUF OPTFQVFEFHSBàDBSMBMÎOFB mm EFPQFSBDJÓOJOGFSJPS QPSRVFOPTFDPOPDFO- 7 OJY# yQPSRVÊDPOCBMBODFTFYUFSOPTOPTFQVFEF DPOPDFSBMHVOBEFFTBTWBSJBCMFT 

Condensador total Líquido o reflujo Sat.

yCMV

Vaporizador parcial

(1er tanteo)

(3er tanteo) (2° tanteo) xCMV

'*(63" 130#-&."4%&4*.6-"$*¶/" $0-6./"&9*45&/5&  # %*"(3"."%&.$$"#&5)*&-&

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

1BSBTFHVJSEFCFNPTVTBSMPTUSFTFMFNFOUPTEFJOGPSNBDJÓORVFUPEBWÎBOPIFNPTVTBEP4PO /SFBM /BMJN SFBMZ&P1PEFNPTFTUJNBSMBDBOUJEBEEFFUBQBTEFFRVJMJCSJPDPO 

/&P/SFBM   /'FOUFSP



&MMVHBSEFMBBMJNFOUBDJÓO/'FOMBTFUBQBTEFFRVJMJCSJPEFCFFTUJNBSTFDPNPFOUFSP QFSPMBDBO UJEBEUPUBM/EFFUBQBTEFFRVJMJCSJPQPESÎBTFSVOOÙNFSPGSBDDJPOBSJP"IPSBQPEFNPTFTDBMPOBS FUBQBTEFFRVJMJCSJPTPCSFMBMÎOFBTVQFSJPSEFPQFSBDJÓO IBTUBMMFHBSBMBFUBQBEFBMJNFOUBDJÓO /'&OFTUFQVOUPEFCFNPTDBNCJBSBMBMÎOFBJOGFSJPSEFPQFSBDJÓO RVFOPTFDPOPDF4JTFVTBFM ÙMUJNPFMFNFOUPEFJOGPSNBDJÓO FMWBMPSEF/ EFCFNPTQSPQPOFSY# HSBàDBSMBMÎOFBJOGFSJPSEF PQFSBDJÓOZWFSJàDBSTJTFBMDBO[BMBTFQBSBDJÓODPO/ DPOUBDUPTEFFRVJMJCSJP FM JODMVZFBM WBQPSJ[BEPSQBSDJBM "TÎ FMQSPCMFNBEFTJNVMBDJÓOFTEFQSVFCBZFSSPSDVBOEPTFVTBVODÃMDVMP EFFUBQBQPSFUBQB&TUFQSPDFEJNJFOUPTFJMVTUSBFOMBàHVSB#/PUFRVFMBFUBQBSFBMEFBMJ NFOUBDJÓOQSPCBCMFNFOUFOPTFSÃMBÓQUJNB 6OBWF[EFUFSNJOBEBY# TFQVFEFOUFSNJOBSMPTCBMBODFTFYUFSOPTZDBMDVMBS# % 2DZ23 m m m "IPSB TFQVFEFODBMDVMBS- 7 - Z7 ZQSPDFEFSBVOBDPNQSPCBDJÓOFYBDUB EFRVF7Z7 TFBO NFOPSFTRVF7NÃY&TUPTFIBDFDBMDVMBOEPVOBWFMPDJEBEQFSNJTJCMFEFWBQPS&MDÃMDVMPFTQBSF DJEPBMEFMBEFUFSNJOBDJÓOEFVQFSNQBSBVOUBNCPSEFEFTUJMBDJÓOJOTUBOUÃOFBRVFTFNVFTUSBFOFM DBQÎUVMP5BNCJÊOTFQVFEFODPNQSPCBSMPTUBNBÒPTEFDPOEFOTBEPSZWBQPSJ[BEPS4JMBTUBTBT EFáVKPTPOEFNBTJBEPHSBOEFTPTJFMDPOEFOTBEPSZFMWBQPSJ[BEPSTPOEFNBTJBEPQFRVFÒPT MB DPMVNOBFYJTUFOUFOPGVODJPOBSÃTBUJTGBDUPSJBNFOUFQBSBPCUFOFSMBTFQBSBDJÓORVFTFRVJFSF4F EFCFEJTNJOVJSMBUBTBEFBMJNFOUBDJÓOPEJTNJOVJS-%&TPCWJPRVFFTUFÙMUJNPDBNCJPSFRVJFSF SFQFUJSUPEPFMDÃMDVMP $VBOEPTFFTQFDJàDBOPUSBTWBSJBCMFT FMDÃMDVMPEFFUBQBQPSFUBQBTJHVFTJFOEPQPSUBOUFPT &MQSPDFEJNJFOUPCÃTJDPFTFMNJTNP FTUPFT DBMDVMBSZHSBàDBSQSJNFSPUPEPMPRVFTFQVFEB QSP QPOFSMBWBSJBCMFOFDFTBSJB ZEFTQVÊTWFSJàDBSTJTFQVFEFPCUFOFSMBTFQBSBDJÓODPOMBDBOUJEBE FYJTUFOUFEFFUBQBT&OFTPTDÃMDVMPTTFTVFMFOFNQMFBSMBTFàDJFODJBTEFFUBQBEF.VSQISFF &TQSPCBCMFRVFMPTQSPCMFNBTEFTJNVMBDJÓOTFBONÃTGÃDJMFTVTBOEPFMNÊUPEPNBUSJDJBMRVF TFFYQMJDBFOFMDBQÎUVMPZTFBEBQUBDPOGBDJMJEBEBMVTPFODPNQVUBEPSB  6404/6&7041"3"$0-6./"47*&+"4

&OSFMBDJÓOFTUSFDIBDPOMBTJNVMBDJÓOFTUÃFMVTPEFTJTUFNBTFYJTUFOUFTPVTBEPTEFEFTUJMBDJÓODPO FMàOEFVTBSMPTFOOVFWBTTFQBSBDJPOFT-BOVFWBBQMJDBDJÓOQVFEFTFSEFFMJNJOBSDVFMMPTEFCPUFMMB  FTEFDJS BVNFOUBSMBDBQBDJEBEQBSBMBNJTNBTFQBSBDJÓO$POMBDSFDJFOUFSFOPWBDJÓOEFQSPEVDUPT  FMQSPCMFNBEFVTBSFRVJQPTWJFKPTQBSBOVFWBTTFQBSBDJPOFTTFFTUÃWPMWJFOEPNVDIPNÃTDPNÙO y1PS RVÊ TF EFCFSÎB VTBS VOB DPMVNOB FYJTUFOUF FO VO QSPCMFNB QBSB FM RVF OP TF EJTFÒÓ  1SJNFSP TVFMFTFSNFOPTDPTUPTPNPEJàDBSVOBDPMVNOBZBQBHBEB RVFDPNQSBSVOBOVFWB&O TFHVOEPMVHBS TVFMFTFSNÃTSÃQJEPIBDFSNPEJàDBDJPOFTNFOPSFTRVFFTQFSBSMBDPOTUSVDDJÓOEF VOBDPMVNOBOVFWB1PSÙMUJNP QBSBNVDIPTJOHFOJFSPT SFTPMWFSMPTQSPCMFNBTJNQMJDBEPTFOMB BEBQUBDJÓOEFVOBDPMVNOBFYJTUFOUFBVOBOVFWBTFQBSBDJÓOSFTVMUBVOEFTBGÎPJOUFSFTBOUF -PQSJNFSPQPSIBDFSDVBOEPTFEFCFOTFQBSBSTVTUBODJBTOVFWBTFTMJNQJBSFMTJTUFNBZSF WJTBSMPBEFUBMMFy&TUÃFOCVFOBTDPOEJDJPOFT 4JOPMPFTUÃ yCBTUBDPONBOUFOJNJFOUPNFOPSZ TVTUJUVDJÓOEFQBSUFTQBSBEFKBSMPFOCVFOBTDPOEJDJPOFT 4JIBZHSBOEFTQSPCMFNBTFTUSVDUVSBMFT  DPNPQPSFKFNQMPHSBODPSSPTJÓO QPESÎBTFSNFOPTDPTUPTPZNFOPTQSPCMFNÃUJDPBMBSHPQMB[P DPNQSBSFRVJQPOVFWP

www.FreeLibros.me

  6TPTOVFWPTQBSBDPMVNOBTWJFKBT



4FIBDFODÃMDVMPTEFTJNVMBDJÓOQBSBEFUFSNJOBSMPDFSDBRVFMMFHBMBDPMVNOBBMDVNQMJNJFOUP EFMBTOVFWBTFTQFDJàDBDJPOFTEFTFQBSBDJÓO$BTJOVODBVOBDPMVNOBFYJTUFOUFTFSÃMBSFTQVFTUB QFSGFDUBQBSBFMOVFWPQSPCMFNB4FQVFEFODMBTJàDBSMBTEJàDVMUBEFTDPNPQSPCMFNBTDPOMBTFQB SBDJÓOSFRVFSJEBZQSPCMFNBTDPOMBDBQBDJEBE y2VÊTFQVFEFIBDFSTJMBDPMVNOBFYJTUFOUFOPQVFEFPCUFOFSMBQVSF[BEFTFBEBFOFMQSPEVD UP &TOFDFTBSJPJOWFTUJHBSMPTJHVJFOUF TFNFODJPOBOBQSPYJNBEBNFOUFQPSDPTUPDSFDJFOUF   %FUFSNJOBSTJFTQPTJCMFNPEJàDBS SFMBKBS MBTFTQFDJàDBDJPOFTEFMQSPEVDUP&TNVDIPNÃTGÃDJM PCUFOFSVOBQVSF[BEFRVFVOBEF  7FSTJDPONBZPSSFMBDJÓOEFSFáVKPTFPCUFOESÃMBTFQBSBDJÓOEFTFBEB3FDVFSEFWFSJàDBSTJMB DBQBDJEBEEFWBQPSEFMBDPMVNOB FMWBQPSJ[BEPSZFMDPOEFOTBEPSTPOTVàDJFOUFNFOUFHSBOEFT 4JFTUPTFDVNQMF MPTDBNCJPTFO-%TÓMPBGFDUBSÃOBMPTDPTUPTEFPQFSBDJÓO  $BNCJBSMBUFNQFSBUVSBEFMBBMJNFOUBDJÓO&TUPIBSÃRVFMBFUBQBEFBMJNFOUBDJÓOOPTFBMB ÓQUJNB  y4FQPESÃOBMDBO[BSMBTFTQFDJàDBDJPOFTEFMQSPEVDUPDPOVOBOVFWBFUBQBFOMBVCJDBDJÓOÓQUJ NB QPSRVFMBFUBQBFYJTUFOUFOPTFBMBÓQUJNB

 $POTJEFSBSMBTVTUJUVDJÓOEFMPTQMBUPT PFNQBRVF QPSVOPTEFNBZPSFàDJFODJB PBEJTUBODJBT NFOPSFT PDPOFNQBRVFOVFWP &TUPFTSFMBUJWBNFOUFDPTUPTP QFSPNFOPTDPTUPTPRVFDPN QSBSVOTJTUFNBOVFWP  7FSJàDBSTJQVFEFODPOFDUBSEPTDPMVNOBTFYJTUFOUFT FOTFSJFQPSFKFNQMP QBSBBMDBO[BSMBTF QBSBDJÓOEFTFBEB-BBMJNFOUBDJÓOQVFEFJOUSPEVDJSTFFOFMQMBUPEFBMJNFOUBDJÓOEFBMHVOBEF MBTDPMVNOBTPFOUSFMBTEPTDPMVNOBT$PNPMPTSFRVJTJUPTEFDBSHBEFWBQPSTPOEJGFSFOUFTFO TFDDJPOFTEJTUJOUBTEFMBDPMVNOB WFBFMDBQÎUVMP

MBTDPMVNOBTOPOFDFTJUBOUFOFSFMNJTNP EJÃNFUSP y:TJMBDPMVNOBFTDBQB[EFPCUFOFSVOQSPEVDUPNVDIPNÃTQVSPRVFMBTFTQFDJàDBDJPOFT &TUF QSPCMFNBFTBHSBEBCMF&OHFOFSBM TFQVFEFEJTNJOVJSMBSFMBDJÓOEFSFáVKP DPOMPRVFEJTNJOVJSÃO MPTHBTUPTEFPQFSBDJÓO -PTQSPCMFNBTDPOMBDBQBDJEBEEFWBQPSTFEFTDSJCFODPONÃTEFUBMMFFOFMDBQÎUVMP&O GPSNBCSFWF TJFMEJÃNFUSPEFMBDPMVNOBOPFTTVàDJFOUFNFOUFHSBOEF TFQVFEFDPOTJEFSBS  5SBCBKBSB-%SFEVDJEB DPOMPRVFTFSFEVDF7&TUPQVFEFEJàDVMUBSFMDVNQMJNJFOUPDPOMBT FTQFDJàDBDJPOFTEFMQSPEVDUP  5SBCBKBSBNBZPSQSFTJÓO DPOMPRVFBVNFOUBMBEFOTJEBEEFMWBQPS1BSBFMMP MBDPMVNOBEFCF IBCFSTJEPEJTFÒBEBQBSBPQFSBSBQSFTJPOFTNBZPSFT$POTJEFSFRVFMBTTVTUBODJBTRVFTFFTUÊO TFQBSBOEPTFBOUÊSNJDBNFOUFFTUBCMFT  6TBSEPTDPMVNOBTFOQBSBMFMP  $BNCJBSMPTUVCPTCBKBOUFTQPSPUSPTNÃTHSBOEFT WFBFMDBQÎUVMP   4VTUJUVJSMPTQMBUPTPFMFNQBRVFQPSPUSPTDPONBZPSDBQBDJEBE/PFTQSPCBCMFBMDBO[BSHSBO EFTBVNFOUPTEFDBQBDJEBE 4JFMEJÃNFUSPEFMBDPMVNOBFTEFNBTJBEPHSBOEF MBTWFMPDJEBEFTEFMWBQPSTFSÃOCBKBT-PTQMBUPT USBCBKBSÃODPOFàDJFODJBTNFOPSFTRVFMBTEJTFÒBEBT ZFODBTPTHSBWFTQVFEFOOPUSBCBKBS QPSRVF FMMÎRVJEPQVFEFFTDVSSJSQPSMPTBHVKFSPT&OUSFMBTTPMVDJPOFTQPTJCMFTFTUÃO  #BKBSMBQSFTJÓOEFMBDPMVNOBQBSBCBKBSMBEFOTJEBEEFMWBQPS&TPBVNFOUBMBWFMPDJEBEMJOFBM EFMWBQPS  4JMBDPMVNOBUJFOFQMBUPTQFSGPSBEPT DVCSJSBMHVOPTEFMPTBHVKFSPT%FFTFNPEPBVNFOUBMB WFMPDJEBEEFMWBQPSFOMPTBHVKFSPTBCJFSUPT EJTNJOVZFOEPFMFTDVSSJNJFOUP

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

 "VNFOUBS-%QBSBBVNFOUBS7  3FDJSDVMBSBMHPEFEFTUJMBEPZGPOEPTQBSBBVNFOUBS'FGFDUJWBNFOUF $POGSFDVFODJB TFSFRVJFSFOTPMVDJPOFTDSFBUJWBTQBSBVTBSDPMVNOBTFYJTUFOUFTFOOVFWBTBQMJ DBDJPOFT&OUPODFT FTPTQSPCMFNBTQVFEFOTFSBMBWF[EFTBàBOUFTZEJWFSUJEPTUBNCJÊODPOGSF DVFODJBTPOMPTRVFTFBTJHOBOBJOHFOJFSPTSFDJÊOFHSFTBEPT  3&'-6+046#&/'3*"%0:7"10340#3&$"-&/5"%0"-1-"50*/'&3*03

y2VÊTVDFEFTJFMMÎRVJEPSFáVKBEPFTUÃTVCFOGSJBEP PFMWBQPSBMGPOEPFTUÃTPCSFDBMFOUBEP :B IFNPTFYBNJOBEPEPTDBTPTQBSFDJEPT EPOEFUFOÎBNPTVOBBMJNFOUBDJÓOEFMÎRVJEPTVCFOGSJBEPP EFWBQPSTPCSFDBMFOUBEP&OFTPTDBTPTWJNPTRVFVOMÎRVJEPTVCFOGSJBEPDPOEFOTBSÃBMHPEFWBQPS FOMBDPMVNOB NJFOUSBTRVFQBSBVOWBQPSTPCSFDBMFOUBEPDBCFFTQFSBSRVFFMWBQPSFWBQPSFBMHP EFMÎRVJEP$PNPFMSFáVKPZFMWBQPSBMGPOEPTPOFOUSBEBTBMBDPMVNOB EFCFNPTFTQFSBSFYBDUB NFOUFFMNJTNPDPNQPSUBNJFOUPTJFTBTDPSSJFOUFTFTUÃOTVCFOGSJBEBTPTPCSFDBMFOUBEBT &MSFáVKPTVCFOGSJBEPTFQSFTFOUBDPOGSFDVFODJBTJFMDPOEFOTBEPSFTUÃBOJWFMEFMTVFMP&O UPODFTTFSFRVJFSFVOBCPNCBQBSBSFHSFTBSMPBMBQBSUFTVQFSJPSEFMBDPMVNOB6OMÎRVJEPTBUV SBEPQSPWPDBSÃDBWJUBDJÓOZEFTUSVJSÃMBCPNCBFOUPODFT TFEFCFTVCFOGSJBSFMMÎRVJEPQBSBQPEFS CPNCFBSMP1BSBBOBMJ[BSFMFGFDUPEFMSFáVKPTVCFOGSJBEP WFBNPTMBQBSUFTVQFSJPSEFMBDPMVNOB RVFBQBSFDFFOMBàHVSB-BDPSSJFOUFEFMÎRVJEPGSÎP - EFCFDBMFOUBSTFIBTUBTVQVOUPEF FCVMMJDJÓO&TUBFOFSHÎBEFCFWFOJSEFMWBQPSDPOEFOTBOUFFOMBFUBQBTVQFSJPS DPSSJFOUFDEFMB àHVSB"TÎ MBTUBTBTEFáVKPFOMBQSJNFSBFUBQBTPOEJGFSFOUFTBMBTEFMSFTUPEFMBTFDDJÓOEF SFDUJàDBDJÓO&MEFSSBNFNPMBMDPOTUBOUFFTWÃMJEPFOFMSFTUPEFMBDPMVNOB-BSFMBDJÓOEFSFáVKP JOUFSOPFOMBDPMVNOBEFSFDUJàDBDJÓOFT-7-7 ZMBMÎOFBTVQFSJPSEFPQFSBDJÓOFT n2

A A m &− m K K 9

"IPSBCJFO -7OPTFQVFEFDBMDVMBSFOGPSNBEJSFDUBBQBSUJSEFMBSFMBDJÓOEFSFáVKPFYUFSOP  -% QPSRVF-Z7DBNCJBOFOMBFUBQBTVQFSJPS -PTCBMBODFTEFMBTDPSSJFOUFTEFWBQPSZMÎRVJEPTPO 

77 D





-- D



TReflujo

'*(63" &/70-7&/5&%&#"-"/$& 1"3"-±26*%046#&/'3*"%0

www.FreeLibros.me

  3FGMVKPTVCFOGSJBEPZWBQPSTPCSFDBMFOUBEPBMQMBUPJOGFSJPS



6OCBMBODFEFFOFSHÎBDPOMBFOWPMWFOUFEFCBMBODFEFMBàHVSBFT 

K&=& A&]& 2A%]gZ[aj_d K'=' 



$POEFSSBNFNPMBSDPOTUBOUFZ) )&OUPODFT MBFDVBDJÓO  TFUSBOTGPSNBFO 7−7 ) -I−-ISFáVKP "MVTBSMBTFDVBDJPOFT  Z 

FTUPTFUSBOTGPSNBFO D)  - D I−-ISFáVKP %FBRVÎTFEFTFBD MBDBOUJEBEDPOEFOTBEB ZRVFEB 

Xs

] a^f − ] gZ[aj_d = kVe − ] a^f

A% 2[X A % 

B

RVFUBNCJÊOTFQVFEFFTDSJCJSFOMBGPSNB 

8 EA I7E − IgZ[aj_d  A% 2[X A %  λ

C

FOFSHÎBQBSBDBMFOUBSSFáVKPBFCVMMJDJÓO

-GD- DBMPSMBUFOUFEFFWBQPSBDJÓO

D

Xs

FTEFDJS 

D 

EPOEFGDFTMBGSBDDJÓODPOEFOTBEBQPSNPMEFSFáVKP"IPSBQPESFNPTDBMDVMBSMBSFMBDJÓOEFSF áVKPJOUFSOP -7-71BSBIBDFSMP DPNFO[BNPTDPOMBSFMBDJÓORVFEFTFFNPTZVTBNPTMBT FDVBDJPOFT 

 

  Z   

A A A X A [ A & [X A % $ K& 2 & 2 % s % X % s  K K& [X A % & [X A % $ K& K&  X K'



-BSFMBDJÓO-7TFDBMDVMBDPOGBDJMJEBEDPO-% DPNPTJHVF 

A% A% $9 2  K& &  A% $9

"MJODMVJSFTUBFDVBDJÓOFOMBFDVBDJÓO  SFTVMUB 

A A & [X A% $ 9 2 & s  K & & [X A% $ 9 K'



/PUFRVFDVBOEPGD MBTEPTFDVBDJPOFT  Z  JOEJDBORVF-7-7"MBVNFOUBS MBGSBDDJÓODPOEFOTBEB TFTVCFOGSÎBNÃTFMSFáVKP

BVNFOUBMBSFMBDJÓOEFSFáVKPJOUFSOP -7 &OUPODFT FMSFTVMUBEPOFUPEFMSFáVKPTVCFOGSJBEPFRVJWBMFBBVNFOUBSMBSFMBDJÓOEFSFáVKP$PO

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

DÃMDVMPTOVNÊSJDPT DPNPFOMPTQSPCMFNBT"P% TFEFNVFTUSBRVFTFSFRVJFSFVOBHSBO DBOUJEBEEFTVCFOGSJBNFOUPQBSBPCTFSWBSVOFGFDUPJNQPSUBOUFFO-7$VBOEPFMSFáVKPFTUÃNVZ TPCSFFOGSJBEP TFEFCFBHSFHBSVOQMBUPBEJDJPOBMQBSBDBMFOUBSFMSFáVKP ,JSTUFS   6OBFOUSBEBEFWBQPSEJSFDUPTPCSFDBMFOUBEPPVOWBQPSTPCSFDBMFOUBEPEJSJHJEPBMQMBUPJO GFSJPSQSPDFEFOUFEFVOWBQPSJ[BEPSUPUBMDBVTBSÃOFWBQPSBDJÓOEFMÎRVJEPEFOUSPEFMBDPMVNOB m &TPFRVJWBMFBVOBVNFOUPOFUPFOMBSFMBDJÓOEFWBQPSBMGPOEP 7 # ZIBDFRVFMBQFOEJFOUFEF MBMÎOFBEFPQFSBDJÓOFOMBTFDDJÓOEFBHPUBNJFOUPUJFOEBB$PNPMBTFOUSBEBTEFWBQPSTPCSF DBMFOUBEPTFQVFEFOBOBMJ[BSEFMBNJTNBNBOFSBRVFFMSFáVKPMÎRVJEPTVCFOGSJBEP TFEFKBSÃDPNP QSPCMFNBEFUBSFB$

 $0.1"3"$*0/&4&/53&-04.­50%04"/"-±5*$04:-04(3¦'*$04

-PTNÊUPEPTEF-FXJTZEF.D$BCF5IJFMFTFCBTBOFOMBIJQÓUFTJTEFMEFSSBNFNPMBMDPOTUBOUF $VBOEPÊTUBFTWÃMJEB MPTCBMBODFTEFFOFSHÎBTFTBUJTGBDFOBVUPNÃUJDBNFOUFZFTPTJNQMJàDBNVDIP MPTDÃMDVMPTEFFUBQBQPSFUBQB-PTUSBCBKPTEFMWBQPSJ[BEPSZFMDPOEFOTBEPS 23Z2D TFEFUFS NJOBODPOMPTCBMBODFTFOUPSOPBUPEBMBDPMVNOB4JFMEFSSBNFNPMBMDPOTUBOUFOPFTWÃMJEP23 Z2DOPTFBMUFSBSÃOTJTFQVFEFVTBSMBNJTNBSFMBDJÓOEFSFáVKPFYUFSOP BVORVFRVJ[ÃFTPOPTFB QPTJCMF&MDÃMDVMPFYBDUP RVFTFQVFEFIBDFSDPOMPTNÊUPEPTFYQMJDBEPTFOFMDBQÎUVMP QVFEF JOEJDBSRVFTJFMEFSSBNFNPMBMDPOTUBOUFFTJOWÃMJEP TFSFRVJFSFVO-%NBZPSPNFOPS $VBOEPTFWBBVTBSVOBDBMDVMBEPSBQSPHSBNBCMFPVOBDPNQVUBEPSB FMNÊUPEPBOBMÎUJDPFT NÃTDPOWFOJFOUF FOFTQFDJBMTJTFVTBVOBIPKBEFDÃMDVMP #VSOTZ4VOH  &TPCWJPRVFTPO NÃTDÓNPEPTMPTDÃMDVMPTFODPNQVUBEPSBTJTFSFRVJFSFVOBHSBODBOUJEBEEFFUBQBT PTJTFSFRVJF SFVOBTPMVDJÓOQPSUBOUFPT PTJTFWBOBSFTPMWFSNVDIPTDBTPTQBSBJOWFTUJHBSFMFGFDUPEFNVDIBT WBSJBCMFT QPSFKFNQMP QBSBBOÃMJTJTFDPOÓNJDP 4JOFNCBSHP DPNPMBFYBDUJUVEFTUÃMJNJUBEBQPS MPTEBUPTEFFRVJMJCSJP MPTDÃMDVMPTFODPNQVUBEPSBOPTPONÃTFYBDUPTRVFFMNÊUPEPHSÃàDP 4JMPTDÃMDVMPTTFWBOBIBDFSBNBOP FMNÊUPEPHSÃàDPFTNÃTSÃQJEPRVFBMUFSOBSFOUSFMBT GPSNBTBOBMÎUJDBTEFMBFDVBDJÓOEFFRVJMJCSJPZMBTFDVBDJPOFTEFPQFSBDJÓO&OFMNÊUPEPEF.D $BCF5IJFMF MBTPMVDJÓOEFMBFDVBDJÓOEFFRVJMJCSJPDPOTJTUFFOUSB[BSVOBSFDUBIBTUBMBDVSWBEF FRVJMJCSJP&OMBTPMVDJÓOBOBMÎUJDB QSJNFSPEFCFNPTBKVTUBSMPTEBUPTEFFRVJMJCSJPBVOBFDVBDJÓO BOBMÎUJDB PEFTBSSPMMBSVOBSVUJOBEFJOUFSQPMBDJÓO"DPOUJOVBDJÓOEFCFNPTSFTPMWFSFTUBFDVBDJÓO  RVFQPESÃTFSOPMJOFBMDBEBWF[RVFIBHBNPTVODÃMDVMPEFFRVJMJCSJP$PNPMBFDVBDJÓOEFPQFSB DJÓOFTMJOFBM MBTPMVDJÓOBOBMÎUJDBFTTFODJMMB$POVOMÃQJ[CJFOBàMBEP QBQFMHSBOEFQBSBHSÃàDBT ZNVDIPDVJEBEP MBUÊDOJDBEF.D$BCF5IJFMFQVFEFTFSUBOFYBDUBDPNPMPTEBUPTEFFRVJMJCSJP EPTDJGSBTTJHOJàDBUJWBT  "MIBDFSMPTDÃMDVMPTEFFUBQBQPSFUBQB PEFBSSJCBBBCBKP TFEFTQFKBOWBMPSFTEFYEFMBSF MBDJÓOEFFRVJMJCSJPZWBMPSFTEFZEFMBFDVBDJÓOEFPQFSBDJÓO4JFTDBMPOBNPTMBTFUBQBTEFBCBKP IBDJBBSSJCB TFDBMDVMBOWBMPSFTEFYDPOMBFDVBDJÓOEFPQFSBDJÓOZWBMPSFTEFZDPOFMFRVJMJCSJP 7FSJàRVFFTUBBàSNBDJÓOFOVOEJBHSBNBEF.D$BCF5IJFMF$PNPTFEJKPBOUFT TFQVFEFEFUFSNJ OBSMBFUBQBÓQUJNBEFBMJNFOUBDJÓODPOMBQSVFCBEFMBFDVBDJÓO  ZFMQVOUPEFJOUFSTFDDJÓO FDVBDJÓO FTNÃTDÓNPEPEFVTBSRVFMBMÎOFBEFBMJNFOUBDJÓO&ODBTPTNÃTDPNQMJDBEPT TF QVFEFEFUFSNJOBSFMQVOUPEFJOUFSTFDDJÓOEFMBMÎOFBEFBMJNFOUBDJÓODPOMBFDVBDJÓOEFPQFSBDJÓO  SFTPMWJFOEPTJNVMUÃOFBNFOUFMBTFDVBDJPOFT&MNBZPSQSPCMFNBBMVTBSFMNÊUPEPEF-FXJTFOMB DPNQVUBEPSBFTPCUFOFSVOCVFOBKVTUFQBSBMPTEBUPTEFFRVJMJCSJP-PTEBUPTTFQVFEFOBKVTUBSB DVSWBTPTFQVFEFVTBSVOBSVUJOBEFJOUFSQPMBDJÓOFOUSFQVOUPTEFEBUPT#VSOTZ4VOH  JOEJ DBORVFMBJOUFSQPMBDJÓOMJOFBMFTFYBDUBTJTFJOHSFTBOTVàDJFOUFTQVOUPTEFEBUPTEFFRVJMJCSJP

www.FreeLibros.me

  $PNQBSBDJPOFTFOUSFMPTNÊUPEPTBOBMÎUJDPTZMPTHSÃGJDPT



Ingresar condiciones especificadas y datos de equilibrio

Ajustar el equilibrio a la forma x = f(y)

Hacer cálculos de balance externo (opcional)

– – Calcular L/V, L /V, ecuación (4-25) y xI ecuación (4-38). Hacer xO = xD, poner i = 1 Calcular yi de la ecuación de operación superior Calcular xi del equilibrio

Poner i = i + 1 ¿Es

Sí Poner i = i + 1 Calcular yi con la ecuación de operación inferior Calcular xi del equilibrio ¿Es

Sí Calcular cantidad fraccionaria de etapas Fin

'*(63" %*"(3"."%&'-6+0%&-$¶.16501"3"6/"$0-6./" %&%&45*-"$*¶/4*.1-&

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

6OBEFMBTGPSNBTNÃTBEFDVBEBTQBSBEFTDSJCJSMPTNÊUPEPTEFDÓNQVUPZEFDÃMDVMPFTDPOSF GFSFODJBBVOEJBHSBNBEFáVKP&MEJBHSBNBEFáVKPFTCBTUBOUFHFOFSBM NJFOUSBTRVFFMQSPHSBNB EFDÓNQVUPFTNVZFTQFDÎàDPQBSBFMMFOHVBKFRVFTFVTF*NBHJOFFMQSPCMFNBFTQFDÎàDPEFEJTFÒP RVFSFTPMWJNPTFOFMFKFNQMP4VQPOHBNPTRVFTFEFTFBOFTDBMPOBSMBTFUBQBTEFBSSJCBBBCBKP "IPSB FMQSPHSBNBEFDÓNQVUPPEFDBMDVMBEPSBQVFEFTFSFMRVFNVFTUSBMBàHVSB)BZPUSPT EJBHSBNBTEFáVKPQPTJCMFT4JFTDBMPOBNPTMBTFUBQBTEFBCBKPIBDJBBSSJCB DBMDVMBSFNPTZJDPOFM FRVJMJCSJPZYJDPOMBFDVBDJÓOEFPQFSBDJÓO/PUFRVFVOEJBHSBNBEF.D$BCF5IJFMFFTNVZÙUJM QBSBEBSTFHVJNJFOUPBMPTSB[POBNJFOUPTEFMEJBHSBNBEFáVKP*OUÊOUFMPDPOMBàHVSB $VBOEPMBDPMVNOBFTNÃTDPNQMFKB FMEJBHSBNBEFáVKPEFMBàHVSBTFQVFEFNPEJàDBS DPNPTJHVF  *ODMVJSFDVBDJPOFTQBSBMÎOFBTEFPQFSBDJÓOJOUFSNFEJBT  *ODMVJSQSVFCBTBEJDJPOBMFTQBSBBMJNFOUBDJPOFTÓQUJNBT  *ODMVJSDPSSJFOUFTMBUFSBMFT -PTNÊUPEPTEFOVFWPTJHVFO FUBQBQPSFUBQB MPTDÃMDVMPTEF.D$BCF5IJFMF &MEFTBSSPMMPEFMBTDPNQVUBEPSBTEJHJUBMFTIBIFDIPRVFMBUÊDOJDBEF.D$BCF5IJFMFTFBPC TPMFUBQBSBDÃMDVMPTEFEJTFÒPEFEFUBMMF"OUFTTFBDPTUVNCSBCBDVCSJSUPEBVOBQBSFEDPOQBQFM EFHSÃàDBTQBSBUSB[BSVOEJBHSBNB.D$BCF5IJFMFDVBOEPTFSFRVFSÎBVOBDBOUJEBENVZHSBOEF EFFUBQBT&TUFNÊUPEPUPEBWÎBFTÙUJMQBSBVOPPEPTDÃMDVMPT QFSPTVTQSJODJQBMFTBQMJDBDJPOFT TPODPNPIFSSBNJFOUBEFFOTFÒBO[BZNÊUPEPEFWJTVBMJ[BDJÓO­TUBFTMBSB[ÓOEFRVFFMQSPDFEJ NJFOUPHSÃàDPQSFTFOUFVOBJNBHFOWJTVBMNVZDMBSBEFMPTDÃMDVMPT NÃTGÃDJMEFFOUFOEFSRVFMBT JOUFSBDDJPOFTFOUSFMBTFDVBDJPOFT-BTHSÃàDBTUBNCJÊOTPOFYUSFNBEBNFOUFÙUJMFTDPNPNÊUPEP RVFBZVEBBEFUFSNJOBSFMFGFDUPEFMDBNCJPEFMBTWBSJBCMFT DPNPEJBHOÓTUJDPDVBOEPQBSFDFRVF FMQSPHSBNBEFDÓNQVUPGVODJPOBNBMZDPNPVOEJBHOÓTUJDPDVBOEPQBSFDFRVFMBDPMVNOBQBSFDF FTUBSNBM ,JTUFS  %FCJEPBFTUFJNQBDUPWJTVBM IFNPTVTBEPFYUFOTBNFOUFFMEJBHSBNBEF .D$BCF5IJFMFQBSBEJWFSTPTTJTUFNBTEFEFTUJMBDJÓO  3&46.&/m0#+&5*704

&OFTUFMBSHPDBQÎUVMPIFNPTEFTBSSPMMBEPMPTCBMBODFTEFFUBQBQPSFUBQBQBSBDPMVNOBTEFEFTUJ MBDJÓOZEFNPTUSBNPTDÓNPSFTPMWFSFTBTFDVBDJPOFTDVBOEPFTWÃMJEPFMEFSSBNFNPMBMDPOTUBOUF 6TUFEEFCFFTUBSDBQBDJUBEPBIPSBQBSBDPOTFHVJSMPTTJHVJFOUFTPCKFUJWPT  &TDSJCJSMPTCBMBODFTEFNBTBZFOFSHÎBZMBTFDVBDJPOFTEFFRVJMJCSJPQBSBDVBMRVJFSFUBQBFOVOB DPMVNOB  &YQMJDBSFMEFSSBNFNPMBMDPOTUBOUFZEFUFSNJOBSTJFTWÃMJEPTVQPOFSMPFOVOBTJUVBDJÓOEFUFS NJOBEB  %FEVDJSMBTFDVBDJPOFTEFPQFSBDJÓOQBSBTJTUFNBTDPOEFSSBNFNPMBMDPOTUBOUF  $BMDVMBSMBDBMJEBEEFMBBMJNFOUBDJÓOZEFUFSNJOBSTVFGFDUPFOMPTáVKPT5SB[BSMBHSÃàDBEFMB MÎOFBEFBMJNFOUBDJÓOFOVOEJBHSBNBZY  %FUFSNJOBSMBDBOUJEBEEFFUBQBTSFRVFSJEBTVTBOEPFMNÊUPEPEF-FXJTZFMEF.D$BCF5IJFMF  %FTBSSPMMBSZFYQMJDBSQFSàMFTEFDPNQPTJDJÓO UFNQFSBUVSBZáVKP  3FTPMWFSDVBMRVJFSQSPCMFNBEFEFTUJMBDJÓOCJOBSJBDVBOEPTFBWÃMJEPFMEFSSBNFNPMBMDPOTUBO UF2VFEBOJODMVJEPT B 7BQPSWJWP C 7BSJBTBMJNFOUBDJPOFT

www.FreeLibros.me

3FGFSFODJBT



D $POEFOTBEPSFTQBSDJBMFTZWBQPSJ[BEPSUPUBM E $PSSJFOUFTMBUFSBMFT F 7BQPSJ[BEPSFTZDPOEFOTBEPSFTJOUFSNFEJPT G $PMVNOBTEFBHPUBNJFOUPZEFFOSJRVFDJNJFOUP H 3FáFKPTNÎOJNPTZUPUBMFT I &àDJFODJBTHFOFSBMZEF.VSQISFF J 1SPCMFNBTEFTJNVMBDJÓO K $VBMRVJFSDPNCJOBDJÓOEFMBTBOUFSJPSFT  *ODMVJSMPTFGFDUPTEFSFáVKPTVCFOGSJBEPPWBQPSBMGPOEPTPCSFDBMFOUBEPFOMPTBOÃMJTJTEF.D $BCF5IJFMFZEF-FXJT  5SB[BSEJBHSBNBTEFáVKPQBSBDVBMRVJFSQSPCMFNBEFEFTUJMBDJÓOCJOBSJB

3&'&3&/$*"4

#SPXO ((Z"TPDJBEPT 6OJU0QFSBUJPOT 8JMFZ /FX:PSL  #VSOT ."Z+$4VOH i%FTJHOPG4FQBSBUJPO6OJUT6TJOH4QSFBETIFFUTu $IFN&OH&EVD   

 *OWJFSOP   'PVTU "4 -"8FO[FM $8$MVNQ -.BVTZ-#"OEFSTFO 1SJODJQMFTPG6OJU0QFSBUJPOT  ‰&E 8JMFZ /FX:PSL  )JNNFMCMBV  % .  #BTJD 1SJODJQMFT BOE $BMDVMBUJPOT JO $IFNJDBM &OHJOFFSJOH  ‰ &E  1SFOUJDF )BMM 6QQFS4BEEMF3JWFS /FX+FSTFZ  )PSXJU[  # "  i)BSEXBSF  4PGUXBSF BOE /PXIFSFu  $IFN &OHS 1SPHSFTT   

  4FQU   ,JTUFS ); %JTUJMMBUJPO0QFSBUJPO .D(SBX)JMM /FX:PSL  ,JTUFS ); i5SPVCMFTIPPU%JTUJMMBUJPO4JNVMBUJPOTu $IFN&OH1SPHSFTT  

 KVOJPEF   -FXJT 8, i5IF&GàDJFODZBOE%FTJHOPG3FDUJGZJOH$PMVNOTGPS#JOBSZ.JYUVSFTu *OE&OH $IFN      -VEXJH && "QQMJFE1SPDFTT%FTJHO ‰&E 7PM (VMG1VCMJTIJOH$P )PVTUPO  .D$BCF 8-Z&85IJFMF i(SBQIJDBM%FTJHOPG'SBDUJPOBUJOH$PMVNOTu *OE&OH$IFN      .VSQISFF &7 i(SBQIJDBM3FDUJGZJOHDPMVNO$BMDVMBUJPOTu *OE&OHS$IFN     1FSSZ  3 )  $ ) $IJMUPO Z 4 % ,JSLBUSJDL &ET

 $IFNJDBM &OHJOFFST )BOECPPL  ‰ &E  .D(SBX)JMM /FX:PSL  1PODIPO . 5FDI.PEFFSOF  Z   4BWBSJU 3 "SUTFU.FUJFST     Z   4PSFM &-B3FDUJGJDBUJPOEFM"MDPPM (BVUJFS7JMMBST 1BSJT 

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

5"3&"

" 1SPCMFNBTQBSBEJTDVTJÓO " &OMBàHVSBTJHVJFOUF yDVÃMFTDPSSJFOUFTFTUÃOSFQSFTFOUBEBTQPSFMQVOUP" y1PSFMQVOUP # y$ÓNPEFUFSNJOBSÎBMBUFNQFSBUVSBEFMBFUBQB y:MBUFNQFSBUVSBFOFMWBQPSJ[BEPS  4JMBDPNQPTJDJÓOEFMBBMJNFOUBDJÓOFTMBRVFTFJOEJDB yDÓNPQVFEFTFSMBDPNQPTJDJÓOEFM MÎRVJEPFOMBFUBQBÓQUJNBUBONVDIPNFOPSRVF[

yCMV

xCMV

" 1BSBFTUFEJBHSBNBEF.D$BCF5IJFMF DPOUFTUFMPTJHVJFOUF B  y$VÃMFTFMQMBUPSFBMEFBMJNFOUBDJÓO   y$VÃMFTMBGSBDDJÓONPMEFMDPNQPOFOUFNÃTWPMÃUJMFOMBBMJNFOUBDJÓO   y$VÃMFTMBDPNQPTJDJÓOEFMWBQPSFOFMQMBUPEFBMJNFOUBDJÓO   y$VÃMFTMBDPNQPTJDJÓOEFMMÎRVJEPFOFMQMBUPEFBMJNFOUBDJÓO C -BBMJNFOUBDJÓOyFTVOWBQPSTPCSFDBMFOUBEP VOWBQPSTBUVSBEP FTUÃFOEPTGBTFT FTVO MÎRVJEPTBUVSBEPPFTVOMÎRVJEPTVCFOGSJBEP D -BUFNQFSBUVSBFOMBFUBQB yFTNBZPS NFOPSPJHVBMBMBEFMBFUBQB

www.FreeLibros.me

5BSFB



yCMV

xCMV

" 4VQPOHBRVFFTWÃMJEPVOEFSSBNFEFNBTBDPOTUBOUF FOMVHBSEFEFSSBNFNPMBMDPOTUBOUF &YQMJRVFDÓNPTFIBDFOMPTQSPDFEJNJFOUPTEF.D$BCF5IJFMFFOFTUFDBTP " %JCVKBS MB HSÃàDB .D$BCF5IJFMF DPNP Z$.7 DPOUSB Y$.7 FT USBEJDJPOBM QFSP OP OFDFTBSJP 3FQJUBFMFKFNQMP QFSPUSBDFZXDPOUSBYX/PUFMBTEJGFSFODJBTFOFMEJBHSBNBy&TQFSB PCUFOFSMBNJTNBSFTQVFTUB " 1BSBEFTUJMBDJÓOBEFSSBNFNPMBMDPOTUBOUF NVFTUSFFTRVFNÃUJDBNFOUFMPTQFSàMFTEFáVKP HSBàRVF-KZ7KFOGVODJÓOEFMMVHBSEFMBFUBQB QBSB B "MJNFOUBDJÓOEFMÎRVJEPTVCFOGSJBEP C "MJNFOUBDJÓOEFEPTGBTFT D "MJNFOUBDJÓOEFWBQPSTPCSFDBMFOUBEP " 4J-7DPOSFáVKPTBUVSBEPFTJHVBMRVF-7DPOSFáVKPTVCFOGSJBEP  2D yFTNBZPS JHVBMP NFOPSRVFQBSBFMDBTPEFSFáVKPTBUVSBEP " y$VÃMFTFMFGFDUPEFMBQSFTJÓOEFMBDPMVNOBTPCSFMBEFTUJMBDJÓO 1BSBJOWFTUJHBSMP DPOTJ EFSFFMFGFDUPEFMBQSFTJÓOTPCSFMBTUFNQFSBUVSBTEFWBQPSJ[BEPSZFMDPOEFOTBEPS MBTUBTBT EFáVKPWPMVNÊUSJDPEFOUSPEFMBDPMVNOBZMBWPMBUJMJEBESFMBUJWB RVFTFQVFEFFTUJNBSQBSB IJESPDBSCVSPTDPOMPTEJBHSBNBTEF%F1SJFTUFS  " y2VÊTVDFEFTJUSBUBNPTEFFTDBMPOBSFUBQBTEFBSSJCBQBSBBCBKPZVOEBUPFT&.7 *OEJRVF DÓNPIBDFSFTUFDÃMDVMP " y$VÃOEPTFSÎBTFHVSPOPUFOFSFODVFOUBFMTVCFOGSJBNJFOUPEFMMÎRVJEPSFáVKBEPZDPOTJEFSBS RVFFMSFáVKPFTMÎRVJEPTBUVSBEP )BHBBMHVOPTDÃMDVMPTOVNÊSJDPTQBSBNFUBOPMZBHVB P QBSBFUBOPMZBHVB DPNPFKFNQMPT

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

" -BTFDVBDJPOFT  Z  TPOCBMBODFTEFNBTBQBSBGBTFTQBSUJDVMBSFTy$VÃOEPTFSÃO WÃMJEBTFTBTFDVBDJPOFT " y$VÃOEP QPESÎB VTUFE VTBS VO DPOEFOTBEPS JOUFSNFEJP FO VOB DPMVNOB  y$VÃMFT TPO TVT QPTJCMFTWFOUBKBT " y$VÃOEPTFVTBSÎBVOBDPMVNOBTÓMPEFFNQPCSFDJNJFOUPPTÓMPEFFOSJRVFDJNJFOUP " y2VÊVUJMJEBEUJFOFDBMDVMBSVOOÙNFSPGSBDDJPOBSJPEFFUBQBEFFRVJMJCSJP " &YQMJRVF DPOVOEJBHSBNBEF.D$BCF5IJFMF MBGPSNBFORVFMPTDBNCJPTEFUFNQFSBUVSB PEFR RVFFTFRVJWBMFOUF QVFEFOBZVEBSBRVFVOBDPMVNOBFYJTUFOUFBMDBODFMBTFTQFDJà DBDJPOFTEFTFBEBTQBSBFMQSPEVDUPOVFWP " 'PSNFVOBUBCMBEFFDVBDJPOFTDMBWFQBSBMBEFTUJMBDJÓOCJOBSJBTFHÙO.D$BCF5IJFMF&TUP FT FOVOBIPKBEFQBQFM IBHBVOSFTVNFOEFUPEPMPRVFOFDFTJUBTBCFSBDFSDBEFMBEFTUJMB DJÓOCJOBSJB&TQSPCBCMFRVFEFCBNPTUSBSJOGPSNBDJÓOBDFSDBEFMÎOFBTEFPQFSBDJÓO MÎOFBT EFBMJNFOUBDJÓO FàDJFODJBT SFáVKPTVCFOGSJBEP FUDÊUFSB # (FOFSBDJÓOEFBMUFSOBUJWBT # *OWFOUFVOQSPCMFNBRVFTFBNVZEJTUJOUPBMPTEFTDSJUPTFOFTUFDBQÎUVMP*OEJRVFDÓNPSF TPMWFSMP # 4FNFODJPOBSPOWBSJBTNBOFSBTEFBEBQUBSDPMVNOBTFYJTUFOUFTBVTPTOVFWPT(FOFSFOVF WPT NÊUPEPT RVF QFSNJUBO RVF TJTUFNBT FYJTUFOUFT TBUJTGBHBO FTQFDJàDBDJPOFT EF QSPEVDUP RVFOPTFQVFEBODVNQMJSTJOIBDFSNPEJàDBDJPOFT5FOHBFODVFOUBRVFVTUFEQVFEFQPTUVMBS VOBDPMVNOBFYJTUFOUFDPNQMFKBDPOVOWBQPSJ[BEPSJOUFSNFEJP $ %FEVDDJPOFT $ 1BSBFMFKFNQMP WBQPSEJSFDUP

EFNVFTUSFRVFMBPSEFOBEBBMPSJHFO Z FTUÃFOYY# $ %FEV[DBMBMÎOFBJOGFSJPSEFPQFSBDJÓOQBSBVOBDPMVNOBDPOVOWBQPSJ[BEPSUPUBM%FNVFT USFRVFFTUFSFTVMUBEPFTFMNJTNPRVFTFPCUJFOFDPOVOWBQPSJ[BEPSQBSDJBM $ %FEV[DBMBTFDVBDJPOFT  Z   $ 1BSBVOBDPSSJFOUFMBUFSBMBCBKPEFMBBMJNFOUBDJÓO B5SBDFVOFTRVFNBDPSSFTQPOEJFOUFBMBàHVSB" C%FEV[DBMBFDVBDJÓOEFPQFSBDJÓOZMBJOUFSTFDDJÓODPOZY D)BHBVOFTRVFNBEFMEJBHSBNBEF.D$BCF5IJFMF $ %FEV[DB MBT FDVBDJPOFT EF PQFSBDJÓO QBSB MBT EPT TFDDJPOFT JOUFSNFEJBT DVBOEP TF VTB VO WBQPSJ[BEPSJOUFSNFEJP WFBMBTàHVSBT"Z# %FNVFTUSFRVFMBMÎOFBEFPQFSBDJÓO DVZBQFOEJFOUFFT- 7 QBTBQPSFMQVOUPZYY# $ %FNVFTUSFRVFMBDBOUJEBEUPUBMEFFOGSJBNJFOUPOFDFTBSJPFTMBNJTNBQBSBVOBDPMVNOBDPO VODPOEFOTBEPSUPUBM 2D RVFQBSBVOBDPOVODPOEFOTBEPSUPUBMZVODPOEFOTBEPSJOUFSNF EJPUPUBM 2D 2* -BTDBOUJEBEFT' [ R Y% Y#Z23TPODPOTUBOUFTFOMPTEPTDBTPT5SBDFVO FTRVFNBEFVOTJTUFNBDPOVODPOEFOTBEPSJOUFSNFEJP%FEV[DBMBTFDVBDJPOFTEFPQFSBDJÓO QBSBMBTEPTMÎOFBTEFPQFSBDJÓOJOUFSNFEJBT ZUSBDFFMEJBHSBNBEF.D$BCF5IJFMF $ 1BSBMBDPMVNOBEFBHPUBNJFOUPEFMBTàHVSBT"Z$ EFNVFTUSFGPSNBMNFOUFRVFMB JOUFSTFDDJÓOEFMBMÎOFBJOGFSJPSEFPQFSBDJÓOZMBMÎOFBEFBMJNFOUBDJÓOFTUÃFOZ%&OPUSBT QBMBCSBT SFTVFMWBQBSBMBJOUFSTFDDJÓOEFFTUBTEPTMÎOFBT $ %FTDSJCBFMQSPDFEJNJFOUPEF.D$BCF5IJFMFQBSBMBDPMVNOBEFFOSJRVFDJNJFOUPEFMBàHV SB# $ 1BSBFMFKFNQMP EFNVFTUSFRVF B -BMÎOFBTVQFSJPSEFPQFSBDJÓOZMBMÎOFBZYTFDSV[BOFOZYY% C -BMÎOFBJOGFSJPSEFPQFSBDJÓOZMBMÎOFBZYTFDSV[BOFOZYY#

www.FreeLibros.me

5BSFB



$ %FEV[DBMBFDVBDJÓO   m mm $ 4FQVFEFFTQFDJàDBSMBSFMBDJÓOEFWBQPSBMGPOEP7 #%FEV[DBVOBFDVBDJÓOQBSB- 7 FO m GVODJÓOEF7 #QBSBVOWBQPSJ[BEPSQBSDJBM m m $ %FNVFTUSFDÓNPEFUFSNJOBS 7 # NÎO%FEV[DBVOBFDVBDJÓOQBSBDBMDVMBS 7 # NÎOBQBSUJS mm EF - 7 NÃY $ 5SBDFFMEJBHSBNBEF.D$BCF5IJFMFTJMBFàDJFODJBMÎRVJEBEF.VSQISFFFTDPOTUBOUF Z &.- mm $ %FEV[DBFDVBDJPOFTQBSBDBMDVMBS- 7 DVBOEPTFVTBWBQPSTPCSFDBMFOUBEPBMGPOEP mm $ %FEV[DBFDVBDJPOFTQBSBDBMDVMBS- 7 DVBOEPTFVTBWBQPSEJSFDUPTPCSFDBMFOUBEP $ *OEJRVFMBGPSNBFORVFTFSFMBDJPOBGDDPORFOMBTFDVBDJPOFT  Z   $ %FEV[DBMBFDVBDJÓOEFPQFSBDJÓOQBSBMBTFDDJÓOEFMBàHVSB%FNVFTUSFRVFMBTFDVB DJPOFTTPOJEÊOUJDBT TFBRVFMBFOWPMWFOUFEFCBMBODFEFNBTBTFEJCVKFFOUPSOPBMBQBSUF TVQFSJPSPBMBQBSUFJOGFSJPSEFMBDPMVNOB $ -BTFDVBDJPOFT  TPOVOBGPSNBEFQSPCBSMBVCJDBDJÓOÓQUJNBEFMBBMJNFOUBDJÓO6ONÊ UPEPBMUFSOBUJWPFTEFUFSNJOBSDVÃMMÎOFBEFPQFSBDJÓOFTNÃTCBKB FODBEBWBMPSEFFRVJMJCSJP B %FTBSSPMMFFTUBQSVFCBQBSBVOBDPMVNOBDPOEPTBMJNFOUBDJPOFT)ÃHBMPCBKBOEPPTV CJFOEPQPSMBDPMVNOB C y'VODJPOBFTUBQSVFCBFOVOBDPMVNOBDPODPSSJFOUFMBUFSBM  7FBMBàHVSB  % 1SPCMFNBT  -BTSFTQVFTUBTBMPTQSPCMFNBTDPOVOBTUFSJTDPTFFODVFOUSBOFOMBQBSUFGJOBMEFMMJCSP % 6OB DPMVNOB EF EFTUJMBDJÓO DPOUJOVB Z FO FTUBEP FTUBCMF UJFOF VO DPOEFOTBEPS UPUBM Z VO WBQPSJ[BEPSQBSDJBM ZTFQBSBNFUBOPMEFBHVBBVOBBUNÓTGFSB WFBMPTEBUPTFOMBUBCMB  -BUBTBEFBMJNFOUBDJÓOFTLHNPMI-BBMJNFOUBDJÓOFTNPMEFNFUBOPMZNPM EFBHVB4FEFTFBUFOFSVOQSPEVDUPEFTUJMBEPRVFUFOHBNPMEFNFUBOPM ZVOPTGPOEPT DPONPMEFNFUBOPM4VQPOHBEFSSBNFNPMBMDPOTUBOUF B 4JMBSFMBDJÓOEFSFáVKPFYUFSOP-% USBDFMBMÎOFBTVQFSJPSEFPQFSBDJÓO m C 4JMBSFMBDJÓOEFWBQPSBMGPOEP7 # USBDFMBMÎOFBJOGFSJPSEFPQFSBDJÓO D &TDBMPOFMBTFUBQBTQBSUJFOEPEFMGPOEP DPOFMWBQPSJ[BEPSQBSDJBM6TFMBFUBQBÓQUJNBEF BMJNFOUBDJÓO*OEJRVFMBFUBQBÓQUJNBEFBMJNFOUBDJÓOZMBDBOUJEBEUPUBMEFFUBQBT E 5SBDFMBMÎOFBEFBMJNFOUBDJÓO$BMDVMFTVQFOEJFOUF$BMDVMFRy2VÊUJQPEFBMJNFOUB DJÓOFT % 1SÃDUJDBQBSBFODPOUSBSMBMÎOFBEFBMJNFOUBDJÓO4FFTUÃBMJNFOUBOEPNFUBOPMZBHVBBVOB DPMVNOBEFEFTUJMBDJÓO BVOBBUNÓTGFSBEFQSFTJÓOUPUBM-PTEBUPTEFFRVJMJCSJPFTUÃOFOMB UBCMB-PTEBUPTEFDBQBDJEBEDBMPSÎàDBZDBMPSMBUFOUFTFFODVFOUSBOFOFMQSPCMFNB% 4VQPOHBEFSSBNFNPMBMDPOTUBOUF$BMDVMFZUSBDFMBHSÃàDBEFMBMÎOFBEFBMJNFOUBDJÓO QBSB DBEBVOBEFMBTQBSUFTTJHVJFOUFT B -BBMJNFOUBDJÓOUJFOFNPMEFNFUBOPMZFTVOWBQPSTBUVSBEP C -BBMJNFOUBDJÓOUJFOFNPMEFNFUBOPMZFTVOMÎRVJEPTBUVSBEP D -BBMJNFOUBDJÓOFTNPMEFNFUBOPMZFTVOBNF[DMBEFEPTGBTFT DPOEFWBQPS E -BBMJNFOUBDJÓOFTNPMEFNFUBOPMZFTVOBNF[DMBEFEPTGBTFTDPOEFMÎRVJEP F -BBMJNFOUBDJÓOUJFOFNPMEFNFUBOPMZFTVOMÎRVJEPTVCFOGSJBEP4FEFCFDPOEFOTBS NPMEFWBQPSQBSBDBMFOUBSNPMFTEFBMJNFOUBDJÓOIBTUBTVQVOUPEFFCVMMJDJÓO G -BBMJNFOUBDJÓOUJFOFNPMEFNFUBOPMZFTVOWBQPSTPCSFDBMFOUBEP4FEFCFFWBQP SBSNPMEFMÎRVJEPQBSBFOGSJBSNPMFTEFBMJNFOUBDJÓOIBTUBTVQVOUPEFFCVMMJDJÓO H -BBMJNFOUBDJÓOFTNPMEFNFUBOPMBž$ MÎRVJEPTVCFOGSJBEP  I -BBMJNFOUBDJÓOUJFOFNPMEFNFUBOPMBž$ WBQPSTPCSFDBMFOUBEP 

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

)BHBVODÃMDVMPBQSPYJNBEPQBSBMBTQBSUFTHZI FTUJNBEPFMDBMPSMBUFOUFDPO BMJN

[.

.

 [X

X

%  B 6OBBMJNFOUBDJÓOFTVOBNF[DMBEFFUBOPMZBHVB DPONPMEFFUBOPM-BBMJNFOUBDJÓO FTUÃBž$ZBVOBQSFTJÓOTVàDJFOUFNFOUFBMUBQBSBRVFTFBMÎRVJEB&OUSBBMBDPMVNOB QBTBOEPQPSVOBWÃMWVMB EPOEFTFFWBQPSBJOTUBOUÃOFBNFOUF-BQSFTJÓOFOMBDPMVNOBFT LHDN$BMDVMFMBQFOEJFOUFEFMBMÎOFBEFBMJNFOUBDJÓO C &TUBNPTTFQBSBOEPFUBOPMEFBHVBFOVOBDPMVNOBEFEFTUJMBDJÓOBMBQSFTJÓOEFLHDN -BBMJNFOUBDJÓODPOUJFOFEFFUBOPMFOQFTP ZTVáVKPFTLHI&TBBMJNFOUBDJÓO JOJDJBMNFOUFFTMÎRVJEBBž$ZTFFWBQPSBJOTUBOUÃOFBNFOUFDVBOEPMBQSFTJÓOCBKBBM FOUSBSBMBDPMVNOB$BMDVMFR-PTEBUPTFTUÃOFOFMQSPCMFNB%ZFOMBàHVSB1VF EFVTUFETVQPOFSRVFFTWÃMJEPFMEFSSBNFNPMBMDPOTUBOUF %  B 6OBBMJNFOUBDJÓOTPCSFDBMFOUBEBEFNPMEFMDPNQPOFOUFNÃTWPMÃUJMFTUÃBž$-B UBTBEFáVKPEFBMJNFOUBDJÓOFTLHNPMI&OFMQMBUPEFBMJNFOUBDJÓOMBUFNQFSBUVSB FTž$1BSBFTUBNF[DMBMBTDBQBDJEBEFTDBMPSÎàDBTQSPNFEJPTPO  $1-DBMHNPMž$   $17DBMHNPMž$  NJFOUSBTRVFFMDBMPSMBUFOUFEFFWBQPSBDJÓOFT DBMHNPM5SBDFMBMÎOFBEFFTUB BMJNFOUBDJÓO C -BBMJNFOUBDJÓOBVOBDPMVNOBFTEFEPTGBTFTDPONPMEFWBQPS$BMDVMFFMWBMPSEF RZMBQFOEJFOUFEFMBMÎOFBEFBMJNFOUBDJÓO D 4JMBBMJNFOUBDJÓOBVOBDPMVNOBFTWBQPSTPCSFDBMFOUBEPZTFFWBQPSBNPMEFMÎRVJEPFO FMQMBUPEFBMJNFOUBDJÓO QBSBFOGSJBSNPMFTEFMBBMJNFOUBDJÓOIBTUBMBUFNQFSBUVSBEF WBQPSTBUVSBEP yDVÃMFTFMWBMPSEFR y$VÃMFTMBQFOEJFOUFEFMBMÎOFBEFBMJNFOUBDJÓO %  6OBDPMVNOBEFEFTUJMBDJÓOUSBCBKBDPOSFáVKPTVCFOGSJBEP-BTDPSSJFOUFTEFWBQPSUJFOFO FOUBMQÎB)) #UVMCNPM NJFOUSBTRVFQBSBFMMÎRVJEPTBUVSBEP IM#UV MCNPM-BFOUBMQÎBEFMBDPSSJFOUFEFSFáVKPFTI#UVMCNPM-BSFMBDJÓOEFSFáVKP FYUFSOPTFBKVTUBB-%$BMDVMFMBSFMBDJÓOEFSFáVKPJOUFSOPFOMBDPMVNOB -7 % 6OBDPMVNOBEFEFTUJMBDJÓOBMBQSFTJÓOEFLHDNFTUÃTFQBSBOEPVOBBMJNFOUBDJÓORVF DPOUJFOFNPMEFFUBOPMZNPMEFBHVB-BBMJNFOUBDJÓOFOUSBDPNPNF[DMBEFEPT GBTFT Bž$$BMDVMFRZMBQFOEJFOUFEFMBMÎOFBEFBMJNFOUBDJÓO6TFEBUPTEFMBàHVSB 5FOHBDVJEBEPDPOMBTVOJEBEFT %  B 6OBDPMVNOBEFEFTUJMBDJÓODPODPOEFOTBEPSUPUBMFTUÃTFQBSBOEPBDFUPOBEFFUBOPM4F EFTFBRVFMBDPODFOUSBDJÓOEFBDFUPOBFOFMEFTUJMBEPDPOUFOHBY% GSBDDJÓONPM $PNPFTWÃMJEPFMEFSSBNFNPMBMDPOTUBOUF -7DPOTUBOUF4J-7FTJHVBMB DBMDVMF MBDPNQPTJDJÓOEFMMÎRVJEPRVFTBMFEFMBRVJOUBFUBQBBCBKPEFMDPOEFOTBEPSUPUBM C 6OBDPMVNOBEFEFTUJMBDJÓORVFTFQBSBBDFUPOBEFFUBOPMUJFOFVOWBQPSJ[BEPSQBSDJBMRVF GVODJPOBDPNPDPOUBDUPEFFRVJMJCSJP4JMBDPNQPTJDJÓOEFMBTDPMBTFTY# GSBDDJÓO m NPMBSEFBDFUPOB ZMBSFMBDJÓOEFWBQPSBMGPOEP7 # DBMDVMFMBDPNQPTJDJÓOEFM WBQPSRVFTBMFEFMBTFHVOEBFUBQBBSSJCBEFMWBQPSJ[BEPSQBSDJBM D -BDPMVNOBEFEFTUJMBDJÓOEFMBTQBSUFTBZCFTUÃTFQBSBOEPBDFUPOBEFFUBOPMZUJFOF m Y% Y# -7Z7 #4JMBDPNQPTJDJÓOEFMBBMJNFOUBDJÓOFT[ UPEBTMBTDPODFOUSBDJPOFTFTUÃOFOGSBDDJÓONPMEFMDPNQPOFOUFNÃTWPMÃUJM

DBMDVMFMB VCJDBDJÓOÓQUJNBEFMQMBUPEFBMJNFOUBDJÓO MBDBOUJEBEUPUBMEFFUBQBTZFMWBMPSEFROF DFTBSJPFOMBBMJNFOUBDJÓO-PTEBUPTEFFRVJMJCSJPQBSBBDFUPOBZFUBOPMBBUNTPOMPT TJHVJFOUFT 1FSSZFUBM  1ÃH 

www.FreeLibros.me

5BSFB



Y"

























Z"

























%  1BSBFMQSPCMFNB%D EFTFQBSBDJÓOEFBDFUPOBZFUBOPM EFUFSNJOF B y$VÃOUBTFUBQBTTFSFRVJFSFODPOSFáVKPUPUBM C y$VÃOUPWBMF -7 NÎO y$VÃOUPWBMF -% NÎO D -B-%VTBEByDVÃOUBTWFDFTFTNBZPSRVF -% NÎO E 4J&.7yDVÃOUBTFUBQBTSFBMFTTFSFRVJFSFOQBSB-7 % 6OBDPMVNOBEFEFTUJMBDJÓODPOVODPOEFOTBEPSUPUBMZVOWBQPSJ[BEPSQBSDJBMFTUÃTFQBSBO EPBDFUPOBZFUBOPM-BBMJNFOUBDJÓOFTLHNPMNJO-BBMJNFOUBDJÓODPOUJFOFEF BDFUPOBZFTMÎRVJEPTBUVSBEP&MEFTUJMBEPDPOUJFOFNPMEFBDFUPOBZTBMFDPNPMÎRVJEP TBUVSBEP-PTGPOEPTDPOUJFOFONPMEFBDFUPOB-BQSFTJÓOEFMBDPMVNOBFTBUN &MSFáVKPSFHSFTBDPNPMÎRVJEPTBUVSBEP-BDPMVNOBFTBEJBCÃUJDB-BSFMBDJÓOEFSFáVKP FYUFSOP FT -%   4VQPOHB EFSSBNF NPMBM DPOTUBOUF &TDBMPOF MBT FUBQBT EF BSSJCB B BCBKP-PTEBUPTEFFRVJMJCSJPFTUÃOFOFMQSPCMFNB% B %FUFSNJOFMBFUBQBÓQUJNBEFBMJNFOUBDJÓOZMBDBOUJEBEUPUBMEFFUBQBTEFFRVJMJCSJP FTDBMPOFMBTFUBQBTEFBSSJCBBCBKP  C $BMDVMF -% NÎO D $BMDVMF/NÎOBSFáVKPUPUBM %  6OBDPMVNOBEFEFTUJMBDJÓOTFQBSBGFOPMEFQDSFTPMBBUNEFQSFTJÓO4FEFTFBRVFMB DPNQPTJDJÓOEFMEFTUJMBEPUFOHBVOBGSBDDJÓONPMBSEFFOGFOPM4FVTBVOBSFMBDJÓOEF SFáVKPFYUFSOPEF-% ZFMSFáVKPSFHSFTBBMBDPMVNOBDPNPMÎRVJEPTBUVSBEP-PTEBUPT EFFRVJMJCSJPTFQVFEFOSFQSFTFOUBSQPSVOBWPMBUJMJEBESFMBUJWBDPOTUBOUF  GFOPMDSFTPM  1FSSZFUBM  1ÃH 4FQVFEFTVQPOFSEFSSBNFNPMBMDPOTUBOUF B y$VÃMFTMBDPNQPTJDJÓOEFMWBQPSRVFTBMFEFMBUFSDFSBFUBQBEFFRVJMJCSJPBCBKPEFM DPOEFOTBEPSUPUBM $POUFTUFFTUPDPOVODÃMDVMPBOBMÎUJDPEFFUBQBQPSFUBQB BMUFSOBOEP FOUSFMBFDVBDJÓOEFPQFSBDJÓOZMBFDVBDJÓOEFFRVJMJCSJP C y$VÃMFTMBDPNQPTJDJÓOEFMÎRVJEPRVFTBMFEFMBTFYUBFUBQBEFFRVJMJCSJPBCBKPEFMDPO EFOTBEPSUPUBM 3FTVFMWBHSÃàDBNFOUFFTUFQSPCMFNB VTBOEPVOEJBHSBNBEF.D$BCF 5IJFMFUSB[BEPQBSB GD % 4FFTUÃTFQBSBOEPVOBNF[DMBEFNFUBOPMZBHVBFOVOBDPMVNOBEFEFTUJMBDJÓO VTBOEPWB QPSEJSFDUP-BBMJNFOUBDJÓOFTLHNPMI$POUJFOFNPMEFNFUBOPMZFTUÃBž$ -BDPMVNOBFTUÃBBUN&MWBQPSEFBHVBFTQVSP Z. ZFTUÃTBUVSBEP&MQSPEVDUP EFTUJMBEPDPOUJFOFNPMEFNFUBOPM ZTBMFDPNPMÎRVJEPTBUVSBEP-BTDPMBTDPOUJFOFO NPMEFNFUBOPZ DPNPTBMFOEFVOBFUBQBEFFRVJMJCSJP EFCFOTFSMÎRVJEPTBUVSBEP -BDPMVNOBFTBEJBCÃUJDB5JFOFVODPOEFOTBEPSUPUBM-BSFMBDJÓOEFSFáVKPFYUFSOPFT-% 4VQPOHBRVFFTWÃMJEPFMEFSSBNFNPMBMDPOTUBOUF-PTEBUPTEFFRVJMJCSJPFTUÃOFOMB UBCMB-PTEBUPTQBSBBHVBZNFUBOPMFTUÃOFOFMQSPCMFNB% B &TUJNFR C $BMDVMFMBFUBQBÓQUJNBEFBMJNFOUBDJÓOZMBDBOUJEBEUPUBMEFFUBQBTEFFRVJMJCSJP FTDB MPOFMBTFUBQBTEFBSSJCBBBCBKP 6TFVOEJBHSBNBEF.D$BCF5IJFMF D $BMDVMF -% NÎO6TFVOEJBHSBNBEF.D$BCF5IJFMF % 3FTVFMWBFMQSPCMFNB%QBSBFMMVHBSÓQUJNPEFMBBMJNFOUBDJÓOZMBDBOUJEBEUPUBMEF FUBQBT4VQPOHBEFSSBNFNPMBMDPOTUBOUFZVTFVOEJBHSBNBEF.D$BCF5IJFMF"NQMÎFMBT QBSUFTEFMEJBHSBNBDFSDBEFMEFTUJMBEPZEFMBTDPMBT QBSBUFOFSNBZPSFYBDUJUVE

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

% 6OBBMJNFOUBDJÓOEFMÎRVJEPTBUVSBEPRVFDPOUJFOFNPMEFBDFUPOBZNPMEF FUBOPM MBBDFUPOBFTNÃTWPMÃUJM TFQSPDFTBFOVOBDPMVNOBEFBHPUBNJFOUP-BUBTBEFáVKP EFBMJNFOUBDJÓOFTLHNPMI-BPQFSBDJÓOFTBBUN&MTJTUFNBUJFOFVOWBQPSJ[BEPS QBSDJBM%FTFBNPTRVFMBTDPMBTQSPEVDJEBTDPOUFOHBONPMEFBDFUPOB-PTEBUPTEF FRVJMJCSJPFTUÃOFOFMQSPCMFNB% m B 4JMBSFMBDJÓOEFMWBQPSBMGPOEPFT7 # DBMDVMFFMWBMPSEFMBGSBDDJÓONPMZEFOFM EFTUJMBEP ZMBDBOUJEBEEFFUBQBTEFFRVJMJCSJPOFDFTBSJBTQBSBMBTFQBSBDJÓO m C y$VÃMFTMBSFMBDJÓONÎOJNBEFWBQPSBMGPOEP 7 # NÎO % 6OBDPMVNOBEFEFTUJMBDJÓOUJFOFDBMFOUBNJFOUPDPOWBQPSEJSFDUPZTFQBSBVOBBMJNFOUB DJÓORVFDPOUJFOFNPMEFNFUBOPMZNPMEFBHVB FOPQFSBDJÓODPOUJOVB-B DPMVNOBUJFOFFUBQBT VODPOEFOTBEPSUPUBMZMBBMJNFOUBDJÓOFTUÃFOMBFUBQB-BPQFSB DJÓOFTBBUN&MWBQPSFTEFBHVB QVSP ZFTUÃTBUVSBEP4FIBTVQVFTUPRVFFTWÃMJEPFM EFSSBNFNPMBMDPOTUBOUF"MBTBN IBDFEÎBT TFDFSSBSPOMPTáVKPTEFBMJNFOUBDJÓO ZEFTUJMBEP %'

QFSPOPTFIBNPEJàDBEPFMáVKPEFWBQPSZFMDPOEFOTBEPSUPUBM TJHVFDPOEFOTBOEPFMWBQPSQBSBGPSNBSMÎRVJEPTBUVSBEP"IPSBMBDPMVNOBIBMMFHBEPB VOBPQFSBDJÓOFOVOOVFWPFTUBEPFTUBCMF B y$VÃMFTMBGSBDDJÓOBDUVBMEFNFUBOPMFOMBTDPMBT C &OFMOVFWPFTUBEPFTUBCMF FTUJNFMBGSBDDJÓONPMBSEFNFUBOPMFOFMMÎRVJEPRVFTBMFEFM DPOEFOTBEPSUPUBM % 6OBDPMVNOBEFEFTUJMBDJÓOTFQBSBEJDMPSVSPEFFUJMFOPZUSJDMPSPFUBOP-PTEBUPTEFFRVJ MJCSJPTFSFQSFTFOUBOQPS -BDPMVNOBUJFOFVODPOEFOTBEPSUPUBMZVOWBQPSJ[BEPS QBSDJBM&MSFáVKPSFHSFTBDPNPMÎRVJEPTBUVSBEP-BBMJNFOUBDJÓODPOUJFOFNPMEF EJDMPSVSP EF FUJMFOP  RVF FT FM DPNQPOFOUF NÃT WPMÃUJM -B UBTB EF BMJNFOUBDJÓO FT  LHNPMI-BGSBDDJÓONPMEFEJDMPSVSPEFFUJMFOPFTFOFMEFTUJMBEPZFOMBTDPMBT 4VQPOHBEFSSBNFNPMBMDPOTUBOUF-BQSFTJÓOFTBUN B $BMDVMF#Z% m C 4JMBSFMBDJÓOEFSFáVKPFYUFSOP-% ZMBSFMBDJÓOEFWBQPSBMGPOEPFT7 #  DBMDVMFMBFUBQBÓQUJNBEFBMJNFOUBDJÓOZMBDBOUJEBEUPUBMEFFUBQBTEFFRVJMJCSJP D y$VÃMFTFMWBMPSEFR y2VÊUJQPEFBMJNFOUBDJÓOFT %  &TUJNFRQBSBFMQSPCMFNB%4VQPOHBRVFMBFUBQBEFBMJNFOUBDJÓOUJFOFMBNJTNBDPN QPTJDJÓORVFMBBMJNFOUBDJÓO % 6OBNF[DMBEFBDFUPOBZFUBOPM MBBDFUPOBFTNÃTWPMÃUJM TFBMJNFOUBBVOBDPMVNOBEF FOSJRVFDJNJFOUP RVFUJFOFVOBFYUSBDDJÓOMBUFSBMMÎRVJEB-BUBTBEFáVKPEFBMJNFOUBDJÓO FTHNPMNJO-BBMJNFOUBDJÓODPOUJFOFNPMEFBDFUPOBZFTVOWBQPSTBUVSBEP &MQSPEVDUPMBUFSBMMÎRVJEPTFTBDBEFMBTFHVOEBFUBQBBCBKPEFMDPOEFOTBEPSUPUBM BVOB UBTBEFáVKPUPUBMEF4HNPMNJOVUP&MSFáVKPTFSFHSFTBDPNPMÎRVJEPTBUVSBEP&M EFTUJMBEPEFCFUFOFSNPMEFBDFUPOB-BSFMBDJÓOEFSFáVKPFYUFSOPFT-%-B QSFTJÓOEFMBDPMVNOBFTBUN-BDPMVNOBFTBEJBCÃUJDB ZFTWÃMJEPFMEFSSBNFNPMBM DPOTUBOUF-PTEBUPTEFFRVJMJCSJPFTUÃOFOFMQSPCMFNB%/PUB/PTFSFRVJFSFIBDFS UBOUFPT  $BMDVMFMBGSBDDJÓONPMEFBDFUPOBFOMBDPSSJFOUFMBUFSBM Y4 MBGSBDDJÓONPMEFBDFUPOBFO MBTDPMBT Y# ZMBDBOUJEBEOFDFTBSJBEFFUBQBTEFFRVJMJCSJP % 6OBDPMVNOBEFEFTUJMBDJÓODPODPOEFOTBEPSUPUBMZWBQPSJ[BEPSQBSDJBMFTUÃTFQBSBOEPBDF UPOBZFUBOPM-BBMJNFOUBDJÓOFTLHNPMNJO$POUJFOFNPMEFBDFUPOBZFTMÎRVJEP TBUVSBEP &M EFTUJMBEP DPOUJFOF  NPM EF BDFUPOB  Z TBMF DPNP MÎRVJEP TBUVSBEP -PT GPOEPTDPOUJFOFONPMEFBDFUPOB-BQSFTJÓOFOMBDPMVNOBFTBUNÓTGFSB&MSFáVKP

www.FreeLibros.me

5BSFB

% 

% 

  %

 % 

% 



SFHSFTBDPNPMÎRVJEPTBUVSBEP-BDPMVNOBFTBEJBCÃUJDB-BSFMBDJÓOEFSFáVKPFYUFSOPFT -%4VQPOHBEFSSBNFNPMBMDPOTUBOUF&TDBMPOFMBTFUBQBTEFBSSJCBBBCBKP6TFFM EJBHSBNBEF.D$BCF5IJFMFDPOEBUPTEFFRVJMJCSJPWBQPSMÎRVJEPEFMQSPCMFNB% B $BMDVMFMBFUBQBÓQUJNBEFBMJNFOUBDJÓOZMBDBOUJEBEUPUBMEFFUBQBTEFFRVJMJCSJP FTDB MPOFMBTFUBQBTEFBSSJCBBBCBKP  C $BMDVMF -% NÎO D$BMDVMF/NÎOBSFáVKPUPUBM 6OBDPMVNOBEFEFTUJMBDJÓOTFQBSBBDFUPOBZFUBOPM%FIFDIPMBDPMVNOBUJFOFTFJTFUBQBT EFFRVJMJCSJPNÃTVOWBQPSJ[BEPSQBSDJBM-BBMJNFOUBDJÓOFTUÃFOEPTGBTFTZMBFUBQBEFBMJ NFOUBDJÓOFTMBDVBSUBEFTEFBSSJCB"IPSB MBDPMVNOBFTUÃGVODJPOBOEPFOVOFTUBEPFTUB CMF DPOMBWÃMWVMBEFTBMJEBEFDPMBTDFSSBEB4JOFNCBSHP TFTBDBVOQSPEVDUPEFTUJMBEPZFM WBQPSIJFSWFFOFMWBQPSJ[BEPS-%&MSFáVKPFTVOMÎRVJEPTBUVSBEP4FQVFEFTVQPOFS EFSSBNFNPMBMDPOTUBOUF-BQSFTJÓOQBUN-PTEBUPTEFFRVJMJCSJPFTUÃOFOFMQSPCMFNB %$BMDVMFMBDPNQPTJDJÓOEFMEFTUJMBEP4JTFTBDBVOBHPUBEFMÎRVJEPFOFMWBQPSJ[BEPSZ TFBOBMJ[B BOUJDJQFDVÃMTFSÃY# 6OBDPMVNOBEFEFTUJMBDJÓODPOVODPOEFOTBEPSUPUBMZVOWBQPSJ[BEPSQBSDJBMFTUÃTFQB SBOEPFUBOPMZBHVBBVOBQSFTJÓOEFLHDN-BBMJNFOUBDJÓOUJFOFVOBGSBDDJÓONPMBSEF EFFUBOPMZFTUÃBž$&MáVKPEFBMJNFOUBDJÓOFTLHNPMI&MQSPEVDUPEFTUJMBEP FT VO MÎRVJEP TBUVSBEP Z DPOUJFOF  NPM EF FUBOPM &M DPOEFOTBEPS FMJNJOB    LDBMI-PTGPOEPTDPOUJFOFOVOBGSBDDJÓONPMBSEFEFFUBOPM4VQPOHBRVFFTWÃMJEPFM EFSSBNFNPMBMDPOTUBOUF$BMDVMFMBDBOUJEBEEFFUBQBTZMBVCJDBDJÓOÓQUJNBEFMBFUBQBEF BMJNFOUBDJÓO %BUPT$1-&U0)DBMHNPMž$Bž$ 0USPTEBUPTTFFODVFOUSBOFOFMQSPCMFNB%&MEJBHSBNBEFFOUBMQÎBDPNQPTJDJÓOFTUÃ FOMBàHVSB ZFMEJBHSBNBZYFOMBàHVSB/PUB$VJEBEPDPOMBTVOJEBEFT 6OBDPMVNOBEFFOSJRVFDJNJFOUPUJFOFEPTBMJNFOUBDJPOFT-BBMJNFOUBDJÓO' FOUSBQPSFM GPOEP FTVOWBQPSTBUVSBEP&MáVKP'LHNPMIZDPOUJFOFNPMEFNFUBOPM ZNPMEFBHVB-BBMJNFOUBDJÓO' FOUSBNÃTBSSJCBFOMBDPMVNOB FTVOBNF[DMBEF EPTGBTFTRVFDPOUJFOFEFMÎRVJEP&MáVKPEF'FTLHNPMI-BBMJNFOUBDJÓO'FTUÃ GPSNBEBQPSNPMEFNFUBOPMZNPMEFBHVB4FEFTFBRVFFMEFTUJMBEPDPOUFOHB NPMEFNFUBOPM&MSFáVKPSFHSFTBFOGPSNBEFMÎRVJEPTBUVSBEP-BQSFTJÓOFTBUN -BSFMBDJÓO-%4VQPOHBEFSSBNFNPMBMDPOTUBOUF-PTEBUPTTFFODVFOUSBOFOMB UBCMB $BMDVMF% # Y# VCJDBDJÓOÓQUJNBEFMBBMJNFOUBDJÓOZDBOUJEBEEFFUBQBTEFFRVJMJCSJP OFDFTBSJBT $VBOEPFMBHVBFTFMDPNQPOFOUFNÃTWPMÃUJMOPTFOFDFTJUBVODPOEFOTBEPSTFQVFEFVTBS FOGSJBNJFOUPEJSFDUPDPOBHVBFOFCVMMJDJÓO&TPTFNPTUSÓFOFMQSPCMFNB%)JDJNPT RVFZ% Y# [ UPEBT GSBDDJPOFTNPMBSFTEFBHVB

MBBMJNFOUBDJÓOFTVO WBQPSTBUVSBEP DPOáVKPEFLHNPMI QBUN&TWÃMJEPFMEFSSBNFNPMBMDPOTUBOUF FMBHVBEFFOGSJBNJFOUPRVFFOUSBFTMÎRVJEPTBUVSBEP FTBHVBQVSBZ8%%FEV[DB ZUSBDFMBMÎOFBTVQFSJPSEFPQFSBDJÓO0CTFSWFRVFOPTFSFRVJFSFOCBMBODFTFYUFSOPT FTUP FT CBMBODFTFOUPSOPBUPEBMBDPMVNOB  $VBOEP FM BHVB FT FM DPNQPOFOUF NÃT WPMÃUJM  OP OFDFTJUBNPT VO DPOEFOTBEPS  Z QPEF NPTVTBSFOGSJBNJFOUPQPSDPOUBDUPEJSFDUP&TUPTFWJPFOFMQSPCMFNB%)JDJNPTRVF Z% Y#  UPEPFOGSBDDJÓONPMEFBHVB MBBMJNFOUBDJÓOFTVOMÎRVJEP TBUVSBEP DPOáVKPEFLHNPMI QBUN&TWÃMJEPFMEFSSBNFNPMBMDPOTUBOUFUPEB

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

FMBHVBEFFOGSJBNJFOUP 8 FTBHVBQVSB Z8%&MBHVBEFFOGSJBNJFOUPRVFMMFHB FTUÃBž'ZTVUFNQFSBUVSBEFFCVMMJDJÓOFTž' 8 EA!L 2&-#%

7ij ! aWbda °;

EB l 2&-!

λL 2&,!)+*#)

7ij aWbda

 %FUFSNJOFMBQFOEJFOUFEFMBMÎOFBTVQFSJPSEFPQFSBDJÓO -7  /PUB/PTFOFDFTJUBOEBUPTEFFRVJMJCSJP % 6OBDPMVNOBEFEFTUJMBDJÓOUJFOFDPOEFOTBEPSQBSDJBMZWBQPSJ[BEPSUPUBMQBSBTFQBSBSVOB BMJNFOUBDJÓOEFLNPMI&TUBBMJNFOUBDJÓODPOUJFOFNPMEFBDFUPOBZ NPMEFFUBOPM-BBMJNFOUBDJÓOFTVOBNF[DMBFOEPTGBTFT DPOEFMÎRVJEP4FEFTFB UFOFSVOWBQPSEFTUJMBEPRVFDPOUFOHBNPMEFBDFUPOBZVOBTDPMBTRVFDPOUFOHBO NPMEFBDFUPOB-BQSFTJÓOFOMBDPMVNOBFTVOBBUNÓTGFSB&MSFáVKPSFHSFTBDPNP MÎRVJEPTBUVSBEP Z-%4VQPOHBEFSSBNFNPMBMDPOTUBOUF-PTEBUPTEFFRVJMJCSJPTF FODVFOUSBOFOFMQSPCMFNB% B %FUFSNJOFMBVCJDBDJÓOÓQUJNBEFMBBMJNFOUBDJÓOZMBDBOUJEBEUPUBMEFFUBQBTEFFRVJMJ CSJP C y$VÃMFTMBSFMBDJÓONÎOJNBEFSFáVKPFYUFSOP D y$VÃMFTMBDBOUJEBENÎOJNBEFFUBQBT SFáVKPUPUBM

% &TUBNPTTFQBSBOEPNFUBOPMZBHVB$BMDVMFMBSFMBDJÓOEFSFáVKPJOUFSOPFOMBDPMVNOB  -7 QBSBMPTTJHVJFOUFTDBTPT-BDPMVNOBFTUÃBL1B-PTEBUPTFTUÃOFOMBUBCMB ZFOFMQSPCMFNB% B &MQSPEVDUPEFTUJMBEPDPOUJFOFNPMEFNFUBOPM-BSFMBDJÓOEFSFáVKPFYUFSOPFT -%&MSFáVKPTFFOGSÎBBž$ FTEFDJS FTUÃTVCFOGSJBEP  C 3FQJUB MB QBSUF B  QFSP FTUB WF[ DPO FM SFáVKP FO FTUBEP MÎRVJEP TBUVSBEP $PNQBSF FM SFTVMUBEPDPOFMEFMBQBSUFB % 6OB DPMVNOB EF EFTUJMBDJÓO DPO DPOEFOTBEPS QBSDJBM Z WBQPSJ[BEPS UPUBM TFQBSB BDFUPOB Z FUBOPM5JFOFEPTBMJNFOUBDJPOFT6OBDPOUJFOFNPMEFBDFUPOB FOUSBBHNPMNJO ZFTWBQPSTPCSFDBMFOUBEPUBMRVFBQSPYJNBEBNFOUFNPMEFMÎRVJEPTFFWBQPSBFOMBFUBQB EFBMJNFOUBDJÓOQPSDBEBNPMFTEFBMJNFOUBDJÓO-BPUSBBMJNFOUBDJÓOFTVOMÎRVJEPTB UVSBEPRVFFOUSBBHNPMNJOZDPOUJFOFNPMEFBDFUPOB4FEFTFBVOQSPEVDUP EFTUJMBEPRVFDPOUFOHBVOBGSBDDJÓONPMZ%EFBDFUPOB ZVOQSPEVDUPEFGPOEPTRVF DPOUFOHBVOBGSBDDJÓONPMY#EFBDFUPOB-BDPMVNOBUJFOFVODPOEFOTBEPSQBSDJBM ZVOWBQPSJ[BEPSUPUBM&MWBQPSBMGPOEPFOUSB SFHSFTB DPNPWBQPSTBUVSBEP-BDPMVNOB USBCBKBBMBQSFTJÓOEFBUN4VQPOHBEFSSBNFNPMBMDPOTUBOUFZVTFVOEJBHSBNBEF.D $BCF5IJFMF-PTEBUPTEFFRVJMJCSJPWBQPSMÎRVJEPTFFODVFOUSBOFOFMQSPCMFNB% m B %FUFSNJOF 7# NÎO USBDFMBTEPTMÎOFBTEFBMJNFOUBDJÓOQBSBEFDJEJSDVÃMVTBS  m m C 5SBCBKFB7#× 7# NÎO&MDPOEFOTBEPSQBSDJBMFTVODPOUBDUPEFFRVJMJCSJP4JDBEB VOBEFMBTFUBQBTUJFOFVOBFàDJFODJBMÎRVJEBEF.VSQISFFEF EFUFSNJOFMBVCJDBDJÓO ÓQUJNBEFDBEBBMJNFOUBDJÓO ZMBDBOUJEBEUPUBMEFFUBQBTSFBMFT FTNÃTGÃDJMDPNFO[BS EFTEFBSSJCBZCBKBS  %  6OBDPMVNOBEFEFTUJMBDJÓOTFQBSBNFUBOPMZBHVBBBUNEFQSFTJÓO-BDPMVNOBUJFOFVO DPOEFOTBEPSUPUBMZVOWBQPSJ[BEPSQBSDJBM"EFNÃT FOUSBVOBDPSSJFOUFEFWBQPSEFBHVB QVSPZTBUVSBEP FOMBTFHVOEBFUBQBBSSJCBEFMWBQPSJ[BEPSQBSDJBM WFBMBàHVSBEFMBQÃHJ OBTJHVJFOUF  -BBMJNFOUBDJÓOFTLHNPMEÎBZDPOUJFOFNPMEFNFUBOPMZNPMEFBHVB&T VOMÎRVJEPTVCFOGSJBEP1PSDBEBNPMFTEFBMJNFOUBDJÓOTFEFCFDPOEFOTBSNPMEFWBQPS EFOUSPEFMBDPMVNOB-BDPNQPTJDJÓOEFMEFTUJMBEPFTNPMEFNFUBOPM&MSFáVKPFTVO

www.FreeLibros.me

5BSFB



Vapor

MÎRVJEPTBUVSBEP Z-%-BDPNQPTJDJÓOEFMBTDPMBTFTNPMEFNFUBOPM-BSFMB m DJÓOEFWBQPSBMGPOEPFT7 #-PTEBUPTEFFRVJMJCSJPFTUÃOFOMBUBCMB4VQPOHB WÃMJEPFMEFSSBNFNPMBMDPOTUBOUF$BMDVMFFMMVHBSÓQUJNPEFBMJNFOUBDJÓOZMBDBOUJEBE UPUBMEFFUBQBTEFFRVJMJCSJPOFDFTBSJBT % 4F EFTFB QSPDFTBS  LHNPMI EF VOB BMJNFOUBDJÓO RVF DPOUJFOF  NPM EF NFUBOPM ZNPMEFBHVB FOVOBDPMVNOBEFBHPUBNJFOUP&TBDPMVNOBUJFOFVOWBQPSJ[BEPS QBSDJBMZEPTFUBQBTEFFRVJMJCSJP FOUPUBM DPOUBDUPTEFFRVJMJCSJP 4FEFTFBRVFMBGSBD DJÓONPMFOMPTGPOEPTTFBEFNFUBOPM-BBMJNFOUBDJÓOFTVOMÎRVJEPTBUVSBEP4VQPOHB EFSSBNFNPMBMDPOTUBOUF&MGVODJPOBNJFOUPFTBBUN-PTEBUPTEFFRVJMJCSJPTFWFOFOMB UBCMB$BMDVMFMBSFMBDJÓOSFRVFSJEBEFWBQPSBMGPOEP MBGSBDDJÓONPMZ%SFTVMUBOUFFOFM EFTUJMBEPZMBTUBTBTEFáVKPEF%Z# % 6OBDPMVNOBEFEFTUJMBDJÓOVTBSÃVCJDBDJÓOÓQUJNBEFFUBQBEFBMJNFOUBDJÓO4FSFUJSBVOB DPSSJFOUFMBUFSBMMÎRVJEBEFMBUFSDFSBFUBQBBCBKPEFMDPOEFOTBEPSUPUBM BVOBUBTBEF LHNPMI-BBMJNFOUBDJÓOFTVOBNF[DMBEFEPTGBTFTDPOEFWBQPS-BBMJNFOUBDJÓO BMBDPMVNOBFTLHNPMIZDPOUJFOFNPMEFBDFUPOBZNPMEFFUBOPM4F EFTFBRVFMBDPNQPTJDJÓOEFMEFTUJMBEPDPOUFOHBNPMEFFUBOPM4FUSBCBKBSÃDPOVOB SFMBDJÓOEFSFáVKPFYUFSOP-%&MQSPEVDUPEFGPOEPTTFSÃNPMEFBDFUPOB4F VTBSÃVOWBQPSJ[BEPSQBSDJBM$BMDVMFMBGSBDDJÓONPMYTEFFUBOPMFOMBDPSSJFOUFMBUFSBM MB VCJDBDJÓOÓQUJNBEFMBBMJNFOUBDJÓOZMBDBOUJEBEUPUBMEFDPOUBDUPTEFFRVJMJCSJPOFDFTBSJPT -PTEBUPTEFFRVJMJCSJPFTUÃOFOFMQSPCMFNB% %  6OBDPMVNOBEFEFTUJMBDJÓOTFQBSBNFUBOPMEFBHVB5JFOFVODPOEFOTBEPSUPUBMRVFTVCFO GSÎBFMSFáVKP EFUBMNPEPRVFTFDPOEFOTBNPMEFWBQPSFOMBDPMVNOBQPSDBEBNPMFTEF SFáVKP-%4FTBDBVOBDPSSJFOUFMÎRVJEBEFMBTFHVOEBFUBQBBCBKPEFMDPOEFOTBEPS &TUBDPSSJFOUFMBUFSBMTFFWBQPSBIBTUBMMFHBSBWBQPSTBUVSBEPZBDPOUJOVBDJÓOTFNF[DMB DPOMBBMJNFOUBDJÓOZTFJOZFDUBFOMBFUBQB-BTBMJEBMBUFSBMFT4LHNPMI-BBMJ NFOUBDJÓOFTVOWBQPSTBUVSBEPRVFDPOUJFOFNPMEFNFUBOPM-BUBTBEFBMJNFOUBDJÓO FT'LHNPMI4FVTBVOWBQPSJ[BEPSUPUBM RVFQSPEVDFVOWBQPSBMGPOEPTBUVSBEP

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

4FEFTFBRVFFMEFTUJMBEPDPOUFOHBNPMEFNFUBOPMZRVFMPTGPOEPTDPOUFOHBONPM EFNFUBOPM4VQPOHBEFSSBNFNPMBMDPOTUBOUF-PTEBUPTEFFRVJMJCSJPFTUÃOFOMBUBCMB $BMDVMF B -BDBOUJEBEUPUBMOFDFTBSJBEFFUBQBTEFFRVJMJCSJP m C &MWBMPSEF7 #

% 4F EFTFB TFQBSBS VOB BMJNFOUBDJÓO GPSNBEB QPS  NPM EF BDFUPOB Z  NPM EF FUBOPM-BUBTBEFBMJNFOUBDJÓOFTLHNPMI4FEFTFBRVFMBDPNQPTJDJÓOEFMEFTUJMB EPDPOUFOHBNPMEFBDFUPOB ZMPTGPOEPTDPOUFOHBONPMEFBDFUPOB$BMDVMF MBSFMBDJÓONÎOJNBEFSFáVKPFYUFSOP FMWBMPSNÎOJNPEFMBSFMBDJÓOEFWBQPSBMGPOEP MB DBOUJEBENÎOJNBBQSPYJNBEB DPOCBTFFOEFSSBNFNPMBMDPOTUBOUF RVFTFOFDFTJUBSÎBFO FMWBQPSJ[BEPSZMBDBOUJEBENÎOJNB DPOCBTFFOEFSSBNFNPMBMDPOTUBOUF OFDFTBSJBEF FOFSHÎBQBSBFMDPOEFOTBEPSUPUBM DPOMBTTJHVJFOUFTBMJNFOUBDJPOFT B 4JMBBMJNFOUBDJÓOFTVOWBQPSTBUVSBEP C 4JMBBMJNFOUBDJÓOFTVOBNF[DMBEFEPTGBTFTRVFDPOUJFOFEFMÎRVJEP D 4JMBBMJNFOUBDJÓOFTVOWBQPSTBUVSBEP E %FTEFFMQVOUPEFWJTUBEFMBFOFSHÎBSFRVFSJEBFOFMWBQPSJ[BEPS yFTNFKPSFWBQPSBS UPEBMBBMJNFOUBDJÓOPQBSUFEFFMMB y:FOFMDPOEFOTBEPS $PNPDBEBL+QBSBDBMFO UBNJFOUPDVFTUBEFBWFDFTNÃTRVFQBSBFOGSJBNJFOUP DVBOEPTFQVFEFVTBSBHVB EF FOGSJBNJFOUP

 yDVÃM BMJNFOUBDJÓO QSPCBCMFNFOUF SFTVMUF FO MPT NFOPSFT DPTUPT EF PQFSBDJÓO -PTEBUPTEFFRVJMJCSJPWBQPSMÎRVJEPTFFODVFOUSBOFOFMQSPCMFNB%$BMPSMBUFOUFEFM FUBOPMQVSP L+LHNPM$BMPSMBUFOUFEFMBBDFUPOBQVSB L+LHNPM F y$VÃOUPTDPOUBDUPTEFFRVJMJCSJPTFSFRVJFSFOQBSBRVFMBTFQBSBDJÓOTFIBHBBSFáVKP UPUBM 0CTFSWFRVFMBSFTQVFTUBFTJHVBMQBSBMBTQBSUFTB CZD

www.FreeLibros.me

5BSFB

% 

% 

%

%

% 



G 4JMBQBSUFCTFIBDFDPO-%Y -% NÎOJNB yDVÃOUBTFUBQBTSFBMFTDPOEFFà DJFODJB.VSQISFFEFWBQPSTFOFDFTJUBO y$VÃMFTFMMVHBSÓQUJNPQBSBMBBMJNFOUBDJÓO  3FDVFSEFRVFFMWBQPSJ[BEPSQBSDJBMGVODJPOBDPNPVODPOUBDUPEFFRVJMJCSJP 6OBDPMVNOBEFEFTUJMBDJÓOTFQBSBBDFUPOBEFFUBOPM-BBMJNFOUBDJÓOFTVOMÎRVJEPTBUVSBEP RVFDPOUJFOFNPMEFBDFUPOB-BUBTBEFBMJNFOUBDJÓOFTLHNPMI-BPQFSBDJÓOFTB BUNZTFQVFEFTVQPOFSEFSSBNFNPMBMDPOTUBOUF-BDPMVNOBUJFOFVODPOEFOTBEPSUPUBMZ VOWBQPSJ[BEPSQBSDJBM)BZPDIPFUBQBTEFFRVJMJCSJPFOMBDPMVNOBZMBBMJNFOUBDJÓOFTUÃFO MBUFSDFSBBSSJCBEFMWBQPSJ[BEPS)BDFUSFTNFTFT TFDFSSÓFMáVKPEFEFTUJMBEP %

QFSP m TFNBOUVWPGVODJPOBOEPMBDPMVNOB-BSFMBDJÓOEFWBQPSBMGPOEPTFBKVTUÓBMWBMPS7 # -PTEBUPTEFFRVJMJCSJPFTUÃOFOFMQSPCMFNB% B y$VÃOUPWBMFY# C 4JTFTBDBSBVOBHPUBEFEFTUJMBEP yDVÃMTFSÎBY% 6OBDPMVNOBEFEFTUJMBDJÓOFTUÃTFQBSBOEPNPMFTIEFVOBBMJNFOUBDJÓODPONPM EFFUBOPMZNPMEFBHVB-BBMJNFOUBDJÓOFOUSBDPNPMÎRVJEPTVCFOGSJBEPRVFDPOEFOTB NPMEFWBQPSFOFMQMBUPEFBMJNFOUBDJÓO QPSDBEBNPMFTEFBMJNFOUBDJÓO-BDPMVNOB UJFOFVODPOEFOTBEPSQBSDJBMZVTBDBMFOUBNJFOUPDPOWBQPSEJSFDUP4FEFTFBRVFFMQSP EVDUPEFTUJMBEPUFOHBZ%ZVOQSPEVDUPEFGPOEPTDPOY#&TWÃMJEPFMEFSSBNF NPMBMDPOTUBOUF&MWBQPSRVFTFVTBFTTBUVSBEP EFBHVBQVSB-PTEBUPTFTUÃOFOMBUBCMB ZFOMBàHVSB B $BMDVMFMBSFMBDJÓONÎOJNBEFSFáVKPFYUFSOP C 6TF-% -% NÎOZDBMDVMFFMOÙNFSPEFFUBQBTSFBMFTZFMMVHBSÓQUJNPEFMBBMJNFO UBDJÓOSFBM TJMBFàDJFODJBEFWBQPS.VSQISFFFTFOUPEBTMBTFUBQBT D $BMDVMFMBUBTBEFáVKPEFWBQPSEFBHVB 6OBDPMVNOBEFEFTUJMBDJÓOTFQBSBBDFUPOBZFUBOPMBBUNEFQSFTJÓO-BBMJNFOUBDJÓOFT VOMÎRVJEPTBUVSBEPDPONPMEFBDFUPOB-BBMJNFOUBDJÓOFTLHNPMI4FEFTFB RVFMBDPSSJFOUFEFDPMBTUFOHBNPMEFBDFUPOBZRVFFMEFTUJMBEPDPOUFOHBNPM EFBDFUPOB-BDPMVNOBUJFOFVOWBQPSJ[BEPSUPUBM&OMVHBSEFVODPOEFOTBEPSTFVTBFUBOPM QVSPFOFCVMMJDJÓO DPSSJFOUF$ DPNPMÎRVJEPSFáVKBEP MBDPMVNOBTFWFDPNPFOFMFTRVF NBEFMQSPCMFNB% -FEFTFBUSBCBKBSBVOBUBTBEFSFáVKPRVFTFBWFDFTMB -% NÎO $BMDVMFMB-%NÎOJNB USBDFMBMÎOFBEFBMJNFOUBDJÓOZMBTMÎOFBTEFPQFSBDJÓO FTDBMPOFMBT FUBQBTVTBOEPFMMVHBSÓQUJNPEFMQMBUPEFBMJNFOUBDJÓOZEFUFSNJOFMBDBOUJEBEUPUBMEFFUBQBT EFFRVJMJCSJPOFDFTBSJBT/PUFRVFFOFTUFQSPCMFNBTFSFRVJFSFEFEVDJSVOBMÎOFBTVQFSJPSEF PQFSBDJÓORVFFTEJGFSFOUFEFMBTMÎOFBTTVQFSJPSFTEFPQFSBDJÓODVBOEPIBZVODPOEFOTBEPS -BMÎOFBEFSFáVKPNÎOJNPUBNCJÊOTFWFSÃEJGFSFOUF5BNCJÊO -7OPFT -%   -%  6OBDPMVNOBEFBHPUBNJFOUPTFQBSB LHNPMEÎBEFVOBBMJNFOUBDJÓOMÎRVJEBTBUVSB EB-BDPMVNOBUJFOFVOWBQPSJ[BEPSQBSDJBM-BBMJNFOUBDJÓODPOUJFOFNPMEFBDFUPOB ZNPMEFFUBOPM4FEFTFBRVFMPTGPOEPTDPOUFOHBONPMEFBDFUPOB4FUSBCBKBB m m VOBUBTBEFWBQPSBMGPOEP7 # 7 # NÎO$BMDVMFZ% / %Z#-PTEBUPTEFFRVJMJCSJP FTUÃOFOFMQSPCMFNB% 6OBDPMVNOBEFEFTUJMBDJÓOUJFOFDPOEFOTBEPSUPUBMZWBQPSJ[BEPSQBSDJBM ZTFQBSBFUBOPM ZBHVB-BBMJNFOUBDJÓOFTVOMÎRVJEPTBUVSBEPGPSNBEPQPSNPMEFFUBOPM-BUBTBEF áVKPEFBMJNFOUBDJÓOFTNPMI&MSFáVKPFTVOMÎRVJEPTBUVSBEPZFTWÃMJEPFMEFSSBNF NPMBMDPOTUBOUF-BDPMVNOBUJFOFUSFTFUBQBTEFFRVJMJCSJP FTEFDJS DVBUSPDPOUBDUPTEF FRVJMJCSJP ZMBFUBQBEFBMJNFOUBDJÓOFTMBTFHVOEBBCBKPEFMDPOEFOTBEPS4FEFTFBRVFMB DPNQPTJDJÓOEFMPTGPOEPTDPOUFOHBNPMEFFUBOPM ZRVFFMEFTUJMBEPDPOUFOHB NPMEFFUBOPM$BMDVMFMBSFMBDJÓOSFRVFSJEBEFSFáVKPFYUFSOP-PTEBUPTTFFODVFOUSBOFO MBUBCMBZFOMBàHVSB

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

%  6OBDPMVNOBEFEFTUJMBDJÓODPOEPTFUBQBTEFFRVJMJCSJPZVOWBQPSJ[BEPSQBSDJBM USFTDPO UBDUPT EF FRVJMJCSJP  TFQBSB NFUBOPM Z BHVB -B DPMVNOB UJFOF VO DPOEFOTBEPS UPUBM -B BMJNFOUBDJÓODPOUJFOFNPMEFNFUBOPMZFOUSBBMBDPMVNOBFOMBTFHVOEBFUBQBBCBKP EFMDPOEFOTBEPS-BUBTBEFBMJNFOUBDJÓOFTNPMI-BBMJNFOUBDJÓOFTVOMÎRVJEPTVCFO GSJBEP1BSBDBMFOUBSNPMFTEFBMJNFOUBDJÓOBMBUFNQFSBUVSBEFMÎRVJEPTBUVSBEP TFEFCF DPOEFOTBSNPMEFWBQPSFOMBFUBQBEFBMJNFOUBDJÓO4FEFTFBRVFMBDPODFOUSBDJÓOEFMEFT UJMBEPTFBNPMEFNFUBOPM&MSFáVKPFTVOMÎRVJEPTBUVSBEPZTFQVFEFTVQPOFSEFSSBNF NPMBMDPOTUBOUF4FVTBVOBSFMBDJÓOEFSFáVKPFYUFSOP-%$BMDVMFMBDPODFOUSBDJÓO RVFSFTVMUBFOMPTGPOEPT Y#-PTEBUPTFTUÃOFOMBUBCMB & &

1SPCMFNBTNÃTDPNQMFKPT "DPOUJOVBDJÓOTFNVFTUSBVOTJTUFNBMMBNBEPCPNCFPEFTVDDJÓO4FTBDBMÎRVJEPTBUVSBEP EFMBFUBQBBSSJCBEFMWBQPSJ[BEPSQBSDJBMZTFSFHSFTBBMBFUBQB TVQPOHBRVFUPEBWÎBFT VOMÎRVJEPTBUVSBEP -BUBTBEFCPNCFPEFTVDDJÓOFT1LHNPMI-BDPMVNOBTFQB SBNFUBOPMZBHVBBL1B-BBMJNFOUBDJÓOFTLHNPMIZDPOUJFOFNPMEF NFUBOPMZNPMEFBHVB&TVOMÎRVJEPTBUVSBEP4FEFTFBRVFFMQSPEVDUPEFGPOEPT UFOHBNPMEFNFUBOPMZFMQSPEVDUPEFTUJMBEPEFCFUFOFSNPMEFNFUBOPM-B DPMVNOBUJFOFVODPOEFOTBEPSUPUBMZFMSFáVKPFTVOMÎRVJEPTBUVSBEP4VQPOHBEFSSBNF NPMBMDPOTUBOUF6TF -% Y -% NÎO-PTEBUPTFTUÃOFOMBUBCMB$BMDVMFYQ MB FUBQBÓQUJNBEFBMJNFOUBDJÓOZMBDBOUJEBEUPUBMEFFUBQBTEFFRVJMJCSJPOFDFTBSJBT D

F 3 2 1

P xp

Bomba

B

&  6OBDPMVNOBEFEFTUJMBDJÓOTFQBSBNFUBOPMZBHVB-BDPMVNOBUJFOFDBMFOUBNJFOUPDPO WBQPSEFBHVBEJSFDUP ZVOUPUBMEFDJODPFUBQBT4FTBDBVOBDPSSJFOUFMBUFSBMMÎRVJEBEFM TFHVOEPQMBUPBSSJCBEFMGPOEP-BBMJNFOUBDJÓODPOUJFOFNPMEFNFUBOPMZFTVOMÎRVJ EPTVCFOGSJBEP6OBNPMEFWBQPSTFDPOEFOTBZDBMJFOUBNPMFTEFBMJNFOUBDJÓOIBTUBMB UFNQFSBUVSBEFMÎRVJEPTBUVSBEPFOFMQMBUPEFBMJNFOUBDJÓO-BBMJNFOUBDJÓOFTNPMI 4FEFTFBRVFMBDPODFOUSBDJÓOEFMPTGPOEPTTFBNPMEFNFUBOPM&MWBQPSRVFTFVTB FTTBUVSBEPQVSPEFBHVB ZTVUBTBEFBMJNFOUBDJÓOTFBKVTUBQBSBRVF 'MVKPEFWBQPSEFBHVBáVKPEFGPOEPT -BTBMJEBMBUFSBMTBMFDPNPMÎRVJEPTBUVSBEP4VUBTBEFáVKPTFBKVTUBQBSBRVFFMáVKPEF DPSSJFOUFMBUFSBMáVKPEFGPOEPT

www.FreeLibros.me

5BSFB



4FVTBVODPOEFOTBEPSUPUBM&MSFáVKPFTVOMÎRVJEPTBUVSBEPZTFQVFEFTVQPOFSEFSSBNF NPMBMDPOTUBOUF$BMDVMFMBDPODFOUSBDJÓOEFMBDPSSJFOUFMBUFSBMZMBDPODFOUSBDJÓOEFMEFT UJMBEP-PTEBUPTFTUÃOFOMBUBCMB &  6OBDPMVNOBEFEFTUJMBDJÓODPODPOEFOTBEPSUPUBMZWBQPSJ[BEPSUPUBMTFQBSBFUBOPMZBHVB&M SFáVKPSFHSFTBDPNPMÎRVJEPTBUVSBEP ZFMWBQPSBMGPOEPFTWBQPSTBUVSBEP4FQVFEFTVQPOFS EFSSBNFNPMBMDPOTUBOUF4VQPOHBRVFMBTFUBQBTTPOEFFRVJMJCSJP-BQSFTJÓOFOMBDPMVNOB FTBUN"MBDPMVNOBFOUSBVOBBMJNFOUBDJÓOMÎRVJEBTBUVSBEBRVFDPOUJFOFNPMEFFUB OPM BLHNPMI-BBMJNFOUBDJÓOEFCFFOUSBSFOMBFUBQBÓQUJNBEFBMJNFOUBDJÓO4FEFTFB RVFMBDPNQPTJDJÓOEFMEFTUJMBEPTFBNPMEFFUBOPMZMBEFMPTGPOEPTNPMEFFUBOPM 4FTBDBVOBDPSSJFOUFMBUFSBMMÎRVJEBFOMBPDUBWBFUBQBEFTEFMBQBSUFTVQFSJPSEFMBDPMVNOB  DPOVOBUBTBEFáVKP4LHNPMI&TUFMÎRVJEPTFNBOEBBVOWBQPSJ[BEPSJOUFSNFEJPZ TFQBTBBWBQPSTBUVSBEP RVFSFHSFTBBMBDPMVNOBFOTVFUBQBÓQUJNBEFBMJNFOUBDJÓO-BSF MBDJÓOEFSFáVKPFYUFSOPFT-%$BMDVMFMBTVCJDBDJPOFTÓQUJNBTEFBMJNFOUBDJÓOZEFM WBQPSEFMWBQPSJ[BEPSJOUFSNFEJP$BMDVMFMBDBOUJEBEUPUBMEFFUBQBTEFFRVJMJCSJPSFRVFSJEBT -PTEBUPTFTUÃOFOMBUBCMB ' '

'

' 

1SPCMFNBTRVFSFRVJFSFOPUSPTSFDVSTPT 6OBDPMVNOBEFEFTUJMBDJÓORVFTFQBSBFUBOPMZBHVBVTBDBMFOUBNJFOUPDPOWBQPSEJSFDUP -BDPNQPTJDJÓOEFDPMBTFT GSBDDJÓONPMEFFUBOPM&MWBQPSRVFFOUSBFTEFBHVB QVSB ZFTUÃTPCSFDBMFOUBEPBž'-BQSFTJÓOFTBUN-BSFMBDJÓOEFMPTáVKPTEFDPMBT BWBQPSEFBHVBFT#4$BMDVMFMBQFOEJFOUFEFMBMÎOFBJOGFSJPSEFPQFSBDJÓO -BQVCMJDBDJÓOEF.D$BCFZ5IJFMF  FTVODMÃTJDPEFMBJOHFOJFSÎBRVÎNJDB-ÊBMP B &TDSJCBVOBDSÎUJDBEFMBQVCMJDBDJÓO FOVOBQÃHJOB C .D$BCFZ5IJFMF  JOEJDBSPOVONÊUPEPQBSBEFUFSNJOBSMÎOFBTEFBMJNFOUBDJÓOZ MÎOFBTJOUFSNFEJBTEFPQFSBDJÓOQBSBVOBDPMVNOBDPOEPTBMJNFOUBDJPOFT RVFBRVÎOP TFJMVTUSB(FOFSBMJDFFTUFNÊUPEPDVBOEPR  4JTFEFTFBOTFQBSBSQPSEFTUJMBDJÓOMPTTJHVJFOUFTTJTUFNBTyFTWÃMJEPFMEFSSBNFNPMBMDPOT UBOUF B .FUBOPMZBHVB C *TPQSPQBOPMZBHVB D ¦DJEPBDÊUJDPZBHVB E O#VUBOPZOQFOUBOP F #FODFOPZUPMVFOP

( (

1SPCMFNBTQBSBDPNQVUBEPSB B 3FTVFMWBFMFKFNQMPDPOVOTJNVMBEPSEFQSPDFTP C 3FQJUBFTUFQSPCMFNB QFSPDPO-% ( 1BSBFMQSPCMFNB% EFUFSNJOFMBFUBQBÓQUJNBEFBMJNFOUBDJÓOZMBDBOUJEBEUPUBMEF FUBQBT VTBOEPVOTJNVMBEPSEFQSPDFTP.FODJPOFFMQBRVFUFEFFRVJMJCSJPWBQPSMÎRVJEP RVFVTF$PNQBSFMBTSFTQVFTUBTDPOMBTEFMQSPCMFNB% (  &TDSJCBVOQSPHSBNBEFDBMDVMBEPSB EFIPKBEFDÃMDVMPPEFDPNQVUBEPSBQBSBEFUFSNJOBS MBDBOUJEBEEFFUBQBTEFFRVJMJCSJPZMBVCJDBDJÓOÓQUJNBEFMQMBUPEFBMJNFOUBDJÓOQBSBVOB EFTUJMBDJÓOCJOBSJBDPOVOBWPMBUJMJEBESFMBUJWBDPOTUBOUF&MTJTUFNBUFOESÃEFSSBNFNPMBM DPOTUBOUF SFáVKPEFMÎRVJEPTBUVSBEP DPOEFOTBEPSUPUBMZWBQPSJ[BEPSQBSDJBM-BTWBSJBCMFT TFSÃO' [' R Y# Y%  Z-%1SVFCFTVQSPHSBNBSFTPMWJFOEPMPTTJHVJFOUFTQSPCMFNBT B 4FQBSBDJÓOEFGFOPMZQDSFTPM' [' R Y# Y%  Z -%

www.FreeLibros.me



(

$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

C 4FQBSBDJÓOEFCFODFOPZUPMVFOP' [' R Y# Y%   Z-% D $PNPMBWPMBUJMJEBESFMBUJWBEFMCFODFOPZFMUPMVFOPQVFEFWBSJBSEFTEFQBSBFMCFO DFOPQVSPIBTUBQBSBFMUPMVFOPQVSP SFQJUBMBQBSUFCDPO  Z &TDSJCBTVQSPHSBNBQBSBRVFDBMDVMFMBDBOUJEBEGSBDDJPOBSJBEFFUBQBTOFDFTBSJBT$PN QSVFCFTVQSPHSBNBIBDJFOEPVODÃMDVMPBNBOP 6TFVOTJNVMBEPSEFQSPDFTPTZEFUFSNJOFMBFUBQBÓQUJNBEFBMJNFOUBDJÓOZMBDBOUJEBE UPUBMEFFUBQBTEFFRVJMJCSJPQBSBFMQSPCMFNB%.FODJPOFMBDPSSFMBDJÓOEFFRVJMJCSJP WBQPSMÎRVJEPRVFVTÓ"OPUFMPTWBMPSFTEF2DPOEFOTBEPSZ2WBQPSJ[BEPS FO#UVI  "1­/%*$&"-$"1±56-04*.6-"$*0/&4%&%&45*-"$*¶/#*/"3*" &/$0.165"%03"

"VORVFMPTQSPCMFNBTEFEFTUJMBDJÓOCJOBSJBTFQVFEFOSFTPMWFSFOVOEJBHSBNBEF.D$BCF5IJF MF  FO FM DBQÎUVMP  WFSFNPT RVF MPT QSPCMFNBT EF EFTUJMBDJÓO EF WBSJPT DPNQPOFOUFT TF QVFEFO SFTPMWFSDPONBZPSGBDJMJEBEDPNPTPMVDJPOFTNBUSJDJBMFTFOQSPCMFNBTEFTJNVMBDJÓO DPOPDJEBT MBDBOUJEBEEFFUBQBTZMBTVCJDBDJPOFTEFMBTBMJNFOUBDJPOFT &OFMDBTPUÎQJDP MPTTJNVMBEPSFT DPNFSDJBMFTSFTVFMWFOUPEPTMPTQSPCMFNBTEFFTUBNBOFSB&MMBCPSBUPSJPFOFTUFBQÊOEJDFFTVOB PQPSUVOJEBEQBSBVTBSVOTJNVMBEPSEFQSPDFTPTFOEFTUJMBDJÓOCJOBSJB"VORVFFOMBTJOTUSVDDJPOFT TFVTB"TQFO1MVT PUSPTTJNVMBEPSFTTFSÃOQBSFDJEPT 1SFSSFRVJTJUP&OFTUFBQÊOEJDFTFTVQPOFRVFVTUFEFTUÃGBNJMJBSJ[BEPZBDPOFMBQÊOEJDFEFMDBQÎ UVMP RVFDPOUFOÎBMPTMBCPSBUPSJPTZ ZRVFQVFEFVTUFEIBDFSMPTQBTPTCÃTJDPTDPOTVTJNVMB EPS4JMPSFRVJFSF VTFMBTJOTUSVDDJPOFTEFMMBCPSBUPSJPDPNPSFQBTPTPCSFFMVTPEF"TQFO1MVT 4JQFSTJTUFOMPTQSPCMFNBTBMUSBUBSEFDPSSFSMBTTJNVMBDJPOFT WFBFMBQÊOEJDF(VÎBEFMPDBMJ[BDJÓO EFGBMMBTFOTFQBSBDJPOFTDPO"TQFO1MVT EFTQVÊTEFMDBQÎUVMP -BCPSBUPSJP-PTPCKFUJWPTEFFTUFMBCPSBUPSJPTPO GBNJMJBSJ[BSTFDPOMBTTJNVMBDJPOFTEF"TQFO 1MVTVTBOEP3"%'3"$QBSBTJTUFNBTEFEFTUJMBDJÓOCJOBSJBZ FYQMPSBSFMFGFDUPEFDBNCJBSMBT WBSJBCMFTEFPQFSBDJÓOTPCSFMPTSFTVMUBEPTEFMBEFTUJMBDJÓOCJOBSJB/PIBZUSBCBKPDPODSFUPQBSB JOUSPEVDJS4JOFNCBSHP DPNQSFOEFSFTUFNBUFSJBMMFEFCFBZVEBSBDPNQSFOEFSFMMJCSPZMPBZV EBSÃBIBDFSMBCPSBUPSJPTQPTUFSJPSFT *OJDJFVOBTJNVMBDJÓOFOCMBODPDPOVOJEBEFTNÊUSJDBTHFOFSBMFT&OMBQBSUFJOGFSJPSEFMBQÃHJOB EF EJBHSBNB EF áVKP IBHB DMJD FO MB QFTUBÒB MMBNBEB iDPMVNOTu DPMVNOBT  6TF FM TJNVMBEPS 3"%'3"$EFDPMVNOBT5SBDFVOEJBHSBNBEFáVKPEFVOBDPMVNOBTFODJMMBDPOVOBBMJNFOUB DJÓO VOQSPEVDUPEFTUJMBEPMÎRVJEP áFDIBSPKB ZVOQSPEVDUPEFDPMBTMÎRVJEP ÊTUBTFSÃMBDPO àHVSBDJÓONÃTDPNÙOQBSBDPMVNOBTEFEFTUJMBDJÓO )BHBDMJDFOMBáFDIBRVFFTUÃBMBEFSFDIB EFMCPUÓO3"%'3"$QBSBWFSFTRVFNBTBMUFSOBUJWPTEFMBDPMVNOB/PVTFVOTJTUFNBEFMFDIP FNQBDBEP-BQBOUBMMBEFCFWFSTFQBSFDJEBBMB'JHVSB" 1BSBFTQFDJàDBSMBTDPMVNOBT "TQFO1MVTMMBNBBMDPOEFOTBEPSUPUBMiFUBQBu ZBMWBQPSJ[BEPSQBS DJBMiFUBQB/u&OUPODFT TJFTQFDJàDBVTUFE/ IBZFUBQBTEFFRVJMJCSJP ZWBQPSJ[BEPSQBSDJBM RVFFTVODPOUBDUPEFFRVJMJCSJP ZVODPOEFOTBEPSUPUBM RVFOPIBDFTFQBSBDJÓO -PTMVHBSFTEF BMJNFOUBDJÓOZDPSSJFOUFTMBUFSBMFTTFDVFOUBO QPSUBOUP IBDJBBCBKPEFTEFMBQBSUFTVQFSJPS FMDPO EFOTBEPSFT &TUBOPUBDJÓODPODVFSEBDPOMBàHVSB &OMBTDPSSJEBTRVFTJHVFO TJTFUFSNJOB3"%'3"$DPOFSSPSFT USBUFEFDPSSFSVOBTFQBSBDJÓO QBSFDJEBRVFDPOWFSKBZEFTQVÊTDPSSBEFOVFWPMBTJNVMBDJÓORVFEFTFF&O"TQFO1MVTTFVTBMB

www.FreeLibros.me

"QÊOEJDFBMDBQÎUVMP 4JNVMBDJPOFTEFEFTUJMBDJÓOCJOBSJBFODPNQVUBEPSB



'*(63"" 1"/5"--"%&"41&/1-641"3"%&45*-"$*¶/4*.1-& DPSSJEBDPOWFSHFOUFBOUFSJPSQBSBJOJDJBMJ[BSMBOVFWBDPSSJEB6OBDPMVNOBRVFDPOWFSKBVOBWF[ QVFEFOPDPOWFSHFSDVBOEPMBTDPOEJDJPOFTTFBOEJGFSFOUFT4JMBDPSSJEBTFBDFSDBBMBDPOWFSHFO DJB MPTWBMPSFTQPESÃOTFSCBTUBOUFSB[POBCMFT6TUFEQVFEFUSBUBSEFDBNCJBSMBTDPOEJDJPOFTZ IBDFSVOBOVFWBDPSSJEB-BTDPSSJEBTDPOFSSPSFTDSÎUJDPTOPEFCFOUFOFSTFFODVFOUB OPFYBNJOF MPTSFTVMUBEPT QPSRVFOPTJHOJàDBOOBEB 4J"TQFO1MVTUJFOFVOFSSPSDSÎUJDP DPNPQPSFKFNQMP RVFMBDPMVNOBTFTFRVF WVÊMWBMPBJOJDJBMJ[BSBOUFTEFIBDFSPUSBDPSSJEB1BSBFTUFMBCPSBUPSJPTF FTDPHJFSPOTJTUFNBTUBMFTRVFEFCFODPOWFSHFS $VBOEPIBHBMBTDPSSJEBT BOPUF-% UBTBEFBMJNFOUBDJÓO DPOEJDJÓOEFMBBMJNFOUBDJÓO GSBDDJÓO EFWBQPSPUFNQFSBUVSB

FMMVHBSEFMBFUBQBEFBMJNFOUBDJÓOZMBDBOUJEBEEFFUBQBT EFCFVTUFE JOEJDBSFTPTWBMPSFT

ZMPTSFTVMUBEPTTFSÃODPNQPTJDJPOFTEFEFTUJMBEPZDPMBT UFNQFSBUVSBTEF EFTUJMBEPZDPMBT áVKPTNÃYJNPTZNÎOJNPTEFMÎRVJEPZWBQPSZMBTDBSHBTUÊSNJDBTFOFMDPOEFOTB EPSZFMWBQPSJ[BEPS/PJNQSJNBUPEPFMJOGPSNFEF"TQFO1MVT  %FTUJMBDJÓOCJOBSJB4FQBSB EJDMPSPFUBOPEF  USJDMPSPFUBOP-BBMJNFOUBDJÓOFTLH NPMIDPOEFEJDMPSPFUBOP-BPQFSBDJÓOFTBBUN-BDPMVNOBUJFOFVODPOEFOTBEPS UPUBMZVOWBQPSJ[BEPSUJQPNBSNJUB&MQBRVFUFEF1FOH3PCJOTPOQBSBFRVJMJCSJPWBQPSMÎRVJEP FT SB[POBCMF "TFHÙSFTF EF TFMFDDJPOBS MPT DPNQPOFOUFT DPSSFDUPT FO FM NFOÙ EF "TQFO1MVT /PUFRVFOPTFEFCFVTBS  USJDMPSPFUBOP QPSRVFTVTQSPQJFEBEFTTPONVZEJGFSFOUFT B 5SBDFFMEJBHSBNBYZEF"TQFO1MVTZDPNQÃSFMPDPOVOBHSÃàDBBQSPYJNBEBDPOWPMBUJMJEBE SFMBUJWBDPOTUBOUFEF FTTJNQMJàDBSEFNBTJBEP QFSPTFBQSPYJNB /PUB*OHSFTFQSJNFSP MPTEBUPTQBSBFMQBTPC

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOFODPMVNOBCBMBODFTJOUFSOPT FUBQBQPSFUBQB

C -BBMJNFOUBDJÓOFTWBQPS QPOHBMBGSBDDJÓOEFWBQPSFOMBBMJNFOUBDJÓOFO 4F RVJFSFVOQSPEVDUPEFTUJMBEPRVFUFOHBNPMEFEJDMPSPFUBOPZVOBTDPMBTRVFUFOHBO NPMEFEJDMPSPFUBOP$PNP"TQFO1MVTFTVOQSPHSBNBTJNVMBEPS OPMFQFSNJUJSÃFTQFDJàDBS FOGPSNBEJSFDUBFTUBTDPODFOUSBDJPOFT&OUPODFTOFDFTJUBSÃIBDFSMBQSVFCBDPOEJTUJOUBTDP MVNOBT DBNCJBOEPDBOUJEBEEFFUBQBTZMVHBSEFBMJNFOUBDJÓO IBTUBFODPOUSBSVOBRVFIBHB FMUSBCBKP6TF-%1POHBFMáVKPEFEFTUJMBEPRVFTBUJTGBHBFMCBMBODFEFNBTB DBMDVMF %Z#DPOCBMBODFTEFNBTB)BHBFTUFDÃMDVMPFYBDUBNFOUF QPSRVFTJOP OVODBUFOESÃMBTP MVDJÓORVFRVJFSB &TDPKBVOBDBOUJEBESB[POBCMFEFFUBQBTZVOBFUBQBSB[POBCMFEFBMJNFO UBDJÓO QSVFCFDPO/ZVOBBMJNFOUBDJÓOFO TPCSFMBFUBQB QBSBDPNFO[BS4JNVMF MBDPMVNOBZWFSJàRVFMBTGSBDDJPOFTNPMBSFTFOFMEFTUJMBEPZMBTDPMBT&TPTFIBDFDPONÃT GBDJMJEBEDPOMPTQFSàMFTEFDPNQPTJDJÓOEFMÎRVJEPQBSBMBFUBQBZ/%FCFOTFSNÃTQVSPT RVFMPRVFVTUFEOFDFTJUB5BNCJÊOWFSJàRVFMPTWBMPSFTEF,ZDBMDVMFMBWPMBUJMJEBESFMBUJWB FOMBFUBQBTVQFSJPS MBEFBMJNFOUBDJÓOZMBJOGFSJPSEFMBDPMVNOB QBSBWFSDVÃOUPWBSÎB D $POUJOÙF MB QBSUF C %FUFSNJOF MB FUBQB ÓQUJNB EF BMJNFOUBDJÓO IBDJFOEP MB QSVFCB DPO EJGFSFOUFTFUBQBT QBSBWFSDVÃMQSPEVDFMBNÃYJNBTFQBSBDJÓO NÃYJNBGSBDDJÓONPMEFEJDMP SPFUBOPFOFMEFTUJMBEP ZNÎOJNBFOMBTDPMBT "DPOUJOVBDJÓOEJTNJOVZBMBDBOUJEBEUPUBMEF FUBQBT VTBOEPDBEBWF[MBFUBQBÓQUJNBEFBMJNFOUBDJÓO IBTUBRVFUFOHBMBDBOUJEBENÎOJNB UPUBMEFFUBQBTRVFUPEBWÎBTBUJTGBHBMBTFTQFDJàDBDJPOFTQBSBEFTUJMBEPZMPTGPOEPT/PUFRVF DPNP MB SFMBDJÓO EF FUBQB ÓQUJNB EF BMJNFOUBDJÓO  DBOUJEBE UPUBM  FT BQSPYJNBEBNFOUF DPOTUBOUF FTQSPCBCMFRVFTÓMPEFCBSFWJTBSUSFTPDVBUSPFUBQBTQPSDBEBOVFWPWBMPSEFMB DBOUJEBEUPUBMEFFUBQBT4JTVHSVQPUSBCBKBFODPOKVOUPZEJTUJOUBTQFSTPOBTWFSJàDBOEJTUJO UBTDPSSJEBT FTPOPEFCFUBSEBSNVDIP E "VNFOUFMBQSFTJÓOBMUSJQMFZSFQJUBMPTQBTPTBZC%FUFSNJOFFMFGFDUPEFNBZPSQSFTJÓO TPCSFMBWPMBUJMJEBESFMBUJWB F 3FHSFTFBQBUNZBTVSFTVMUBEPEFMBQBSUFD"IPSBBVNFOUFMBUFNQFSBUVSBEFMBBMJNFO UBDJÓO FOMVHBSEFFTQFDJàDBSVOBGSBDDJÓOEFWBQPSJHVBMBy2VÊTVDFEF m G 3FHSFTFBMBTJNVMBDJÓOEFMBQBSUFD%FUFSNJOFMBSFMBDJÓOEFWBQPSBMGPOEP 7WBQPSJ[BEPS#  "IPSBDPSSBMBTJNVMBDJÓODPOFMMB FOMVHBSEFFTQFDJàDBSFMáVKPEFEFTUJMBEP"DPOUJOVBDJÓO DPNJFODFBEJTNJOVJSMBSFMBDJÓOEFWBQPSBMGPOEPFOMBTJNVMBDJÓOy2VÊTVDFEF H 3FHSFTFBMBTJNVMBDJÓOEFMBQBSUFF&OMVHBSEFJOEJDBSMBGSBDDJÓOWBQPSJ[BEBFOMBBMJ NFOUBDJÓO àKFMBUFNQFSBUVSBEFMBBMJNFOUBDJÓO FTQFDJàRVF-%ZSFMBDJÓOEFWBQPSBM GPOEP /ZMVHBSEFMBBMJNFOUBDJÓO "VNFOUFMBUFNQFSBUVSBEFMBBMJNFOUBDJÓOZWFBRVÊ TVDFEF I 3FHSFTFBMBQBSUFC QFSPUSBUFEFRVFFMQSPEVDUPEFTUJMBEPDPOUFOHBEFEJDMPSPFUB OP ZMBTDPMBTDPOUFOHBOEFEJDMPSPFUBOP)BHB DPOFYBDUJUVE MPTCBMBODFTEFNBTBZ EFUFSNJOFMPTWBMPSFTEFUBTBEFáVKPEFEFTUJMBEP5SBUFEFDBMDVMBS/ZMBVCJDBDJÓOEFMB BMJNFOUBDJÓORVFBQFOBTMPHSFFTUBTFQBSBDJÓODPO-%/PUFRVFOPEFCFSÎBTFSQPTJCMF FTUBTFQBSBDJÓO QPSRVFMBSFMBDJÓOEFSFáVKPFYUFSOP -% FTEFNBTJBEPCBKB7FBMPRVF TVDFEFBMBVNFOUBS-% QSVFCFDPOZ  &OFMBQÊOEJDFEFMDBQÎUVMPVTBSFNPTTJNVMBEPSFTEFQSPDFTPDPODÃMDVMPTEFEFTUJMBDJÓO DPOWBSJPTDPNQPOFOUFT "ÊTUBTZUPEBTMBTEFNÃTTJNVMBDJPOFTTFBQMJDBVOBBEWFSUFODJB&MQSPHSBNBTÓMPQVFEF SFTPMWFSFMQSPCMFNBRVFMFQMBOUFFVTUFE4JDPNFUFVOFSSPSEFEBUPT QPSFKFNQMP OPJODMV ZFOEPVODPNQPOFOUFTFDVOEBSJPRVFBQBSF[DBFOMBQMBOUB

FMTJNVMBEPSOPQVFEFBOUJDJQBS RVÊTVDFEFSÃFOSFBMJEBEFOMBQMBOUB6OBTJNVMBDJÓORVFFTDPSSFDUBQBSBFMQSPCMFNBOP TFSÃEFVUJMJEBETJFTFQSPCMFNBOPDPJODJEFDPOMBTDPOEJDJPOFTEFMBQMBOUB4JFNQSFTFEFCF BQMJDBSFMKVJDJPEFJOHFOJFSÎBRVÎNJDBBMVTBSVOTJNVMBEPSEFQSPDFTPT )PSXJU[  

www.FreeLibros.me

$"1±56-0 

*OUSPEVDDJÓOBMBEFTUJMBDJÓO EFWBSJPTDPNQPOFOUFT

-PTQSPCMFNBTEFEFTUJMBDJÓOCJOBSJBTFQVFEFOSFTPMWFSEFGPSNBEJSFDUBDPOVODÃMDVMPEFFUBQB QPSFUBQBRVFQVFEFIBDFSTFZBTFBFODPNQVUBEPSB HSÃàDBNFOUFPDPOVOEJBHSBNBEF.D$B CF5IJFMF$VBOEPTFBHSFHBONÃTDPNQPOFOUFT FMQSPCMFNBTFWVFMWFNÃTDPNQMFKPZQVFEFTFS RVFMBTPMVDJÓOOPTFBUBOEJSFDUB&OFTUFDBQÎUVMPEFTDSJCJSFNPTQSJNFSPQPSRVÊMBEFTUJMBDJÓO EFWBSJPTDPNQPOFOUFT PEFTUJMBDJÓOEFNVMUJDPNQPOFOUFT FTNÃTDPNQMJDBEBRVFMBEFTUJMBDJÓO CJOBSJB " DPOUJOVBDJÓO WFSFNPT MBT GPSNBT DBSBDUFSÎTUJDBT EF QFSàMFT EF MB EFTUJMBDJÓO EF WBSJPT DPNQPOFOUFT&OFMDBQÎUVMPBQMJDBSFNPTNÊUPEPTNBUSJDJBMFTEFDÃMDVMPBMBEFTUJMBDJÓOEFWBSJPT DPNQPOFOUFT MPTNÊUPEPTBQSPYJNBEPTTFQSFTFOUBSÃOFOFMDBQÎUVMP   %*'*$6-5"%&4%&$¦-$6-0

7FBFMFTRVFNBEFVOBDPMVNOBEFEFTUJMBDJÓOEFQMBUPTDPOVODPOEFOTBEPSUPUBMZVOWBQPSJ[BEPS QBSDJBMFOMBàHVSB4VQPOHBRVFIBZEFSSBNFNPMBMDPOTUBOUF $.0 EFDPOTUBOUNPMBMPWFS GMPX

QSFTJÓODPOTUBOUFZOPIBZFTDBQFTEFDBMPS $POMBTIJQÓUFTJTEFQSFTJÓODPOTUBOUFZTJOQÊSEJEBTEFDBMPS VOBOÃMJTJTEFHSBEPTEFMJCFSUBE FOUPSOPBMBDPMVNOBSFTVMUBFO$ HSBEPTEFMJCFSUBE EPOEF$FTMBDBOUJEBEEFDPNQPOFOUFT 1BSBMBEFTUJMBDJÓOCJOBSJB FTPFRVJWBMFBHSBEPTEFMJCFSUBE&OVOQSPCMFNBEFEJTFÒP FOHFOF SBMFTQFDJàDBSÎBNPTFTBTWBSJBCMFTDPNPTJHVF WFBMBTUBCMBTZ ' [ DBMJEBEEFBMJNFOUBDJÓO R DPNQPTJDJÓOEFEFTUJMBEPY% UFNQFSBUVSBEFMEFTUJMBEP MÎRVJEPTBUVSBEP

DPNQPTJDJÓOEFMBTDP MBTY# SFMBDJÓOEFSFáVKPFYUFSOP-%ZMBFUBQBÓQUJNBEFBMJNFOUBDJÓO&TDPHJEBTFTBTWBSJBCMFT  MBTMÎOFBTEFPQFSBDJÓORVFEBOEFàOJEBTZQPESFNPTFTDBMPOBSMBTFUBQBTEFTEFDVBMRVJFSFYUSFNP EFMBDPMVNOBDPOFMNÊUPEPEF.D$BCF5IJFMF "IPSB TJBHSFHBNPTVOUFSDFSDPNQPOFOUF BVNFOUBNPTMPTHSBEPTEFMJCFSUBEB-BTOVFWF WBSJBCMFTRVFTFQPESÎBOFTQFDJàDBSFOFMEJTFÒPEFVOBDPMVNOBEFEFTUJMBDJÓOUFSOBSJBTFNFODJP OBOFOMBUBCMB"MDPNQBSBSMBDPOMBTUBCMBTZ WFNPTRVFFMHSBEPEFMJCFSUBEBEJDJPOBM TFVTBQBSBFTQFDJàDBSQPSDPNQMFUPMBDPNQPTJDJÓOEFMBBMJNFOUBDJÓO4JIBZDVBUSPDPNQPOFOUFT  IBCSÃHSBEPTEFMJCFSUBE&MHSBEPEFMJCFSUBEBEJDJPOBMUBNCJÊOEFCFVTBSTFQBSBFTQFDJàDBSQPS DPNQMFUPMBDPNQPTJDJÓOEFMBBMJNFOUBDJÓO 

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT

'*(63" $0-6./"%&%&45*-"$*¶/ 0CTFSWFRVFFOMBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFTOPTFFTQFDJàDBOQPSDPNQMFUPMBTDPN QPTJDJPOFTEFMEFTUJMBEPOJEFMPTGPOEPT ZBRVFOPTFEJTQPOFEFTVàDJFOUFTWBSJBCMFTQBSBIBDFSMP -BJODBQBDJEBEEFFTQFDJàDBSQPSDPNQMFUPMBTDPNQPTJDJPOFTEFEFTUJMBEPZGPOEPTUJFOFVOFGFDUP JNQPSUBOUFTPCSFFMQSPDFEJNJFOUPEFDÃMDVMP-PTDPNQPOFOUFTRVFTÎUJFOFOSFDVQFSBDJPOFTGSBD DJPOBSJBTFOEFTUJMBEPZGPOEPT DPNPFMDPNQPOFOUFFOFMEFTUJMBEP ZFMDPNQPOFOUFFOMPT GPOEPT FOMBUBCMB TFMMBNBODPNQPOFOUFTDMBWF&MNÃTWPMÃUJMEFMPTDPNQPOFOUFTDMBWFTF MMBNBDMBWFMJHFSB -, EFMJHIULFZP$-FOFTQBÒPM ZFMNFOPTWPMÃUJMTFMMBNBDMBWFQFTBEB ),  EFIFBWZLFZP$1FOFTQBÒPM -PTEFNÃTDPNQPOFOUFTTPOOPDMBWFT /, EFOPOLFZP/$FO FTQBÒPM 4JVOBOPDMBWFFTNÃTWPMÃUJM NÃTMJHFSB RVFMBDMBWFQFTBEB FTVOBOPDMBWFQFTBEB )/, EFIFBWZOPOLFZ P/$1FOFTQBÒPM  -BTFDVBDJPOFTEFCBMBODFFYUFSOPQBSBMBDPMVNOBEFMBàHVSBTFEFEVDFODPOGBDJMJEBE 4POMBTFDVBDJPOFTEFCBMBODFHFOFSBM 5"#-" 7"3*"#-&4%&%*4&µ0&41&$*'*$"%"41"3"%&45*-"$*¶/5&3/"3*" $BOUJEBEEFWBSJBCMFT

7BSJBCMF

 'MVKPEFBMJNFOUBDJÓO '  $PNQPTJDJÓOEFBMJNFOUBDJÓO [ [ [−[−[

 $BMJEBEEFBMJNFOUBDJÓO R PI'P5'

 %FTUJMBEP Y EFTU PI EFTUP% PVOBSFDVQFSBDJÓOGSBDDJPOBSJB

 $PMBT Y DPMB PY DPMBPVOBSFDVQFSBDJÓOGSBDDJPOBSJB

 -%P7#P23  3FáVKPEFMÎRVJEPTBUVSBEPP5SFG  6CJDBDJÓOÓQUJNBEFQMBUPEFBMJNFOUBDJÓO   -BQSFTJÓOEFMBDPMVNOBZ2DPMZBTFFTQFDJàDBSPO

www.FreeLibros.me

  %JGJDVMUBEFTEFDÃMDVMP





'# %



'[J#YJ DPMB %YJ EFTU  J  $



ZMBFDVBDJÓOEFMCBMBODFHFOFSBMEFFOFSHÎB 

ZMBFDVBDJÓOEFMCBMBODFHFOFSBMEFFOFSHÎB 

;]; FX FG 27]7 9]9 



-BTGSBDDJPOFTNPMEFCFOTVNBS 8



m ^!YZhi 2&#% 

B

m ^!XdaV 2&#% 

C

^2& 8



^2&

1BSBVOTJTUFNBUFSDJBSJP MBTFDVBDJPOFT  TFQVFEFOFTDSJCJSUSFTWFDFT QFSPBMTVNBSTFEFCF PCUFOFSTFMBFDVBDJÓO  1PSMPRVFEPTEFMBTFDVBDJPOFT  NÃTMB 

TPOJOEFQFOEJFOUFT 1BSBVOBDPMVNOBDPOVOBTPMBBMJNFOUBDJÓOQPESFNPTSFTPMWFSTJNVMUÃOFBNFOUFDVBMRVJFSB EF MBT FDVBDJPOFT   DPO MB FDVBDJÓO   QBSB PCUFOFS SFTVMUBEPT BOÃMPHPT B MBT FDVBDJPOFT CJOBSJBT  Z   92

o ^ − m ^!XdaV ; m ^!YZhi − m ^!XdaV



72

m ^!YZhi − o ^ ; m ^!YZhi − m ^!XdaV 







4JTFFTQFDJàDBOMBTDPNQPTJDJPOFTEFBMJNFOUBDJÓO GPOEPTZEFTUJMBEPEFUPEPTMPTDPNQPOFOUFT  QPESFNPTEFTQFKBS%Z#"EFNÃT MBTFDVBDJPOFTNVFTUSBORVFMBSFMBDJÓOEFEJGFSFODJBTEFDPO DFOUSBDJÓOQBSBUPEPTMPTDPNQPOFOUFTEFCFTFSJEÊOUJDB %PIFSUZZ.BMPOF  &TBTFDVBDJPOFT TPOÙUJMFT QFSPOPSFTVFMWFOUPEPFMQSPCMFNB BVODVBOEPTFFTQFDJàRVFOYJ EFTUZYJ GPOEPQBSBVODPN QPOFOUFFTUPEFCJEPBRVFTFEFTDPOPDFOMBTEFNÃTGSBDDJPOFTNPMFOFMEFTUJMBEPZFOMPTGPOEPT &OUPODFT yDÓNPTFSFTVFMWFOQPSDPNQMFUPMPTCBMBODFTEFNBTBFYUFSOPT -BTJODÓHOJUBTTPO # % Y EFTU Y EFTU Y GPOEPZY GPOEP)BZJODÓHOJUBTZFDVBDJPOFTJOEFQFOEJFOUFTy4FQVFEFIBMMBS VOBFDVBDJÓONÃT %FTBGPSUVOBEBNFOUF MBTFDVBDJPOFTBEJDJPOBMFT CBMBODFTEFFOFSHÎBZFDVBDJP OFTEFFRVJMJCSJP TJFNQSFBHSFHBONÃTWBSJBCMFT WFBFMQSPCMFNB"

QPSMPRVFOPQPEFNPT DPNFO[BSSFTPMWJFOEPMPTCBMBODFTFYUFSOPTEFNBTBZFOFSHÎB­TUBFTMBQSJNFSBHSBOEJGFSFODJB FOUSFMBEFTUJMBDJÓOCJOBSJBZMBEFWBSJPTDPNQPOFOUFT y4FQVFEFOIBDFSQSJNFSPDÃMDVMPTEFFUBQBQPSFUBQBZEFTQVÊTSFTPMWFSMPTCBMBODFTFYUFS OPT 1BSBDPNFO[BSFMQSPDFEJNJFOUPEFDÃMDVMPEFFUBQBQPSFUBQBFOVOBDPMVNOBEFEFTUJMBDJÓO  OFDFTJUBNPTDPOPDFSUPEBTMBTDPNQPTJDJPOFTFOVOFYUSFNPEFMBDPMVNOB1BSBMPTTJTUFNBUFSOB SJPT DPOMBTWBSJBCMFTFTQFDJàDBEBTDPNPFOMBUBCMB FTBTDPNQPTJDJPOFTTFEFTDPOPDFO1BSB JOJDJBSFMBOÃMJTJTIBCSÎBRVFTVQPOFSVOBEFFMMBT&OUPODFT MPTDÃMDVMPTJOUFSOPTFOMPTQSPCMFNBT EFEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFTTPOEFQSVFCBZFSSPS­TUBFTMBTFHVOEBHSBOEJGFSFODJBFO USFMPTQSPCMFNBTCJOBSJPTZMPTEFWBSJPTDPNQPOFOUFT

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT

1PS GPSUVOB  FO NVDIPT DBTPT FT GÃDJM IBDFS VOB QSJNFSB UFOUBUJWB  BEFDVBEB Z RVF QFSNJUB IBDFSMPTCBMBODFTFYUFSOPT4JTFSFRVJFSFVOBTFQBSBDJÓOCJFOEFàOJEBEFMBTDMBWFT FOUPODFTDBTJ UPEPTMPTQFTBEPTOPDMBWFTBQBSFDFSÃOFOMPTGPOEPTZDBTJUPEPTMPTMJHFSPTOPDMBWFTBQBSFDFSÃO TÓMPFOFMEFTUJMBEP-BIJQÓUFTJTPCWJBFTRVFUPEPTMPTQFTBEPTOPDMBWFTÓMPBQBSF[DBOFOFMEFT UJMBEP ZUPEPTMPTQFTBEPTOPDMBWFTBQBSFDFOTÓMPFOMPTGPOEPT&OUPODFT 

Y-/, GPOEPT

B



Y)/, EFTU

C

&TUBTIJQÓUFTJTOPTQFSNJUFOUFSNJOBSMPTCBMBODFTFYUFSOPTEFNBTB&MQSPDFEJNJFOUPTFJMVTUSBSÃ FOFMFKFNQMP &+&.1-0 #BMBODFTFYUFSOPTVTBOEPSFDVQFSBDJPOFTGSBDDJPOBSJBT 4FEFTFBEFTUJMBSLHNPMIEFVOBBMJNFOUBDJÓOMÎRVJEBTBUVSBEB-BBMJNFOUBDJÓO FO GSBDDJPOFTNPM DPOUJFOFEFQSPQBOP EFOCVUBOP EFOQFOUBOPZFMSFTUP FTOIFYBOP-BDPMVNOBUSBCBKBBL1BZUJFOFVODPOEFOTBEPSUPUBMZVOWBQPSJ[BEPS QBSDJBM-BSFMBDJÓOEFSFáVKPFT-%ZFMSFáVKPFTMÎRVJEPTBUVSBEP4FWBBVTBSMB FUBQBÓQUJNBEFBMJNFOUBDJÓO4FEFTFBRVFFMEFTUJMBEPUFOHBVOBSFDVQFSBDJÓOEF EFOCVUBOPZRVFMPTGPOEPTUFOHBOEFOQFOUBOP&TUJNFMBTDPNQPTJDJPOFTZáV KPTEFMEFTUJMBEPZGPOEPT 4PMVDJÓO " %FGJOB4FNVFTUSBVOFTRVFNBEFMBDPMVNOB

99.4% recuperado de C4 L/D = 3.5, líquido saturado p = 101.3 Plato óptimo de alimentación

99.7% recuperado de C5

 $BMDVMFYJ EFTU YJ DPMB %Z# # &YQMPSF1BSFDFTFSVOBBQMJDBDJÓOEJSFDUBEFMPTCBMBODFTFYUFSOPTEFNBTB FYDFQUP QPSRVFIBZEPTWBSJBCMFTNÃT"TÎ IBCSÃRVFTVQPOFSMBTSFDVQFSBDJPOFTPDPODFOUSB DJPOFTEFEPTEFMPTDPNQPOFOUFT6OWJTUB[PBMBTHSÃàDBTEF%F1SJFTUFS àHVSBT Z NVFTUSBRVFFMPSEFOEFWPMBUJMJEBEFTFTQSPQBOPOCVUBOPOQFOUBOP OIFYBOP&OUPODFT OCVUBOPFTMBDMBWFMJHFSBZFMOQFOUBOPFTMBDMBWFQFTBEB&TP

www.FreeLibros.me

  %JGJDVMUBEFTEFDÃMDVMP



IBDFBVUPNÃUJDBNFOUFRVFFMQSPQBOPTFBMBOPDMBWFMJHFSBZFMIFYBOPMBOPDMBWF QFTBEB$PNPMBTSFDVQFSBDJPOFTEFMBTDMBWFTTPOCBTUBOUFBMUBT FTSB[POBCMFTVQPOFS RVFUPEBMBOPDMBWFMJHFSBTFKVOUBFOFMEFTUJMBEP ZUPEBMBOPDMBWFQFTBEBTFSFÙOF FOMPTGPOEPT&TUJNBSFNPTBMEFTUJMBEPZGPOEPTDPOCBTFFOFTUBTIJQÓUFTJT $ 1MBOFF/VFTUSBTIJQÓUFTJTEFMBTGSBDDJPOFTOPDMBWFTFQVFEFOFTDSJCJSFOMBGPSNB 

%Y$ EFTU'[$  Z  #Y$ GPOEPT'[$

B C

#Y$ GPOEPT  Z  %Y$ EFTU

B C

PCJFO 

WFBFMQSPCMFNB"  4FQVFEFVTBSMBSFDVQFSBDJÓOGSBDDJPOBSJBEFOCVUBOPFOFMEFTUJMBEPQBSBFTDSJCJS 

%Y$ EFTU GSBDDSFDVQFSBEBEF$FOEFTUJMBEP '[$ 



/PUFRVFFTUPUBNCJÊOJNQMJDBRVF 

#Y$ GPOEPT −GSBDDSFDVQFSBEBEF$FOEFTU '[$ 



1BSBFMOQFOUBOP MBTFDVBDJPOFTTPO 

#Y$ GPOEPT GSBDSFD$FOGPOEPT '[$





%Y$ EFTU −GSBDSFD$FOGPOEPT '[$



-BT FDVBDJPOFT   B   SFQSFTFOUBO PDIP FDVBDJPOFT DPO EJF[ JODÓHOJUBT DVBUSP DPNQPTJDJPOFT UBOUPFOEFTUJMBEPDPNPFOGPOEPT NÃT%Z# -BTFDVBDJPOFT  TPO EPTBEJDJPOBMFTRVFFTDSJCJSFNPTFOMBGPSNB 8



m ^!YZhi 29 

B

m ^!XdaV 27 

C

^2&

8

 ^2&

&TUBTEJF[FDVBDJPOFTTFQVFEFOSFTPMWFSDPOGBDJMJEBEQPSRVFMPTDÃMDVMPTEFEFTUJMBEPZ GPOEPTTFQVFEFOIBDFSQPSTFQBSBEP %)ÃHBMP$PNJFODFDPOFMEFTUJMBEP %Y$ EFTU'[$    %Y$ EFTU %Y$ EFTU     %Y$ EFTU     &OUPODFT  )

92

9m ^!YZhi 2,*( ^2&

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT



m ^!YZhi 2

9m ^!YZhi  9





"TÎ  m 8(!YZhi 2

&&' 2%#&)-,!n ,*(#%)

m 8)!Y 2 +(-#&* 2%#-),)!m 8*!Y 2 '#-. 2%#%%(-!m 8+!Y 2% ,*(#%) ,*(#%)

$PNQSPCBDJÓO )

m ^!YZhi 2%#....!RVFFTDPSSFDUP ^2&



-PT GPOEPT TF QVFEFO EFUFSNJOBS DPO MBT FDVBDJPOFT C

 B

 

   Z C -PTSFTVMUBEPTTPOYD GPOEPT Y$ GPOEPT Y$ GPOEPT Y$ GPOEPT Z#3FDVFSEFRVFTPOFTUJNBDJPOFTCBTBEBTFOOVFTUSBIJQÓUFTJTTPCSF MBTGSBDDJPOFTEFMBOPDMBWF & $PNQSVFCF)BZEPTWFSJàDBDJPOFTRVFTPOBEFDVBEBT-PTSFTVMUBEPT EFBDVFSEPDPO OVFTUSBTIJQÓUFTJT TFQVFEFOWFSJàDBSDPNQSPCBOEPTJTBUJTGBDFOMPTCBMBODFTFYUFSOPT EFNBTB FDVBDJPOFT  Z  &TBTFDVBDJPOFTRVFEBOTBUJTGFDIBT-BTFHVOEBDPN QSPCBDJÓOFTSFWJTBSMBTIJQÓUFTJT QBSBMPDVBMTFSFRVJFSFBOÃMJTJTJOUFSOPEFFUBQBQPS FUBQB&TUPFTNVDIPNÃTEJGÎDJM&OFTUFDBTP MBTIJQÓUFTJTGVFSPOCBTUBOUFCVFOBT ' (FOFSBMJDF&TUBDMBTFEFQSPDFEJNJFOUPTFQVFEFBQMJDBSBNVDIPTQSPCMFNBTEFEFT UJMBDJÓO EF WBSJPT DPNQPOFOUFT $PO NÃT GSFDVFODJB TF FTQFDJàDBO SFDVQFSBDJPOFT GSBDDJPOBSJBT OPDPODFOUSBDJPOFT MPRVFFTNÃTDÓNPEP %FNBOFSBTPSQSFOEFOUF MBDBQBDJEBEEFIBDFSCBMBODFTFYUFSOPTEFNBTBDPOVOBFYBDUJUVE SB[POBCMFDPOCBTFFOVOQSJNFSUBOUFP OPHBSBOUJ[BRVFMPTDÃMDVMPTJOUFSOPTEFFUBQBQPSFUBQB TFBOFYBDUPT&OFMQSPCMFNBEFMFKFNQMPTFSÎBNVZEJGÎDJMIBDFSDÃMDVMPTEFFUBQBQPSFUBQB*O EBHBSFNPTQPSRVÊ &OMBFUBQBEFBMJNFOUBDJÓOEFCFOFTUBSQSFTFOUFTUPEPTMPTDPNQPOFOUFTFODPODFOUSBDJPOFT àOJUBT4JEFTFBNPTFTDBMPOBSMBTFUBQBTEFBCBKPIBDJBBSSJCB OPQPEFNPTVTBSY$ GPOEPT QPSRVF OPSFTVMUBSÎBVOBDPODFOUSBDJÓOEFQSPQBOPEJTUJOUBEFDFSPFOMBFUBQBEFBMJNFOUBDJÓO&OUPODFT  Y$ GPOEPTEFCFTFSQFRVFÒB QFSPOPDFSP%FTBGPSUVOBEBNFOUFOPTBCFNPTTJFMWBMPSDPSSFDUPEF CFSÎBTFS− − −P−&OUPODFT FMQPSDFOUBKFEFFSSPSFOY$ GPOEPTTFSÃHSBOEFZTFSÃEJGÎDJM PCUFOFSDPOWFSHFODJBEFMQSPCMFNBQPSQSVFCBZFSSPS4JUSBUBNPTEFFTDBMPOBSFUBQBTEFBSSJCB BBCBKP Y$ EFTUTFDPOPDFDPOFYBDUJUVE QFSPY$ EFTUOP&OUPODFT DVBOEPIBZQSFTFOUFTQFTBEPTZ MJHFSPTOPDMBWFTBMBWF[ TFEJàDVMUBOMPTDÃMDVMPTEFFUBQBQPSFUBQB)FOHTUFCFDL  JOWFOUÓ FMVTPEFQTFVEPDPNQPOFOUFTQBSBDÃMDVMPTBQSPYJNBEPTEFWBSJPTDPNQPOFOUFTFOVOEJBHSBNB EF.D$BCF5IJFMF-BTDMBWFTMJHFSBTZMBTOPDMBWFTMJHFSBTTFBHSVQBO ZUBNCJÊOMBTDMBWFTQFTBEBT ZOPDMBWFTQFTBEBT$PNPWFSFNPTFOMBTJHVJFOUFTFDDJÓO FTPTSFTVMUBEPTTÓMPQVFEFOTFSBQSPYJ NBEPTQBSBQSPEVDJSSFTVMUBEPTFYBDUPTFTOFDFTBSJPVTBSPUSPTQSPDFEJNJFOUPTEFEJTFÒP 4JTÓMPIBZOPDMBWFTMJHFSBTPTÓMPOPDMBWFTQFTBEBT TFQVFEFQSPQPOFSVOWBMPSFYBDUPEFDPN QPTJDJÓOQBSBFMQSJNFSJOUFOUP4VQPOHBRVFFTQFDJàDÃSBNPTEFSFDVQFSBDJÓOEFQSPQBOPFO

www.FreeLibros.me

  1FSGJMFTQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT



FMEFTUJMBEPZEFSFDVQFSBDJÓOEFOCVUBOPFOMPTGPOEPT$POFMMP FMQSPQBOPFTMBDMBWFMJ HFSB FMOCVUBOPFTMBDMBWFQFTBEB ZFMOQFOUBOPZOIFYBOPTPOMBTOPDMBWFTQFTBEBT-BIJQÓUFTJT RVFUPEBTMBTOPDMBWFTQFTBEBTBQBSFDFOFOMBTDPMBTFTVOQSJNFSWBMPSUFOUBUJWPFYDFMFOUFFOUPODFT TFQVFEFODBMDVMBSMBTDPNQPTJDJPOFTEFEFTUJMBEPZDPMBTNFEJBOUFCBMBODFTFYUFSOPTEFNBTB-B DPNQPTJDJÓODBMDVMBEBFOMPTGPOEPTFTCBTUBOUFFYBDUB"TÎ FOFTUFDBTP QPESFNPTFTDBMPOBSMBT FUBQBTEFBCBKPIBDJBBSSJCB DPOàBOEPCBTUBOUFFORVFMPTSFTVMUBEPTTFSÃOFYBDUPT4JTÓMPIBZOP DMBWFTMJHFSBT FMDÃMDVMPEFFUBQBQPSFUBQBTFEFCFIBDFSEFBSSJCBIBDJBBCBKP&TUPTNÊUPEPTEF FUBQBQPSFUBQBTFEFTDSJCFODPOEFUBMMFFOMBTQVCMJDBDJPOFTEF,JOH  Z8BOLBU    1&3'*-&41"3"%&45*-"$*¶/%&7"3*04$0.10/&/5&4

y$ÓNP TF WFO MPT QFSàMFT EF áVKP  UFNQFSBUVSB Z DPNQPTJDJÓO  /VFTUSB JOUVJDJÓO OPT EJSÎB RVF FTPTQFSàMFTTFQBSFDFSÃOBMPTEFMBEFTUJMBDJÓOCJOBSJB$PNPWFSFNPT FTPFTDJFSUPQBSBMPTáVKPT UPUBMFTZMBUFNQFSBUVSB QFSPOPQBSBMPTEFDPNQPTJDJÓO 4JFTWÃMJEPFMEFSSBNFNPMBMDPOTUBOUF MPTáVKPTUPUBMFTEFWBQPSZMÎRVJEPTFSÃODPOTUBOUFTFO DBEBTFDDJÓOEFMBDPMVNOB-BTUBTBTEFáVKPUPUBMQVFEFODBNCJBSFODBEBFUBQBEFBMJNFOUBDJÓO PFUBQBEFTBMJEBMBUFSBM&TUFDPNQPSUBNJFOUPTFJMVTUSBFOVOBTJNVMBDJÓOQPSDPNQVUBEPSBQBSB VOBBMJNFOUBDJÓOMÎRVJEBTBUVSBEBFOMBàHVSB­TUFDPSSFTQPOEFBMDPNQPSUBNJFOUPFTQFSBEP FOVOTJTUFNBCJOBSJP1BSBEFSSBNFNPMBMOPDPOTUBOUF MBTUBTBTUPUBMFTEFáVKPWBSJBSÃOEFVOB TFDDJÓOBPUSB&TPUBNCJÊOTFWFFOMBàHVSB"VORVFMPTáVKPTUBOUPEFMÎRVJEPDPNPWBQPS QVFEFOWBSJBSCBTUBOUF MBSFMBDJÓO-7TFSÃNVDIPNÃTDPOTUBOUF &MQFSàMEFUFNQFSBUVSBEFDSFDFFOGPSNBNPOÓUPOBEFTEFFMWBQPSJ[BEPSIBTUBFMDPOEFOTB EPS&TUPTFJMVTUSBFOMBàHVSBDPOMBNJTNBTJNVMBDJÓOFODPNQVUBEPSB5BNCJÊOBRVÎTFQBSF DFBMDPNQPSUBNJFOUPEFMPTTJTUFNBTCJOBSJPT0CTFSWFRVFMBTNFTFUBTDPNJFO[BOBGPSNBSTFEPO EFIBZQPDPDBNCJPEFUFNQFSBUVSBFOUSFMBTFUBQBT$VBOEPIBZVOBHSBODBOUJEBEEFFUBQBT FTUBT NFTFUBTQVFEFOTFSCBTUBOUFQSPOVODJBEBT3FQSFTFOUBOQVOUPTEFFTUSJDDJÓOFOMBTDPMVNOBT -BTDPNQPTJDJPOFTFOMBDPMVNOBTPONVDIPNÃTDPNQMFKBT1BSBFTUVEJBSMBTWFSFNPTQSJNFSP EPTTJNVMBDJPOFTFODPNQVUBEPSBQBSBMBEFTUJMBDJÓOEFCFODFOP UPMVFOPZDVNFOPFOVOBDPMVN OBDPODPOUBDUPTEFFRVJMJCSJP-PTQFSàMFTEFáVKPUPUBMZEFUFNQFSBUVSB QBSBFTUBTJNVMBDJÓO  TFNVFTUSBOFOMBTàHVSBTZ SFTQFDUJWBNFOUF$POVOBSFDVQFSBDJÓOFTQFDJàDBEBEFEF CFODFOPFOFMEFTUJMBEP MBTGSBDDJPOFTNPMFOMÎRVJEPTFWFOFOMBàHVSB "MQSJODJQJP MBàHVSBDPOGVOEFCBTUBOUF QFSPUFOESÃTFOUJEPEFTQVÊTEFIBCFSMBSFDPSSJEB FUBQBQPSFUBQB$PNPMBSFDVQFSBDJÓOEFCFODFOPFOFMEFTUJMBEPTFFTQFDJàDÓDPNP FOUPODFT FMCFODFOPFTMBDMBWFMJHFSB%FGPSNBUÎQJDB FMTJHVJFOUFDPNQPOFOUFNFOPTWPMÃUJM FMUPMVFOP TFSÃ MBDMBWFQFTBEB&OUPODFT FMDVNFOPFTMBOPDMBWFQFTBEBZOPIBZOPDMBWFMJHFSB"MTFHVJSMBDVS WBEFMCFODFOP WFNPTRVFMBGSBDDJÓONPMEFCFODFOPFTNVZCBKBFOFMWBQPSJ[BEPSZBVNFOUBFO GPSNBNPOÓUPOBIBTUBMMFHBSBVOWBMPSBMUPFOFMDPOEFOTBEPSUPUBM&T FOFTFODJB FMNJTNPDPN QPSUBNJFOUPRVFFMDPNQPOFOUFNÃTWPMÃUJMFOMBEFTUJMBDJÓOCJOBSJB QPSFKFNQMP WFBMBàHVSB  &OFTUFQSPCMFNB FMCFODFOPTJFNQSFFTFMNÃTWPMÃUJM QPSMPRVFTVDPNQPSUBNJFOUPFTTJNQMF &OWJTUBEFRVFFMDVNFOPFTMBOPDMBWFQFTBEB DBCSÎBTVQPOFSRVFUPEPFMDVNFOPTBMFEF MBDPMVNOBFOMPTGPOEPT-BàHVSBNVFTUSBRVFFTPFTFTFODJBMNFOUFDJFSUP TFDBMDVMÓRVFMB GSBDDJÓONPMEFDVNFOPFOFMEFTUJMBEPFT×− $PNFO[BOEPFOFMWBQPSJ[BEPS MBGSBDDJÓO NPMEFDVNFOPEFDSFDFDPOSBQJEF[ZEFTQVÊTTFOJWFMBFOVOWBMPSNFTFUBIBTUBMBFUBQBEFBMJNFO UBDJÓO"SSJCBEFMBFUBQBEFBMJNFOUBDJÓO MBGSBDDJÓONPMEFDVNFOPEJTNJOVZFDPOSBQJEF[&TUF DPNQPSUBNJFOUPFTCBTUBOUFGÃDJMEFDPNQSFOEFS -BGSBDDJÓONPMEFDVNFOPEJTNJOVZFBSSJCBEFMWBQPSJ[BEPSQPSRVFFTFMDPNQPOFOUFNFOPT WPMÃUJM$PNPIBZVOBHSBODBOUJEBEEFDVNFOPFOMBBMJNFOUBDJÓO EFCFIBCFSVOBDPODFOUSBDJÓO

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT

Líquido Líquido, Derr. molal Const.

Flujo total

Vapor, Derr. molal Const. Líquido

No. de etapa

'*(63" '-6+04505"-&4%&-±26*%0:7"1034*.6-"$*¶/%&.&;$-"#&/$&/0 50-6&/0$6.&/04&%&4&"%&3&$61&3"$*¶/%&#&/$&/0-"4'3"$$*0/&4 .0-"-&4&/-""-*.&/5"$*¶/40/%&#&/$&/0 %&50-6&/0:%& $6.&/0&46/-±26*%04"563"%0',(.0-)&-1-"50%&"-*.&/5"$*¶/&4 &-"33*#"%&-7"103*;"%031"3$*"- :)":&5"1"4%&&26*-*#3*0.¦46/ 7"103*;"%031"3$*"-4&64"6/$0/%&/4"%03505"-1,1"70-"5*-*%"%&4 3&-"5*7"4 #&/  50-  $6. -%

'*(63" 1&3'*-%&5&.1&3"563"1"3"-" %&45*-"$*¶/%&#&/$&/050-6&/0$6.&/0.*4.0 130#-&."26&&/-"4'*(63"4:

www.FreeLibros.me

No. de etapa

  1FSGJMFTQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT



Benceno (C. L.) Tolueno (C. P.)

Cumeno (no C.P.)

Número de etapa

'*(63" 1&3'*-&4%&$0.104*$*¶/%&'"4&-±26*%"1"3"-" %&45*-"$*¶/%&#&/$&/050-6&/0$6.&/0.*4."4$0/%*$*0/&426&&/-"4 '*(63"4:1"3"%&33".&.0-"-/0$0/45"/5&&-#&/$&/0&4-" $-"7&-*(&3":&-50-6&/0&4-"$-"7&1&4"%"-"&5"1"&4-"&5"1" %&"-*.&/5"$*¶/ àOJUBFOMBFUBQBEFBMJNFOUBDJÓO&OUPODFT EFTQVÊTEFMBEJTNJOVDJÓOJOJDJBMIBZVOBNFTFUBIBTUB MBFUBQBEFBMJNFOUBDJÓO0CTFSWFRVFMBDPODFOUSBDJÓOEFDVNFOPFOMBFUBQBEFBMJNFOUBDJÓOOP FTJHVBMRVFMBEFMBBMJNFOUBDJÓO"SSJCBEFMBFUBQBEFBMJNFOUBDJÓO MBDPODFOUSBDJÓOEFDVNFOP EJTNJOVZFDPOSBQJEF[ QPSRVFFMDVNFOPFTFMDPNQPOFOUFNFOPTWPMÃUJM &MQFSàMEFDPODFOUSBDJÓOQBSBFMUPMVFOP DMBWFQFTBEB FTNVZDPNQMJDBEPFOFTUFFKFNQMP &MDPNQPSUBNJFOUPEFMBDMBWFQFTBEBTFQVFEFFYQMJDBSBMPCTFSWBSRVÊQBSFTCJOBSJPTEFDPNQP OFOUFTFTUÃOEFTUJMBOEPFODBEBQBSUFEFMBDPMVNOB&OFMWBQPSJ[BEPSZFOMBTFUBQBTZIBZ NVZQPDPCFODFOP DMBWFMJHFSB ZMBEFTUJMBDJÓOFTFOUSFMBDMBWFQFTBEBZMBOPDMBWFQFTBEB&O FTBTFUBQBT MBDPODFOUSBDJÓOEFUPMVFOP DMBWFQFTBEB BVNFOUBBMTVCJSQPSMBDPMVNOBQPSRVFFM UPMVFOPFTFMNÃTWPMÃUJMEFMPTEPTDPNQVFTUPTRVFEFTUJMBO&OMBTFUBQBTB MBDPODFOUSBDJÓO EFDVNFOP OPDMBWFQFTBEB TFOJWFMB&OUPODFT MBEFTUJMBDJÓOFTFOUSFMBDMBWFMJHFSBZMBDMBWF QFTBEB"IPSBFMUPMVFOPFTFMDPNQPOFOUFNFOPTWPMÃUJMZTVDPODFOUSBDJÓOEJTNJOVZFBMTVCJS QPSMBDPMVNOB&TPDBVTBFMNÃYJNPQSJNBSJPFOMBDPODFOUSBDJÓOEFMBDMBWFQFTBEBFOMBFUBQB "SSJCBEFMBFUBQBEFBMJNFOUBDJÓO FOMBTFUBQBT Z MBDPODFOUSBDJÓOEFMBOPDMBWFQFTBEB CBKBFOQJDBEB-BQSJODJQBMEFTUJMBDJÓOWVFMWFBTFSFOUSFMBDMBWFQFTBEBZMBOPDMBWFQFTBEB$PNP MBDMBWFQFTBEBFTFMNÃTWPMÃUJM UFNQPSBMNFOUF EFFTPTDPNQPOFOUFT MBDPODFOUSBDJÓOBVNFOUB BMTVCJSQPSMBDPMVNOBZMMFHBBMNÃYJNPFOMBFUBQB%FTQVÊTEFMBFUBQBIBZNVZQPDBOP DMBWFQFTBEBQSFTFOUFZMBQSJODJQBMEFTUJMBDJÓOFTFOUSFCFODFOPZUPMVFOP&OUPODFT MBDPODFO USBDJÓOEFUPMVFOPEJTNJOVZFBMDPOUJOVBSTVCJFOEPIBTUBFMDPOEFOTBEPS&MNÃYJNPTFDVOEBSJP BSSJCBEFMBFUBQBEFBMJNFOUBDJÓOFT DPOGSFDVFODJB NVDIPNFOPSRVFFMRVFNVFTUSBMBàHVSB -BTDBOUJEBEFTEFDVNFOPFOFTUFFKFNQMPDBVTBOVONÃYJNPTFDVOEBSJPNBZPSRVFVONÃYJNP TFDVOEBSJPOPSNBM

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT

&OFTUFFKFNQMP MBOPDMBWFQFTBEB DVNFOP

DBVTBMPTEPTNÃYJNPTFOFMQFSàMEFDPODFOUSB DJÓOEFMBDMBWFQFTBEB UPMVFOP $PNPOPIBZOPDMBWFMJHFSB MBDMBWFMJHFSB CFODFOP OPUJFOF NÃYJNPT1VFEFTFSÙUJMWPMWFSBIBDFSFMFKFNQMPEFMBTàHVSBTBNBOUFOJFOEPUPEPJHVBM  FYDFQUPQPSMBFTQFDJàDBDJÓOEFEFSFDVQFSBDJÓOEFUPMVFOPFOFMEFTUJMBEP"IPSB FMUPMVFOP FTMBDMBWFMJHFSB FMDVNFOPFTMBDMBWFQFTBEBZFMCFODFOPFTVOBOPDMBWFMJHFSB&MSFTVMUBEPRVF TFPCUJFOFBTÎTFQSFTFOUBFOMBàHVSBÊTUBUBNCJÊOTFQVFEFFYQMJDBSDVBMJUBUJWBNFOUFFOGVO DJÓOEFMBEFTUJMBDJÓOEFQBSFTCJOBSJPT WFBFMQSPCMFNB" 0CTFSWFRVFTJOPIBZOPDMBWFT QFTBEBT MBDPODFOUSBDJÓOEFMBDMBWFQFTBEBOPQSFTFOUBNÃYJNPBMHVOP y2VÊTVDFEFDPOVOBEFTUJMBDJÓOEFDVBUSPDPNQPOFOUFTTJIBZQSFTFOUFTDMBWFTMJHFSBT DMBWFTQF TBEBT OPDMBWFTMJHFSBTZOPDMBWFTQFTBEBT $PNPIBZVOBOPDMBWFMJHFSB DBCFFTQFSBSRVFMBDVSWB EFMBDMBWFMJHFSBNVFTUSFNÃYJNPT ZDPNPIBZVOBOPDMBWFQFTBEB DBCFFTQFSBSRVFIBZBNÃYJNPT FOFMQFSàMEFDPODFOUSBDJÓOEFMBDMBWFQFTBEB&TFMDBTPRVFNVFTUSBMBàHVSB EFMBEFTUJMBDJÓO EFVOBNF[DMBEFCFODFOPUPMVFOPYJMFOPZDVNFOP/PUFRVFFOFTUBàHVSB MPTNÃYJNPTTFDVOEB SJPTDFSDBEFMBFUBQBEFBMJNFOUBDJÓOEJTNJOVZFOFOGPSNBESÃTUJDB QFSPMPTNÃYJNPTQSJNBSJPTTF SFDPOPDFODPOGBDJMJEBE &TJOUFSFTBOUFDPNQBSBSMBTQVSF[BTEFMPTQSPEVDUPTEFTUJMBEPZGPOEPTFOMBTàHVSBTB &OMBàHVSB TJOOPDMBWFMJHFSB

FMCFODFOP DMBWFMJHFSB QVFEFFTUBSQVSPFOFMEFTUJMBEP QFSP FTDMBSPRVFMPTGPOEPT DMBWFQFTBEBZDMBWFOPQFTBEB OPTPOQVSPT&OMBàHVSB TJODMBWFOP QFTBEB

FMDVNFOP DMBWFQFTBEB QVFEFFTUBSQVSPFOMBTDPMBT QFSPFMEFTUJMBEP DMBWFMJHFSBZOP DMBWFMJHFSBQSFTFOUFT OPFTQVSP&OMBàHVSB QSFTFOUFTOPDMBWFMJHFSBZOPDMBWFQFTBEB OJFM EFTUJMBEPOJMBTDPMBTQVFEFOTFSQVSPT-BTDPMVNOBTEFEFTUJMBDJÓOTJNQMFTTFQBSBOMBBMJNFOUBDJÓO FOEPTGSBDDJPOFTZVOBTPMBDPMVNOBQVFEFQSPEVDJSFMDPNQPOFOUFNÃTWPMÃUJMQVSP IBDJFOEPRVF TFBMBDMBWFMJHFSB PQVFEFQSPEVDJSFMDPNQPOFOUFNFOPTWPMÃUJMQVSPFOGPSNBEFGPOEPT IBDJÊOEP MPMBDMBWFQFTBEB4JEFTFBNPTTFQBSBSQPSDPNQMFUPVOBNF[DMBEFWBSJPTDPNQPOFOUFT OFDFTJUBNPT BDPQMBSWBSJBTDPMVNOBTFOUSFTÎ WFBFMMBCPSBUPSJPFOFMBQÊOEJDFEFMDBQÎUVMPZMBTFDDJÓO  )BZVODBTPNÃTBDPOTJEFSBS4VQPOHBNPTRVFFTUÃOMPTDVBUSPDPNQPOFOUFTCFODFOP UP MVFOP DVNFOPZYJMFOP ZRVFPQUBNPTQPSRVFFMDVNFOPTFBMBDMBWFQFTBEBZFMUPMVFOPMBDMBWF

Tolueno (CL)

'*(63" 1&3'*-&4%&$0.104*$*¶/ %&'"4&-±26*%"1"3"%&45*-"$*¶/%& #&/$&/0 $/1 $-"7&/01&4"%"

 50-6&/0 $- $-"7&-*(&3" :$6.&/0 $1 $-"7&1&4"%" .*4.0130#-&."26& &/-"4'*(63"4" &9$&15026&4& &41&$*'*$"6/"3&$61&3"$*¶/%&%& 50-6&/0&/&-%&45*-"%0

www.FreeLibros.me

Cumeno (CP)

Benceno (CNP) Número de etapa

  1FSGJMFTQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT



Tolueno (CL)

Xileno (CP)

Cumeno (CNP)

Benceno (CNL)

N° de etapa

'*(63" 1&3'*-&4%&$0.104*$*¶/%&-±26*%01"3"%&45*-"$*¶/%&#&/$&/0 $/-  $-"7&/0-*(&3"

50-6&/0 $- $-"7&-*(&3"

9*-&/0 $1 $-"7&1&4"%" :$6.&/0 $/1 $-"7&/01&4"%" -"4'3"$$*0/&4.0-"-&4&/-""-*.&/5"$*¶/40/%& #&/$&/0 %&50-6&/0 %&9*-&/0:%&$6.&/03&$61&3"$*¶/%&50-6&/0 &/&-%&45*-"%07*4$04*%"%&43&-"5*7"4 #&/  50-  9*-  $6. MJHFSB&TPIBDFRVFFMCFODFOPTFBMBOPDMBWFMJHFSByQFSP ZFMYJMFOP &OFTUFDBTP FMYJMFOPFT VODPNQPOFOUFJOUFSNFEJP PEFFNQBSFEBEP RVFFTVODPNQPOFOUFOPDMBWFDPOVOBWPMBUJMJEBE FOUSFMBEFMPTEPTDPNQPOFOUFTDMBWF-PTDPNQPOFOUFTEFFNQBSFEBEPUFOEFSÃOBDPODFOUSBSTFB MBNJUBEEFMBDPMVNOB QPSRVFTPONFOPTWPMÃUJMFTRVFMBDMBWFMJHFSBFOMBTFDDJÓOEFSFDUJàDBDJÓO ZNÃTWPMÃUJMFTRVFMBDMBWFQFTBEBFOMBTFDDJÓOEFBHPUBNJFOUP1BSBBOUJDJQBSTVEJTUSJCVDJÓOàOBM TFSFRVJFSFEFVOBTJNVMBDJÓODPNQMFUB 4JMBUFNQFSBUVSBTVQFSJPSFTNVZCBKBZMBEFMGPOEPFTNVZBMUBQBSBQFSNJUJSRVFTBMHBODPNQP OFOUFTEFFNQBSFEBEPDPOFMáVKPDPOFMRVFFOUSBOBMBDPMVNOB FOUPODFT ÊTUPTRVFEBOBUSBQBEPT FOFMDFOUSPEFMBDPMVNOBZTFDPODFOUSBOBMMÎ ,JTUFS  &TUBBDVNVMBDJÓOQVFEFTFSCBTUBOUF BMUBQBSBDPNQPOFOUFTIVFMMBFOMBBMJNFOUBDJÓOZQVFEFDBVTBSJODMVTPJOVOEBDJÓOEFMBDPMVNOB Z GPSNBDJÓO EF VOB TFHVOEB GBTF MÎRVJEB &M QSPCMFNB TF QVFEF JEFOUJàDBS EFTEF MB TJNVMBDJÓO  TJ FMJOHFOJFSPDPOPDFUPEPTMPTDPNQPOFOUFTIVFMMBRVFIBZFOMBBMJNFOUBDJÓO TJIBZDPSSFMBDJPOFT FYBDUBTEFFRVJMJCSJPWBQPSMÎRVJEPZTJFMTJNVMBEPSQFSNJUFMBFYJTUFODJBEFEPTGBTFTEFMÎRVJEPZ VOBGBTFEFWBQPS%FTBGPSUVOBEBNFOUF FMFRVJMJCSJPWBQPSMÎRVJEPQVFEFTFSBMUBNFOUFOPJEFBM ZMPTDPNQPOFOUFTIVFMMBQPESÃOOPBDVNVMBSTFEPOEFTFDSFFRVFMPIBSÎBO1PSFKFNQMP DVBOEPTF EFTUJMBOFUBOPMZBHVBDPOGSFDVFODJBIBZIVFMMBTEFBMDPIPMFTTVQFSJPSFTQSFTFOUFT-PTBMDPIPMFTDPO DVBUSPDBSCPOPTPNÃT CVUBOPMZNÃTQFTBEPT TPOTÓMPQBSDJBMNFOUFNJTDJCMFTFOBHVB4FTFQBSBO DPOGBDJMJEBEEFVOBGBTFEFBHVB WPMBUJMJEBESFMBUJWB

QFSPDVBOEPIBZQPDBBHVB TPONFOPT WPMÃUJMFTRVFFMFUBOPM&OUPODFT TFBDVNVMBOFOBMHÙOMVHBSFOMBQBSUFNFEJBEFMBDPMVNOB EPOEF QVFEFOGPSNBSVOBTFHVOEBGBTFMÎRVJEBDPOMPTBMDPIPMFTQFTBEPTEFCBKBWPMBUJMJEBE-BTPMVDJÓO DPNÙOBFTUFQSPCMFNBFTJOTUBMBSVOBTBMJEBMBUFSBM TFQBSBSFMDPNQPOFOUFJOUFSNFEJPEFMPTEFNÃT

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT

DPNQPOFOUFT ZSFHSFTBSMPTBMBDPMVNOB&TUPTTJTUFNBTIFUFSPHÊOFPTTFEFTDSJCJSÃOFOEFUBMMFFOFM DBQÎUVMP -BTEJGFSFODJBTFOMPTQFSàMFTEFDPNQPTJDJÓOQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFTZMBCJ OBSJB DVBOEPMPTEBUPTEFFRVJMJCSJPWBQPSMÎRVJEPTPOSFMBUJWBNFOUFJEFBMFTZOPIBZB[FÓUSPQPT  TFSFTVNFOFO  &OMBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT MBTDPODFOUSBDJPOFTEFDPNQPOFOUFTDMBWFQVFEFOUF OFSNÃYJNPT  -BOPDMBWFFOHFOFSBMOPTFEJTUSJCVZF&TUPFT MBTOPDMBWFTQFTBEBTTVFMFOBQBSFDFSTÓMPFOMPT GPOEPTZMBTOPDMBWFTMJHFSBTTÓMPFOFMEFTUJMBEP  -BOPDMBWFQBTBDPOGSFDVFODJBQPSVOBSFHJÓOEFNFTFUBEFDPNQPTJDJÓODBTJDPOTUBOUF  5PEPTMPTDPNQPOFOUFTEFCFOFTUBSQSFTFOUFTFOMBFUBQBEFBMJNFOUBDJÓO QFSPFOFTBFUBQB  DBNCJBMBEFTUJMBDJÓOQSJNBSJB&OUPODFT FOMBFUBQBEFBMJNFOUBDJÓOIBZEJTDPOUJOVJEBEFT &TÙUJMDPNQSFOEFSMBTEJGFSFODJBTFOUSFEFTUJMBDJÓOCJOBSJBZEFNVMUJDPNQPOFOUFTDVBOEPTFIBDFO DÃMDVMPTEFEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT  3&46.&/m0#+&5*704

"MàOBMEFFTUFDBQÎUVMPEFCFVTUFEBMDBO[BSMPTTJHVJFOUFTPCKFUJWPT  &YQMJDBSQPSRVÊMBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFTTFDBMDVMBQPSUBOUFPT  )BDFSIJQÓUFTJTBEFDVBEBTZSFTPMWFSMPTCBMBODFTFYUFSOPTEFNBTB  &YQMJDBSMPTQFSàMFTEFáVKP UFNQFSBUVSBZDPNQPTJDJÓOQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT 3&'&3&/$*"4

)FOHTUCFDL 3+ %JTUJMMBUJPO1SJODJQMFTBOE%FTJHO 3FJOIPME /FX:PSL  ,JOH $+ 4FQBSBUJPO1SPDFTTFT ‰&E .D(SBX)JMM /FX:PSL  ,JTUFS ); i$PNQPOFOU5SBQQJOHJO%JTUJMMBUJPO5PXFST$BVTFT 4ZNQUPNTBOE$VSFTu $IFN &OH1SPHSFTT   

 BHPTUPEF  8BOLBU 1$ &RVJMJCSJVN4UBHFE4FQBSBUJPOT 1SFOUJDF)BMM 6QQFS4BEEMF3JWFS /+  5"3&"

" 1SPCMFNBTQBSBEJTDVTJÓO " &YQMJRVFQPSRVÊOPQVFEFOSFTPMWFSTFMPTCBMBODFTFYUFSOPTEFNBTBQBSBVOTJTUFNBEFEFT UJMBDJÓOUFSOBSJBTJOIBDFSVOBIJQÓUFTJTBEJDJPOBMy1PSRVÊOPTPOÙUJMFTMBTFDVBDJPOFTQBSB MPTJHVJFOUF B #BMBODFFYUFSOPEFFOFSHÎB C #BMBODFEFFOFSHÎBFOUPSOPBMDPOEFOTBEPS D &DVBDJÓOEFFRVJMJCSJPFOFMWBQPSJ[BEPS " &OFMFKFNQMP QBSUFD PCTFSWBNPTEPTGPSNBTFORVFTFQPESÎBFTDSJCJSOVFTUSBIJQÓUFTJT FDVBDJPOFTP &YQMJRVFQPSRVÊTPOFRVJWBMFOUFT " %FàOBMPTJHVJFOUF B$MBWFQFTBEB C/PDMBWFQFTBEB

www.FreeLibros.me

5BSFB

"

" "

"

"



D$PNQPOFOUFEFFNQBSFEBEP WFBFMQSPCMFNB"

E&UBQBÓQUJNBEFBMJNFOUBDJÓO F3FMBDJÓOEFSFáVKPNÎOJNB 4FEFTUJMBVOBNF[DMBEFEPTOPDMBWFTQFTBEBT VOBDMBWFQFTBEBZVOBDMBWFMJHFSB)BHBVO CPTRVFKPEFMPTQFSàMFTEFDPODFOUSBDJÓORVFTFFTQFSBO YJFOGVODJÓOEFMOÙNFSPEFFUB QB  1BSBVOBEFTUJMBDJÓOEFDJODPDPNQPOFOUFTDPOEPTOPDMBWFTQFTBEBT VOBDMBWFMJHFSB VOB DMBWFQFTBEBZVOBOPDMBWFQFTBEB yFORVÊMVHBSEFMBDPMVNOBMBUFNQFSBUVSBFTNÎOJNB 6OBDPMVNOBEFEFTUJMBDJÓOTFQBSBNFUBOP FUBOP QSPQBOPZCVUBOP4FMFDDJPOBNPTBMNFUB OPZQSPQBOPDPNPDMBWFT&TPRVJFSFEFDJSRVFFMFUBOPFTVODPNQPOFOUFEFFNQBSFEBEP B *OEJRVFMPTQFSàMFTEFDPNQPTJDJÓOBQSPYJNBEPTQBSBDBEBVOPEFMPTDVBUSPDPNQPOFO UFT*EFOUJàRVFDBEBDVSWB C &YQMJRVFDPOEFUBMMFFMSB[POBNJFOUPRVFVTÓQBSBPCUFOFSFMQFSàMEFMFUBOP 4FFTUÃTFQBSBOEPVOBNF[DMBGPSNBEBQPSNPMEFNFUBOPM NPMEFFUBOPM  NPMEFOQSPQBOPMZNPMEFOCVUBOPMFOVOBDPMVNOBEFEFTUJMBDJÓO&MNFUBOPMFTFM NÃTWPMÃUJMZFMOCVUBOPMFTFMNFOPTWPMÃUJM-BBMJNFOUBDJÓOFTVOMÎRVJEPTBUVSBEP%FTFB NPTSFDVQFSBSEFMFUBOPMFOFMEFTUJMBEPZEFMOQSPQBOPMFOMPTGPOEPT-BDPMVNOB UJFOFVODPOEFOTBEPSUPUBMZVOWBQPSJ[BEPSQBSDJBM-BUBTBEFBMJNFOUBDJÓOFTLHNPMI -BQSFTJÓOFTBUNZ-%  -BDPMVNOBUJFOFNÃYJNBUFNQFSBUVSBFO B &MDPOEFOTBEPS C &MQMBUPEFBMJNFOUBDJÓO D &MWBQPSJ[BEPS  &OMBTFDDJÓOEFSFDUJàDBDJÓO FOSJRVFDJNJFOUP  B 5BTBEFáVKPEFMÎRVJEPUBTBEFáVKPEFWBQPS C 5BTBEFáVKPEFMÎRVJEPUBTBEFáVKPEFWBQPS D 5BTBEFáVKPEFMÎRVJEPUBTBEFáVKPEFWBQPS  "MDPNQBSBSMBTFDDJÓOEFBHPUBNJFOUPDPOMBEFSFDUJàDBDJÓO B 5BTBEFáVKPEFMÎRVJEPFOMBTFDDJÓOEFBHPUBNJFOUPUBTBEFáVKPEFMÎRVJEPFOMB TFDDJÓOEFSFDUJàDBDJÓO C 5BTBEFáVKPEFMÎRVJEPFOMBTFDDJÓOEFBHPUBNJFOUPUBTBEFáVKPEFMÎRVJEPFOMB TFDDJÓOEFSFDUJàDBDJÓO D 5BTBEFáVKPEFMÎRVJEPFOMBTFDDJÓOEFBHPUBNJFOUPUBTBEFáVKPEFMÎRVJEPFOMB TFDDJÓOEFSFDUJàDBDJÓO  -BDMBWFQFTBEBFT B .FUBOPM C &UBOPM D OQSPQBOPM E OCVUBOPM  4JUVWJFSBVTUFERVFIBDFSCBMBODFTFYUFSOPTFOUPSOPBMBDPMVNOBQBSBDBMDVMBS#Z% MB NFKPSIJQÓUFTJTRVFQVFEFIBDFSFT B 5PEPFMNFUBOPMZFMOQSPQBOPMFTUÃOFOFMEFTUJMBEP C 5PEPFMNFUBOPMFTUÃFOFMEFTUJMBEPZUPEPFMOCVUBOPMFTUÃFOMPTGPOEPT D 5PEPFMFUBOPMFTUÃFOFMEFTUJMBEPZUPEPFMOQSPQBOPMFTUÃFOMPTGPOEPT E 5PEPFMOQSPQBOPMZFMOCVUBOPMFTUÃOFOMPTGPOEPT 1BSBFMQSPCMFNBJMVTUSBEPFOMBàHVSB EFNVFTUSFRVF-7FTNÃTDPOTUBOUFRVF-P7 DVBOEPOPFTWÃMJEPFMEFSSBNFNPMBMDPOTUBOUF&YQMJRVFQPSRVÊFTBTÎ

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT

" 5SBDFMPTQFSàMFTEFáVKPUPUBMQBSBVOBEFTUJMBDJÓODPODJODPDPNQPOFOUFT EPOEFMBBMJNFO UBDJÓOFTVOWBQPSTPCSFDBMFOUBEP*OEJRVF-Z7 " )BHBVOBUBCMBEFSFMBDJPOFTDMBWFQBSBFTUFDBQÎUVMP&TQSPCBCMFRVFEFCBJODMVJSBMHVOPT FTRVFNBT " &OMBàHVSB VOBSFDVQFSBDJÓOEFEFCFODFOPOPQSPEVDFVOBHSBOQVSF[BEFCFODF OPy1PSRVÊ y2VÊDBNCJBSÎBVTUFEQBSBRVFMBQVSF[BEFMEFTUJMBEPFOCFODFOPTFBBMUB " &YQMJRVFMBàHVSBFOUÊSNJOPTEFMBEFTUJMBDJÓOEFQBSFTCJOBSJPT " &OMBàHVSB MBTDPODFOUSBDJPOFTEFOPDMBWFQFTBEBZDMBWFQFTBEBTFDSV[BODFSDBEFMGPO EPEFMBTDPMVNOBT ZFOMBàHVSBMBTDPODFOUSBDJPOFTEFDMBWFMJHFSBZOPDMBWFMJHFSBOP TFDSV[BODFSDBEFMBQBSUFTVQFSJPSEFMBDPMVNOB&YQMJRVFDVÃOEPTFDSV[BOZOPTFDSV[BO MBTDPODFOUSBDJPOFTEFQBSFTEFDMBWFQFTBEBZOPDMBWFQFTBEB ZEFDMBWFMJHFSBZOPDMBWF MJHFSB " -B àHVSB  NVFTUSB MB EFTUJMBDJÓO EF VOB NF[DMB EF DVBUSP DPNQPOFOUFT y$ÓNP FTQFSB VTUFERVFTFWFBOMPTQFSàMFTTJFMCFODFOPGVFSBMBDMBWFMJHFSBZFMUPMVFOPMBDMBWFQFTBEB  y:TJFMYJMFOPGVFSBMBDMBWFMJHFSBZFMDVNFOPMBDMBWFQFTBEB % 1SPCMFNBT  -BTSFTQVFTUBTEFMPTQSPCMFNBTDPOVOBTUFSJTDPTFFODVFOUSBOFOMBQBSUFGJOBMEFMMJCSP % 1BSBFMQSPCMFNB" QSPQPOHBMBTIJQÓUFTJTBEFDVBEBTZEFTQFKFMPTáVKPTEFEFTUJMBEPZEF DPMBT % 4FFTUÃEFTUJMBOEPVOBNF[DMBEFCFODFOP UPMVFOPZOBGUBMFOP-BBMJNFOUBDJÓOFTUÃGPSNBEB QPSFOQFTPEFCFODFOP FOQFTPEFUPMVFOPZFOQFTPEFOBGUBMFOP&M QSPEVDUP EFTUJMBEP EFCF DPOUFOFS  FO QFTP EF CFODFOP 5BNCJÊO  FO FM EFTUJMBEP TF EFCFSFDVQFSBSEFMCFODFOP$BMDVMF B 'MVKPEFEFTUJMBEPZEFGPOEPT C $PNQPTJDJPOFTEFEFTUJMBEPZGPOEPT D 'SBDDJPOFTEFMUPMVFOPBMJNFOUBEPRVFTFSFDVQFSBFOMPTGPOEPT %  4FUJFOFVOBNF[DMBFOMBBMJNFOUBDJÓODPONPMEFNFUBOPM NPMEFFUBOPM  NPMEFOQSPQBOPMZNPMEFOCVUBOPM-BBMJNFOUBDJÓOFTMÎRVJEPTBUVSBEPZ'  LHNPMEÎB4FEFTFBUFOFSEFSFDVQFSBDJÓOEFNFUBOPMFOFMEFTUJMBEPZRVFMBGSBDDJÓO NPMEFNFUBOPMFOFMEFTUJMBEPTFB B $BMDVMF%Z# C $BMDVMFMBTDPNQPTJDJPOFTEFMEFTUJMBEPZGPOEPT %  &TUBNPTTFQBSBOEPVOBNF[DMBGPSNBEBQPSNPMEFJTPQFOUBOP NPMEFOIFYBOP ZNPMEFOIFQUBOP%FTFBNPTVOBSFDVQFSBDJÓOEFEFOIFYBOPFOMBTDPMBT ZEF EFJTPQFOUBOPFOFMEFTUJMBEP'LHNPMI-BBMJNFOUBDJÓOFTVOBNF[DMBEFEPT GBTFTDPOEFWBQPS-% B $BMDVMF%Z#)BHBVOBMJTUBEFMBTIJQÓUFTJTOFDFTBSJBT C $BMDVMFMBTDPNQPTJDJPOFTEFEFTUJMBEPZDPMBT m m D $BMDVMF- 7 - Z7 TVQPOJFOEPEFSSBNFNPMBMDPOTUBOUF E *OEJRVF  FTRVFNÃUJDBNFOUF  MPT QFSàMFT EF DPNQPTJDJÓO RVF FTQFSB QBSB JTPQFOUBOP  O IFYBOPZOIFQUBOP*EFOUJàRVFMBTDVSWBT % 6OBDPMVNOBEFEFTUJMBDJÓODPODPOEFOTBEPSUPUBMZWBQPSJ[BEPSQBSDJBMFTUÃTFQBSBOEPEPT BMJNFOUBDJPOFT-BQSJNFSBBMJNFOUBDJÓOFTVOMÎRVJEPTBUVSBEPBLHNPMIZDPOUJFOF NPMEFNFUBOPM NPMEFFUBOPM NPMEFQSPQBOPMZNPMEFCVUB OPM-BTFHVOEBFTVOMÎRVJEPTBUVSBEPRVFFOUSBBLHNPMI­TUBDPOUJFOFNPMEF

www.FreeLibros.me

5BSFB



NFUBOPM NPMEFFUBOPM NPMEFQSPQBOPMZNPMEFCVUBOPM%FTFBNPT SFDVQFSBSEFQSPQBOPMFOFMEFTUJMBEPZEFMCVUBOPMFOMPTGPOEPT$BMDVMFMPT áVKPTEFEFTUJMBEPZGPOEPTZMBTGSBDDJPOFTNPMFOMPTQSPEVDUPTEFEFTUJMBEPZGPOEPT % 6OBDPMVNOBEFEFTUJMBDJÓOFTUÃTFQBSBOEPNFUBOPM FUBOPMZCVUBOPMBBUNÓTGFSBTEFQSF TJÓO-BDPMVNOBUJFOFVODPOEFOTBEPSUPUBMZVOWBQPSJ[BEPSQBSDJBM-BBMJNFOUBDJÓOFTVO MÎRVJEPTBUVSBEPZTVáVKPFTLHNPMI5JFOFNPMEFNFUBOPM NPMEFFUBOPM ZNPMEFCVUBOPM-BSB[ÓOEFSFáVKPFT-% ZFMSFáVKPSFHSFTBDPNPMÎRVJEP TBUVSBEP%FTFBNPTRVFMBSFDVQFSBDJÓOEFFUBOPMFOFMEFTUJMBEPTFBZRVFMBSFDVQFSB DJÓOEFCVUBOPMFOMPTGPOEPTTFB$BMDVMF%Z# ZMBTGSBDDJPOFTNPMBMFTFOEFTUJMBEP ZFODPMBT % &TUBNPTTFQBSBOEPIJESPDBSCVSPTFOVOBDPMVNOBDPOEPTBMJNFOUBDJPOFT-BDPMVNOBGVO DJPOBBQTJH5JFOFVODPOEFOTBEPSUPUBMZVOWBQPSJ[BEPSQBSDJBM-BQSJNFSBBMJNFOUBDJÓO UJFOFEFFUBOPFOQFTP EFQSPQJMFOPFOQFTP EFQSPQBOPFOQFTP EF OCVUBOPFOQFTPZEFOQFOUBOPFOQFTP-BBMJNFOUBDJÓOFTVOMÎRVJEPTBUVSBEPRVFFOUSBB LHI-BTFHVOEBBMJNFOUBDJÓODPOUJFOFEFFUBOPFOQFTP FOQFTPEFQSPQJMFOP FOQFTP EFQSPQBOPFOQFTP EFOCVUBOPFOQFTP EFOQFOUBOPFOQFTPZ EFOIFYBOPFOQFTP&TBBMJNFOUBDJÓOFOUSBBLHIDPNPMÎRVJEPTBUVSBEP%FTFB NPTEFSFDVQFSBDJÓOEFMQSPQBOPFOFMEFTUJMBEPZEFSFDVQFSBDJÓOEFOCVUBOPFO MBTDPMBT1SPQPOHBUPEBTMBTIJQÓUFTJTOFDFTBSJBTZDBMDVMFMBTUBTBTEFáVKPEFEFTUJMBEPZGPO EPT5BNCJÊODBMDVMFMBTGSBDDJPOFTFOQFTPEFDBEBDPNQPOFOUFFOMBTDPSSJFOUFTEFEFTUJMBEP ZGPOEPT % 4F UJFOF VOB DPMVNOB EF EFTUJMBDJÓO RVF FTUÃ TFQBSBOEP FUBOP EF OQFOUBOP Z OIFYBOP Z GVODJPOBBL1B5JFOFVODPOEFOTBEPSUPUBMZVOWBQPSJ[BEPSQBSDJBM-BUBTBEFáVKPEF MB BMJNFOUBDJÓO FO GPSNB EF MÎRVJEP TBUVSBEP FT  LHNPMI -B BMJNFOUBDJÓO DPOUJFOF NPMEFFUBOP NPMEFOQFOUBOPZFMSFTUPFTOIFYBOP%FTFBNPTSFDVQFSBS EFMFUBOPFOFMEFTUJMBEPZEFMOQFOUBOPFOMPTGPOEPT6TFVOBSFMBDJÓOEFWBQPS BMGPOEPJHVBMB4VQPOHBWÃMJEPFMEFSSBNFNPMBMDPOTUBOUF B $BMDVMFFMáVKPEFGPOEPT C $BMDVMFMBTGSBDDJPOFTNPMBMFTEFMPTDPNQPOFOUFTFOMPTGPOEPT m m D $BMDVMF- Z7 

www.FreeLibros.me

$"1±56-0 

1SPDFEJNJFOUPTEFDÃMDVMPFYBDUP QBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT

:BRVFMPTDÃMDVMPTDPOWBSJPTDPNQPOFOUFTTFIBDFOQPSUBOUFPT DPOWJFOFIBDFSMPTFODPNQV UBEPSB$PNPMPTDÃMDVMPTEFFUBQBQPSFUBQBTFMJNJUBOBQSPCMFNBTFOMPTRVFTFQVFEFQSPQPOFS VOCVFOWBMPSUFOUBUJWPEFMBTDPNQPTJDJPOFTFOBMHÙOQVOUPEFMBDPMVNOB TFVTBONÊUPEPTNBUSJ DJBMFTQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT&TPTNÊUPEPTOPTFSFTUSJOHFOBDBTPTFOMPTRVFTF QVFEFQSPQPOFSVOBCVFOBQSJNFSBFTUJNBDJÓO  * /530%6$$*¶/"-"40-6$*¶/."53*$*"-1"3"%&45*-"$*¶/ %&7"3*04$0.10/&/5&4

$PNPMBEFTUJMBDJÓOFTVOBUÊDOJDBNVZEFTFQBSBDJÓOJNQPSUBOUF TFIBOIFDIPHSBOEFTFTGVFS[PT QBSBQSPQPOFSNFKPSFTNÊUPEPTEFDÃMDVMP­TUPTTFFODVFOUSBOFOEFUBMMFFOEJWFSTPTMJCSPTEF UFYUP 4FBEFSZ)FOMFZ )PMMBOE ,JOH Z4NJUI  &OFTUBTFDDJÓOTFFYQMJDBSÃ VONÊUPEPNBUSJDJBMSFMBUJWBNFOUFTFODJMMP RVFVTBFMNÊUPEPuEFDPOWFSHFODJB &M DPNQPSUBNJFOUP HFOFSBM QBSB DPMVNOBT EF WBSJPT DPNQPOFOUFT WFB FM DBQÎUVMP   Z MPT CBMBODFTCÃTJDPTEFNBTBZFOFSHÎB ZMBTSFMBDJPOFTEFFRVJMJCSJPOPDBNCJBODVBOEPTFVTBOEJGF SFOUFTQSPDFEJNJFOUPTEFDÃMDVMP FTEFDJS MBPQFSBDJÓOGÎTJDBOPDBNCJBFOUPODFT MBTMFZFTZMPTSF TVMUBEPTCÃTJDPTTPOJOWBSJBOUFT -PTEJGFSFOUFTQSPDFEJNJFOUPTEFDÃMDVMPPSEFOBOMBTFDVBDJPOFT QBSBBVNFOUBSMBDPOWFSHFODJB FOFTQFDJBMDVBOEPFTEJGÎDJMIBDFSVOBCVFOBQSJNFSBFTUJNBDJÓO &MNÊUPEPNÃTDPNÙOFTBHSVQBSZSFTPMWFSMBTFDVBDJPOFTQPSUJQPZOPFUBQBQPSFUBQB&TUPFT  TFBHSVQBOUPEPTMPTCBMBODFTEFNBTBQBSBFMDPNQPOFOUFJZTFSFTVFMWFOTJNVMUÃOFBNFOUFTF BHSVQBOUPEPTMPTCBMBODFTEFFOFSHÎBZTFSFTVFMWFOTJNVMUÃOFBNFOUF FUDÊUFSB-BNBZPSÎBEFMBT FDVBDJPOFTTFQVFEFOFTDSJCJSGÃDJMNFOUFFOGPSNBNBUSJDJBM-BTSVUJOBTEFDÓNQVUPQBSBMBTPMV DJÓOTJNVMUÃOFBEFFTUBTFDVBDJPOFTEFFTDSJCFODPOGBDJMJEBE-BWFOUBKBEFFTUFNÊUPEPFTRVFTF QVFEFIBDFSRVFDPOWFSKBOIBTUBMPTQSPCMFNBTNVZEJGÎDJMFT &MDPOKVOUPEFWBSJBCMFTNÃTDÓNPEPEFFTQFDJàDBSFT' [J 5' / /' Q 5SFG -%Z%4FQVFEF FTQFDJàDBSWBSJBTBMJNFOUBDJPOFT&OUPODFT FTVOQSPCMFNBEFTJNVMBDJÓODPOáVKPEFEFTUJMBEP FTQFDJàDBEP1BSBQSPCMFNBTEFEJTFÒPEFCFQSPQPOFSTFVOCVFOQSJNFSWBMPSUFOUBUJWPEF/Z/' WFBFMDBQÎUVMP ZEFTQVÊTTFSFTVFMWFVOBTFSJFEFQSPCMFNBTEFTJNVMBDJÓOQBSBMPHSBSFMNFKPS EJTFÒP 

www.FreeLibros.me

  *OUSPEVDDJÓOBMBTPMVDJÓONBUSJDJBMQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT



Ingresar: Datos de equilibrio y entalpía Ingresar: Condiciones especificadas Seleccionar Lj, Vj y Tj iniciales en cada etapa Calcular valores de K para todos los componentes en cada etapa Resolver el balance de masa de componentes y las ecuaciones de equilibrio en forma matricial, Ecs. (6-1) a (6-13) Sustitución directa nueva Tj

Calcular temperaturas en cada etapa usando convergencia u y cálculos de punto de burbuja. Ecs. (6-17) a (6-25)

No

Prueba de convergencia: ¿Es u = 1.00?

Sustitución directa, nuevas Lj y vj

Sí Guardar balance de energía en cada etapa. Calcular Lj y Vj. Ecs. (6-26) a (6-39) Prueba de convergencia: Ecs. (6-40)

No se satisface

Se satisface Fin

'*(63" %*"(3"."%&'-6+01"3"&-$¦-$6-0."53*$*"-%&%&45*-"$*¶/ $0/7"3*04$0.10/&/5&4 -PTQSPCMFNBTEFEFTUJMBDJÓODPOWFSHFONFKPSTJTFIBDFVODÃMDVMPEFBMJNFOUBDJÓODPOFCV MMJDJÓOFTUSFDIB FOMVHBSEFMDÃMDVMPEFBMJNFOUBDJÓODPOFCVMMJDJÓOBNQMJBRVFTFVTÓQBSBMBEFTUJ MBDJÓOJOTUBOUÃOFBFOFMDBQÎUVMP&MQSPDFEJNJFOUPEFFCVMMJDJÓOFTUSFDIB PEFQVOUPEFCVSCVKB  TFWFFOMBàHVSB&OÊTUBTFVTBOMPTDÃMDVMPTEFFRVJMJCSJP QVOUPEFCVSCVKB QBSBEFUFSNJOBS OVFWBTUFNQFSBUVSBTFMCBMBODFEFFOFSHÎBTFVTBQBSBDBMDVMBSOVFWBTUBTBTEFáVKP-BTUFNQFSB UVSBTTFDBMDVMBOZTFIBDFODPOWFSHFSQSJNFSPZEFTQVÊTTFEFUFSNJOBOOVFWBTUBTBTEFáVKP&TUF QSPDFEJNJFOUP UJFOF TFOUJEP QPSRVF TF QVFEF IBDFS VOB CVFOB QSJNFSB FTUJNBDJÓO EF MPT áVKPT EFMÎRVJEPZWBQPSTVQPOJFOEPEFSSBNFNPMBMDPOTUBOUF"TÎ MBTUFNQFSBUVSBTTFDBMDVMBOVTBOEP WBMPSFTSB[POBCMFTEFUBTBTEFáVKP-PTCBMBODFTEFFOFSHÎBTFVTBOBMÙMUJNP QPSRVFSFRVJFSFO WBMPSFTEFYJ K ZJ KZ5K

www.FreeLibros.me



$BQÎUVMP  1SPDFEJNJFOUPTEFDÃMDVMPFYBDUPQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT

-BàHVSBGVFFMBCPSBEBQBSBVOTJTUFNBJEFBM EPOEFMBT,JEFQFOEFOTÓMPEFMBUFNQFSBUVSB ZMBQSFTJÓO4JMBT,JEFQFOEFOEFMBTDPNQPTJDJPOFT ÊTUBTEFCFOFTUJNBSTFZDPSSFHJSTFBOUFTEF IBDFSFMDÃMDVMPEFMBUFNQFSBUVSB4ÓMPEFTDSJCJSFNPTBRVÎTJTUFNBTFOMPTRVF,J,J 5 Q   #"-"/$&4%&."4"%&$0.10/&/5&4&/'03."%&."53*$&4

1BSBQPOFSFOGPSNBBEFDVBEBMPTCBMBODFTEFNBTBFOGPSNBNBUSJDJBM TFOVNFSBMBDPMVNOBDPNP TFWFFOMBàHVSB-BFUBQBFTFMDPOEFOTBEPSUPUBM MBFUBQBFTMBFUBQBTVQFSJPSEFMBDPMVN OB MBFUBQB/−FTMBFUBQBEFMGPOEPZFMWBQPSJ[BEPSQBSDJBMFTMBFUBQB/1BSBVOBFUBQBHFOFSBM KEFOUSPEFMBDPMVNOB àHVSB

FMCBMBODFEFNBTBQBSBDVBMRVJFSDPNQPOFOUFFT 

K_ n_ A_ m _ − K_ & n_ & − A _−&m _−& 2;_ o _ 



-BTDPNQPTJDJPOFTEFTDPOPDJEBTEFWBQPS ZKZZK  TFQVFEFOTVTUJUVJSVTBOEPMBTFDVBDJPOFTEF FRVJMJCSJP 

n_ 2@ _ m _

n

n_ & 2@ _ & m _ & 



EPOEFMPTWBMPSFTEF,EFQFOEFOEF5ZQ4JUBNCJÊOTVTUJUVJNPTBYKZYK−DPO m _ 2,_ $A _!m _−& 2,_−&$A _−& 



B C

EPOEF,KZ,K−TPOMBTUBTBTEFáVKPEFMDPNQPOFOUFMÎRVJEP SFTVMUB 

− &,_−&

&

K_ @_ A_

,_

−

K_ &@ _ A_

&

,_ & 2;_o _ 

&

'*(63" $0-6./"%&%&45*-"$*¶/ 1"3""/¦-*4*4."53*$*"-

www.FreeLibros.me



  #BMBODFTEFNBTBEFDPNQPOFOUFTFOGPSNBEFNBUSJDFT



'*(63" &5"1"(&/&3"-&/-"$0-6./"

&TUBFDVBDJÓOTFQVFEFFTDSJCJSFOMBGPSNBHFOFSBM 6 _ ,_−& 7_ ,_ 8_,_ & 29_ 





-BTDPOTUBOUFT"K #K $KZ%KTFDBMDVMBODPOGBDJMJEBEDPNQBSBOEPMBTFDVBDJPOFT  Z   

6_ 2−

_

2&

K_ @ _ A_

_

2−

K_ & @ _ A_

& _

2;_ o _ 



&

-BTFDVBDJPOFT  Z  TPOWÃMJEBTQBSBUPEBTMBTFUBQBTFOMBDPMVNOB  K /− ZTFSFQJUFO QBSBDBEBVOPEFMPT$DPNQPOFOUFT4JVOBFUBQBOPUJFOFBMJNFOUBDJÓO FOUPODFT'K%K 1BSBVODPOEFOTBEPSUPUBM FMCBMBODFEFNBTBFT 

A&m& 9m9 − K'n' 2;&o& 



$PNPYY% Z,YZY,- FMFRVJMJCSJPTFUSBOTGPSNBFO 

8& ,' 7& ,& 29& 



8& 2−@'K'$A'!7& 2& 9$A&!9& 2;&o& 



TJFOEP 

0CTFSWFRVFTÓMP#OPTFBQFHBBMBTGÓSNVMBTHFOFSBMFTEFMBFDVBDJÓO  &TUPQBTBQPSRVFFM DPOEFOTBEPSUPUBMOPFTVODPOUBDUPEFFRVJMJCSJP 1BSBFMWBQPSJ[BEPS FMCBMBODFEFNBTBFT 

−AC−&mC−& KCnC 7mXdaV 2;CoC 



"MTVTUJUVJSZ/,/,/Z,/-/9/#YDPMB SFTVMUB 

6 C ,C−& 7C ,C 29C 

www.FreeLibros.me





$BQÎUVMP  1SPDFEJNJFOUPTEFDÃMDVMPFYBDUPQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT

FOEPOEF 6 C 2−



C

2&

KC @ C 2& AC

KC @ C 7

C

2;C o C 



&OOPUBDJÓONBUSJDJBM QBSBDBEBDPNQPOFOUF FMCBMBODFEFNBTBZMBFDVBDJÓOEFFRVJMJCSJPTPO

™ % % % & % % 6 7 8 ™ % % % & % % 8 6 7 ™ % % % & ™ ™ ™ ™ ™ ™ ™ ™ ™ ™ % % % % % ™ 6 7 8 & % % % % % ™ % 6 7 & 7&

8&

'

'

'

(

(

%

%

%

(

C−&



&

9&

'

9'

(

9( 2

™

C−&

C−&

C−&

9C−&

C

C

C

9C





&TUFDPOKVOUPEFFDVBDJPOFTBMHFCSBJDBTMJOFBMFTZTJNVMUÃOFBTTFQVFEFSFTPMWFSJOWJSUJFOEPMBNB USJ[EF"#$&TPTFIBDFVTBOEPDVBMRVJFSSVUJOBOPSNBMEFJOWFSTJÓOEFNBUSJDFT-BGPSNBNBUSJ DJBMRVFNVFTUSBMBFDVBDJÓO  TFMMBNBNBUSJ[USJEJBHPOBM RVFFTFTQFDJBMNFOUFGÃDJMEFJOWFSUJS VTBOEPFMBMHPSJUNPEF5IPNBT WFBMBUBCMB  -BQJEVT ,JOH  -BJOWFSTJÓOEFMB NBUSJ["#$QFSNJUFIBDFSMBEFUFSNJOBDJÓOEJSFDUBEFMáVKPEFDPNQPOFOUFMÎRVJEPMKRVFTBMFEF DBEBDPOUBDUP6TUFEEFCFGPSNBSMBNBUSJ["#$FJOWFSUJSMB QBSBDBEBVOPEFMPTDPNQPOFOUFT -PTUÊSNJOPT" #Z$FOMBFDVBDJÓO  TFEFCFODBMDVMBS QFSPEFQFOEFOEFMPTáVKPTEF MÎRVJEPZWBQPS ZEFMBUFNQFSBUVSB FOMPTWBMPSFTEF, FODBEBFUBQB RVFOPTFDPOPDFO1BSB DPNFO[BSTFQSPQPOFO-K 7KZ5KQBSBDBEBFUBQBK1BSBTJTUFNBTJEFBMFT TFQVFEFODBMDVMBSMPT WBMPSFTEF,QBSBDBEBDPNQPOFOUFFODBEBFUBQBFOUPODFTFTQPTJCMFDBMDVMBSMPTUÊSNJOPT" #Z $QBSBDBEBDPNQPOFOUFFODBEBFUBQB$POMBJOWFSTJÓOEFMBTNBUSJDFTQBSBDBEBDPNQPOFOUFTF 5"#-" "-(03*5.0%&5)0."41"3"*/7&35*3."53*$&453*%*"(0/"-&4 1BSBDBMDVMBSMBTPMVDJÓOEFVOBNBUSJ[FOMBGPSNBEFMBFDVBDJÓO 

FOEPOEFTFDPOPDFOUPEPTMPT DPFàDJFOUFT"K #K $KZ%K  $BMDVMFUSFTWBSJBCMFTJOUFSNFEJBTQBSBDBEBSFOHMÓOEFMBNBUSJ[ DPNFO[BOEPDPOK1BSB &≤ _≤ C! K&_ 27_ − 6_K(_−& K'_ 2P9_ − 6_K'_−&R$K&_ K(_ 28_$K&_ ZBRVF"   7 #Z 7 % 7   *OJDJBMJDF 7 Z 7  QBSBQPEFSVTBSMBTGÓSNVMBTHFOFSBMFT  $BMDVMFUPEBTMBTJODÓHOJUBT6K$PNJFODFDPOK/ZDBMDVMF 6/ 7 / &OUPODFT ZFOEPEFK/−IBDJBK DBMDVMF6/− 6/−  6 DPO 6K 7 K− 7 K6K     K /−

www.FreeLibros.me

  $ÃMDVMPTEFQVOUPEFCVSCVKB



PCUJFOFMBMK-BTUBTBTEFáVKPEFDPNQPOFOUFTMÎRVJEPTTPODPSSFDUBTQBSBMPT-K 7KZ5KTVQVFTUPT -PTWBMPSFTEFYKQBSBDBEBDPNQPOFOUFTFQVFEFOEFUFSNJOBSDPOMBFDVBDJÓO B   130104*$*¶/*/*$*"-1"3"5"4"4%&'-6+0

6OBQSPQVFTUBJOJDJBMSB[POBCMFQBSB-KZ7KFTTVQPOFSEFSSBNFNPMBMDPOTUBOUF&TUFEFSSBNFOP GVFTVQVFTUPFOMBTFDVBDJPOFT  B  $POMBIJQÓUFTJTEFEFSSBNFNPMBMDPOTUBOUF QPEFNPT VTBSMPTCBMBODFTHFOFSBMFTEFNBTBQBSBDBMDVMBSUPEPTMPT-KZ7K 1BSBJOJDJBSFMDÃMDVMPOFDFTJUBNPTTVQPOFSMBEJWJTJÓOQBSBDPNQPOFOUFTOPDMBWFT /$ -B QSJNFSB IJQÓUFTJT PCWJB FT RVF UPEB MB OP DMBWF MJHFSB /$-  TBMF FO FM EFTUJMBEP  EF NPEP RVF Y/$- GPOEPTZ%Y/$- EFTU'[/$-ZUPEBTMBTOPDMBWFTQFTBEBT /$1 TBMFOFOMBTDPMBT Y/$1 EFTU Z #Y/$1 GPOEPT'[/$1"IPSBQPESFNPTIBDFSMPTCBMBODFTFYUFSOPTEFNBTBQBSBEFUFSNJOBSUPEBTMBT DPNQPTJDJPOFTZáVKPTEFEFTUJMBEPZGPOEPT&TUPTFWJPFOFMDBQÎUVMP6OBWF[IFDIP TFEFUFS NJOBO-Z7FOMBTFDDJÓOEFSFDUJàDBDJÓO$PNPTFTVQPOFEFSSBNFNPMBMDPOTUBOUF A2

A% 9! 9

K2A 9

&OMBFUBQBEFBMJNFOUBDJÓO RTFQVFEFFTUJNBSBQBSUJSEFMBTFOUBMQÎBTDPNPTJHVF fs

=− ] Va^b =− ]

PCJFO R-''TFQVFEFEFUFSNJOBSDPOVODÃMDVMPEFFWBQPSBDJÓOJOTUBOUÃOFBFOMBDPSSJFOUFEF m m BMJNFOUBDJÓO&OUPODFTTFEFUFSNJOBO- Z7 DPOMPTCBMBODFTFOMBFUBQBEFBMJNFOUBDJÓO A 2A f;!

K 2K &− f;

$POFTPTFUFSNJOBOMPTDÃMDVMPTQSFMJNJOBSFTEFMBTUBTBTEFáVKP  $¦-$6-04%&16/50%&#63#6+"

-BUFNQFSBUVSBTFQVFEFFTUJNBSDPODÃMDVMPTEFQVOUPEFCVSCVKB$POGSFDVFODJBCBTUBIBDFSVO DÃMDVMPEFQVOUPEFCVSCVKBQBSBMBBMJNFOUBDJÓO QBSBQPEFSVTBSFTUBUFNQFSBUVSBFODBEBQMBUP 4FQVFEFPCUFOFSVONFKPSWBMPSQSPQVFTUPFTUJNBOEPMBTDPNQPTJDJPOFTEFEFTUJMBEPZDPMBT FO HFOFSBM MBTOPDMBWFTOPTFEJTUSJCVZFO ZIBDJFOEPDÃMDVMPTEFQVOUPEFCVSCVKBQBSBBNCBT%FT QVÊT TFTVQPOFRVFMBUFNQFSBUVSBWBSÎBFOGPSNBMJOFBMEFVOBBPUSBFUBQB -BUFNQFSBUVSBEFQVOUPEFCVSCVKB 51# FTBRVFMMBBMBRVFMBNF[DMBMÎRVJEBDPNJFO[BBIFSWJS 1BSBVODÃMDVMPEFQVOUPEFCVSCVKBTFEFCFOFTQFDJàDBSMBQSFTJÓOQZMBTGSBDDJPOFTNPMEFMMÎRVJEP  YJ4FEFTFBEFUFSNJOBSMBUFNQFSBUVSB51#BMBRVF ZJMBTZJTFDBMDVMBODPNPZJ,J 51# YJ4JTF EJTQPOFEFVOBFDVBDJÓOTFODJMMBQBSB,JFOGVODJÓOEFMBUFNQFSBUVSB QPESFNPTSFTPMWFSMBFDVBDJÓO RVFSFTVMUFQBSBMBUFNQFSBUVSB%FOPTFSBTÎTFOFDFTJUBSÃVOBUÊDOJDBEFEFUFSNJOBDJÓOEFSBÎDFTP VOQSPDFEJNJFOUPEFUBOUFPT$VBOEPTFVTBOHSÃàDBTPUBCMBT TJFNQSFTFOFDFTJUBVOQSPDFEJNJFOUP EFUBOUFPT&TUFQSPDFEJNJFOUPTFNVFTUSBFOMBàHVSB$VBOEPTFUFSNJOBOMPTDÃMDVMPT MBTZJ DBMDVMBEBTDPSSFTQPOEFOBMBTGSBDDJPOFTNPMEFMBQSJNFSBCVSCVKBEFHBTRVFTFGPSNB y$ÓNPFTUJNBSVOCVFOQSJNFSWBMPSUFOUBUJWPQBSBMBUFNQFSBUVSBJOJDJBM /PUFRVF YJ ZRVF ,JYJ4JUPEBTMBT,J TFEFCFDVNQMJSRVF ,JYJ4JUPEBTMBT ,J FOUPODFT ,JYJ1PSDPOTJHVJFOUF TFEFCFSÎBFTDPHFSVOBUFNQFSBUVSBUBMRVFBMHVOBT

www.FreeLibros.me



$BQÎUVMP  1SPDFEJNJFOUPTEFDÃMDVMPFYBDUPQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT

Estimar T

Calcular Ki(T, p, xi)

¿Es Estimar nueva T



'*(63" %*"(3"."%&'-6+01"3"&- $¦-$6-0%&16/50%&#63#6+"

FIN T = TPB

,JTFBONBZPSFTRVFZBMHVOBTNFOPSFTRVF6OBGPSNBEFIBDFSMPFTEFUFSNJOBSMBUFNQF SBUVSBEFFCVMMJDJÓOEFDBEBDPNQPOFOUF ,J ZFTUJNBS5DPNP5 [J5J ,J  y$ÓNPTFTFMFDDJPOBVOBOVFWBUFNQFSBUVSBDVBOEPFMUBOUFPBOUFSJPSOPGVFFYBDUP 4JWFNPTMBTHSÃàDBTEF%F1SJFTUFSPMBFDVBDJÓO 

OPUBSFNPTRVFMBT,JTPOGVODJPOFT DPNQMFKBTEFMBUFNQFSBUVSB4JOFNCBSHP MBGVODJÓOFTCBTUBOUFQBSFDJEBQBSBUPEBTMBT,&OUPO DFT MBWBSJBDJÓOEF,QBSBVODPNQPOFOUF FMDPNQPOFOUFEFSFGFSFODJB ZMBWBSJBDJÓOFOFMWBMPS EF ,JYJ TFSÃCBTUBOUFQBSFDJEB1PESFNPTFTUJNBSFMWBMPSBEFDVBEPEF,QBSBFMDPNQPOFOUFEF SFGFSFODJBDPO 

@gZ[

cjZkV

2

@gZ[ I Vci 8





@^ m ^  XVaX ^2&

-BUFNQFSBUVSBQBSBFMTJHVJFOUFJOUFOUPTFEFUFSNJOBBQBSUJSEFMOVFWPWBMPS ,SFG 5OVFWB &TUFQSP DFEJNJFOUPEFCFDPOWFSHFSSÃQJEBNFOUF$PNPBMUFSOBUJWBTFQVFEFVTBSVOFTRVFNBEFDPOWFS HFODJBEF/FXUPO4JMBTWFMPDJEBEFTSFMBUJWBTTPODPOTUBOUFT TFQVFEFDBMDVMBSFMWBMPSEF,SFGDPO 

@gZ[ 2

& 8



B

m ^ α ^−gZ[ 

^2&

ZMBTGSBDDJPOFTNPMFOFMWBQPSTPO 

n^ 2

m^ α



8

m ^



^2&

www.FreeLibros.me

C

  $ÃMDVMPTEFQVOUPEFCVSCVKB



&+&.1-0 5FNQFSBUVSBEFQVOUPEFCVSCVKB y$VÃMFTMBUFNQFSBUVSBEFQVOUPEFCVSCVKBEFVOBNF[DMBRVFDPOUJFOFNPMEFJTP QFOUBOP J$

NPMEFOQFOUBOP O$ ZNPMEFOIFYBOP O$ -BQSFTJÓO FTBUN 4PMVDJÓO " %FGJOB4FOFDFTJUBVOB5QBSBMBDVBM ZJ ,JYJ # &YQMPSF4FRVJFSFVTBSVOQSPDFEJNJFOUPEFQSVFCBZFSSPS4JVTBNPTMBTHSÃàDBTEF %F1SJFTUFS àHVSBTZ ZDPOWFSUJNPTMBQSFTJÓOEFBUNBL1B e2&#%Vib

&%&#(`EV 2&%&#(`EV &#%Vib

5BNCJÊOTFQVFEFVTBSMBFDVBDJÓO  -BVTBSFNPTQBSBFMQBTPEFWFSJàDBDJÓO $ 1MBOFF1BSBMBQSJNFSB5 VTBSFNPTVOBQBSBMBDVBM,JD,OD,OD VTFVOB HSÃàDB EF %F1SJFTUFS  &OUPODFT  VTF MB FDVBDJÓO   QBSB DBMDVMBS ,SFG Z DPO MB HSÃàDB EF %F1SJFTUFS  EFUFSNJOF 5 &TDPKB O$ DPNP FM DPNQPOFOUF EF SFGFSFODJB BSCJUSBSJBNFOUF  % )ÃHBMP1SJNFSJOUFOUP6TBOEPMBàHVSBBž$,JD ,OD ,OD &OUPODFT ž$ ZNVDIBTPUSBTUFNQFSBUVSBT TBUJTGBDFOVFTUSPTDSJUFSJPTQBSBQSJNF SBUFOUBUJWB 7FSJàDBDJÓO (

(

@ ^ m ^ 

n^ 2 ^2&

^2&

2'#%'#%&* &#**%#(% %#*+%#**2&#%,+

&TNVZBMUP ZMBUFNQFSBUVSBEFž$FTBMUB $POMBFDVBDJÓO  DBMDVMBS @X+cjZkV 2

@X+Vci %#*+ 2 2%#*' Σ@^m^ &#%,+

$POMBHSÃàDBEF%F1SJFTUFS TFWFRVFMBUFNQFSBUVSBDPSSFTQPOEJFOUFFT5ž$ "FTUBUFNQFSBUVSB ,JD ,OD0CTFSWFRVFUPEBTMBT,TPONFOPSFT Z FOUPODFTMBTVNBTFSÃNFOPS&OUPODFT Σn^ 2Σ@^m^ 2&#.'%#&* &#*%%#(% %#*'%#**2&#%')

-BTJHVJFOUF,D   RVFDPSSFTQPOEFB5ž$ "FTUBUFNQFSBUVSB ,JD ,OD 7FSJàDBDJÓO ,JYJ            &TNÃTPNFOPTMPNÃTRVFTFQVFEFVOPBDFSDBSDPOMBHSÃàDBEF%F1SJFTUFS"TÎ MBUFN QFSBUVSBEFMQVOUPEFCVSCVKBFTž$ -PTWBMPSFTEFZJTPOJHVBMFTB,JYJ"TÎ ZJD    ZOD      ZOD   -PTWBMPSFTEFZTFEFCFOSFEPOEFBSBEPTDJGSBT TJHOJàDBUJWBTDVBOEPBQBSF[DBOFOBMHÙOJOGPSNF

www.FreeLibros.me



$BQÎUVMP  1SPDFEJNJFOUPTEFDÃMDVMPFYBDUPQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT

& $PNQSVFCF$POMBFDVBDJÓO  TFQVFEFPCUFOFSVOBTPMVDJÓOBMUFSOBUJWB"DPO UJOVBDJÓOTFEFTDSJCFDPOCSFWFEBEFTUFQSPDFEJNJFOUP FSWBMPSQSPQVFTUP 5ž$ž' ž3 QQTJB 1BSBJ$ O$ O$ MBFDVBDJÓO  TFTJNQMJàDBB ac@2V I& 



&  V I+ V e&ace I' 

B

DVZPSFTVMUBEPFT,J$ ,O$ ,O$&OUPODFT n& 2

@ ^ m ^ 2'#%%+*%#&* &#*('*%#( %#*+,+%#**2&#%,'.

&TEFNBTJBEPHSBOEF1BSBMBTJHVJFOUFEFUFSNJOBDJÓO VTFMBFDVBDJÓO   @8+cjZkV 2

@8+6ci

2

%#*+,+

2%#*'.%

&#%,'.

@ ^m ^

%FMBFDVBDJÓO B TFEFTQFKB5 I2



VI&

&$'

,c@− VI+ − Ve&,ce− Ve' $e' − Ve( $e

C



ZFMSFTVMUBEPFT5ž36TBSFNPTFTUFOVFWPWBMPSQBSBDPOUJOVBS&MSFTVMUBEPFT 5ž3ž$&TUFSFTVMUBEPRVFEBEFOUSPEFMNBSHFOEFFSSPSEFMBFDVBDJÓO  

BMDPNQBSBSMPDPOMPTž$EFUFSNJOBEPTDPOMBTHSÃàDBTEF%F1SJFTUFS-BFDVBDJÓO C FTWÃMJEBQBSBUPEPTMPTIJESPDBSCVSPTRVFBQBSFDFOFOMBTHSÃàDBTEF%F1SJFTUFS  FYDFQUPOPDUBOPZOEFDBOP ' (FOFSBMJDF4JMPTWBMPSFTEF,EFQFOEFOEFMBDPNQPTJDJÓO TFOFDFTJUBSÃVODJDMPBEJ DJPOBMFOFMQSPDFEJNJFOUPEFUBOUFPT$VBOEPMPTWBMPSFT,FTUÃOFOGPSNBEFFDVB DJÓO DPNPMBFDVBDJÓO 

MPTDÃMDVMPTEFQVOUPEFCVSCVKBTPOGÃDJMFTEFQSPHSBNBS FODBMDVMBEPSBTPDPNQVUBEPSBT$PO,FOGPSNBEFFDVBDJÓOUBNCJÊOTFQVFEFFTDSJ CJS ,JYJDPNPVOBTPMBFDVBDJÓO ZEFTQFKBS5OVNÊSJDBNFOUF$POVOTJNVMBEPS EFQSPDFTPTFVTBSÃVOBEFMBTDPSSFMBDJPOFTEFFRVJMJCSJPWBQPSMÎRVJEP WFBMBUBCMB 

QBSBDBMDVMBS51#ZMPTWBMPSFTEFZJ  .­50%0 %&$0/7&3(&/$*"

%FTQVÊTEFMQSJNFSWBMPSUFOUBUJWPZMBTPMVDJÓOEFMBTFDVBDJPOFTNBUSJDJBMFTEFCFDPSSFHJSTFMB UFNQFSBUVSB&TPTFIBDFDPODÃMDVMPTEFQVOUPEFCVSCVKBFODBEBFUBQB%FTBGPSUVOBEBNFOUF  FMQFSàMEFUFNQFSBUVSBUJFOEFBOPDPOWFSHFS4FQVFEFPCUFOFSMBDPOWFSHFODJBDPOVONÊUPEP  MMBNBEPNÊUPEPu&OÊTUF QSJNFSPTFBKVTUBOMBTUBTBTEFáVKPEFDPNQPOFOUFTQBSBTBUJTGBDFSMB UBTBEFáVKPEFEFTUJMBEPFTQFDJàDBEB%FTQVÊTTFEFUFSNJOBOMBTGSBDDJPOFTNPMBSFTDPOFTUBTUBTBT EFáVKPEFDPNQPOFOUFBKVTUBEBTZTFIBDFOMPTDÃMDVMPTEFQVOUPEFCVSCVKBFODBEBFUBQBQBSB DBMDVMBSMBOVFWBUFNQFSBUVSBFODBEBFUBQB &M NÊUPEP u )PMMBOE    ,JOH    4FBEFS Z )FOMFZ    4NJUI    TF EFàOF VOB DBOUJEBEuRVFIBDFTBUJTGBDFS BGVFS[B MBTJHVJFOUFFDVBDJÓO

www.FreeLibros.me

  .ÊUPEPuEFDPOWFSHFODJB



8



9ZheZX 2 ^2&

;o ^  & θ 7m ^!XdaV$ 9m ^!XVaX XVaX



&OPUSBTQBMBCSBT  FTMBSBÎ[EFMBFDVBDJÓO  &TUBFDVBDJÓOUJFOFVOBSBÎ[SFBMZQPTJUJWB  RVF TF EFUFSNJOB DPO GBDJMJEBE NFEJBOUF VO QSPDFEJNJFOUP EF DPOWFSHFODJB EF /FXUPO 4J FTB FDVBDJÓOTFFTDSJCFFOMBGPSNB 8



;o^ & θ 7m ^!XdaV $ 9m ^!XVaX XVaX

[θ  2 ^2&

9ZheZX 2 % 



FOUPODFT FMOVFWPWBMPSUFOUBUJWPEFuFT ` &

2

[ `

8



^2&

`

;o ^ 7m ^!XdaV $ 9m ^!XVaX XVaX P&  ` 7m ^!XdaV $ 9m ^!XVaX XVaX R' 



&OFTUBTFDVBDJPOFT  #YJ DPMB DBMDZ %YJ EFTU DBMDTPOMPTWBMPSFTDBMDVMBEPTDPOMBTPMVDJÓOEFMBFDVBDJÓO   

#YJ DPMB DBMD*/ J

B



%YJ EFTU DBMD* J -% 

C

6OBWF[EFUFSNJOBEBu TFQVFEFDPSSFHJSMBTUBTBTEFáVKPEFMPTDPNQPOFOUFT&TUBTUBTBT DPSSFHJEBT QBSBDBEBDPNQPOFOUF TPO 

9m ^!YZhi Xdgg 2

;o ^  & θ 7m ^!XdaV $ 9m ^!YZhi XVaX

7m ^!XdaV Xdgg 2 9m ^!YZhiXdgg θ 

7m ^!XdaV  9m ^!YZhi XVaX

B

C

  0CTFSWFRVFMBTFDVBDJPOFT 

 B Z C EBODPNPSFTVMUBEP 8

B

9m ^!YZhi Xdgg 29 ZheZX ^2&





8

C

7m ^!XdaV Xdgg 2 ;−9ZheZX 27 ^2&

  %FFTUFNPEP FMNÊUPEPuIBDFRVFFMDÃMDVMPTBUJTGBHBMBUBTBEFáVKPFTQFDJàDBEBQBSBMBEFTUJ MBDJÓO &OMBTFDDJÓOEFSFDUJàDBDJÓOTFDPSSJHFOMBTUBTBTEFáVKPEFDPNQPOFOUFT ,^!_ Xdgg 2



9m ^!YZhi Xdgg ,  9m ^!YZhi XVaX ^!_ cdXdgg

www.FreeLibros.me







$BQÎUVMP  1SPDFEJNJFOUPTEFDÃMDVMPFYBDUPQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT

&OMBTFDDJÓOEFBHPUBNJFOUPTFVTB ,^!_ Xdgg 2

7m ^!XdaV Xdgg ,   7m ^!XdaV XVaX ^!_ cdXdgg



 "IPSB MBTUBTBTEFáVKPEFDPNQPOFOUFTDPSSFHJEBTTFVTBOQBSBEFUFSNJOBSMBTGSBDDJPOFTNPMEF MPTMÎRVJEPT m ^!_ 2



,^!_ Xdgg 8

,^!_ Xdgg





^2&

&TUFQSPDFEJNJFOUPIBDFRVFMBTGSBDDJPOFTNPMDPSSFHJEBTFODBEBFUBQBTVNFOGPS[PTBNFOUF 6OBWF[RVFTFIBOEFUFSNJOBEPMBTGSBDDJPOFTNPM TFDBMDVMBOMBTOVFWBTUFNQFSBUVSBTFODBEB FUBQBDPODÃMDVMPTEFQVOUPEFCVSCVKB TFDDJÓO  -BTOVFWBTUFNQFSBUVSBTTFVTBOQBSBDBMDVMBSOVFWPTWBMPSFT, WFBMBàHVSB ZBDPOUJ OVBDJÓOOVFWPTDPFàDJFOUFT" #Z$ QBSBMBFDVBDJÓO  -BTNBUSJDFTEFCBMBODFEFNBTBEF DPNQPOFOUFTTFJOWJFSUFO QBSBUPEPTMPTDPNQPOFOUFT ZTFEFUFSNJOBOOVFWBTMJ K4FBQMJDBEFOVF WPFMNÊUPEP EFDPOWFSHFODJB&TUFQSPDFEJNJFOUPTFDPOUJOÙBIBTUBRVFFMMB[PEFMBUFNQFSBUVSB IBDPOWFSHJEP MPDVBMTFTBCFDVBOEP ™− &+&.1-0 $ÃMDVMPEFNBUSJDFTZDPOWFSHFODJBDPO 6OBDPMVNOBEFEFTUJMBDJÓODPOVOWBQPSJ[BEPSQBSDJBMZVODPOEFOTBEPSUPUBMFTUÃTFQB SBOEPO$ /$ZO$&TUBDPMVNOBUJFOFEPTFUBQBTEFFRVJMJCSJP VOUPUBMEFUSFTDPOUBD UPTEFFRVJMJCSJP ZMBBMJNFOUBDJÓOFTVOMÎRVJEPTBUVSBEPRVFFOUSBFOMBFUBQBEFMGPOEP -BDPMVNOBUSBCBKBBBUN-BUBTBEFBMJNFOUBDJÓOFTLHNPMI[$ [$ Z[$ GSBDDJPOFTNPM &MSFáVKPFTVOMÎRVJEPTBUVSBEP Z-%&MáVKPEFEFT UJMBEPFT%LHNPMI4VQPOHBEFSSBNFNPMBMDPOTUBOUF6TFMBHSÃàDBEF%F1SJFTUFS QBSBEFUFSNJOBSWBMPSFTEF,$PNPQSJNFSBUFOUBUJWB TVQPOHBRVFMBTUFNQFSBUVSBTFO UPEBTMBTFUBQBTZFOFMWBQPSJ[BEPSTPOJHVBMFTBMBUFNQFSBUVSBEFQVOUPEFCVSCVKBEFMB BMJNFOUBDJÓO6TFVOBNBUSJ[QBSBSFTPMWFSMPTCBMBODFTEFNBTB6TFFMNÊUPEPEFDPO WFSHFODJBuDPOFMBSSFHMPEFQVOUPEFCVSCVKBQBSBIBDFSVOBJUFSBDJÓOIBDJBMBTPMVDJÓO QBSBDPNQPTJDJPOFTEFFUBQBZUBNCJÊOBOUJDJQFMBTOVFWBTUFNQFSBUVSBTRVFTFQPESÎBO VTBSQBSBVOBTFHVOEBJUFSBDJÓO"OPUFMBTDPNQPTJDJPOFTZMBUFNQFSBUVSBFODBEBFUBQB ZFOFMWBQPSJ[BEPS 4PMVDJÓO

  

­TUFFTVOQSPCMFNBMBSHPZDPNQMJDBEP4FJOEJDBSÃMBTPMVDJÓOTJOUPEPTMPTDÃMDVMPTJO UFSNFEJPT $PNFO[BSFNPTDPOVODÃMDVMPEFQVOUPEFCVSCVKBFOMBBMJNFOUBDJÓO  [J,J 5QC  ­TUFDPOWFSHFIBDJB5ž$BQL1B-PTWBMPSFTEF,TPO,$ ,$  ,$ [J,J  "DPOUJOVBDJÓO DBMDVMFMPTáVKPT - -% %    LHNPMI- - 7- %LHNPMI7 7 7 m - - 'LHNPMI- #LHNPMI-

www.FreeLibros.me

  .ÊUPEPuEFDPOWFSHFODJB



$BMDVMFMBTWBSJBCMFTNBUSJDJBMFT" # $Z%QBSBDBEBDPNQPOFOUF WFBMBUBCMB DPO TPMVDJÓOEFO$  _2&8dcYZchVYdgidiVa/8& 2 _2'/8' 2

−@'K' ! 7& 2& A'

−K( @( !7' 2& A(

_2(:iVeVYZVa^bZciVX^‹c/8( 2

9 !9& 2% A&

K' @ ' !6 ' 2−&!9' 2% A'

−@)K) !7( 2& A)

K( @ ( !6( 2−&!9( 2;o A(

K) @ ) !6 ) 2−&!9) 2% A)

KVedg^oVYdg_2)/7) 2&

*OWJFSUBMBNBUSJ[USJEJBHPOBMZBTFBDPOVOBIPKBEFDÃMDVMPPDPOFMBMHPSJUNPEF5IPNBT RVFBRVÎTFNVFTUSB -PTQBSÃNFUSPTEF5IPNBTQBSBDBEBDPNQPOFOUF WFBFOMBUBCMB MBTPMVDJÓOQBSBO$ TPO K&& 27& !K&' 27' − 6'K(&!ZiX# K'& 29& $K&&!K&' 2

9' − 6'K'& !ZiX# K&'

K(& 28 & $K&&!K(' 28' $K&'!ZiX#

$BMDVMFMBUBTBEFáVKPEFDBEBDPNQPOFOUFFODBEBFUBQB WFBMBUBCMB DPOMBTPMVDJÓO QBSBO$  a ) 2K') !a ( 2K'( − K(( a ) a ' 2K'' − K(a (!a & 2K'& − K(&a '

-PTSFTVMUBEPTTPO c8) '-%#'&, .(#*.( &')#).' &'#')&

,& ,' ,( ,)

c8* (%(#%(, '-.#&)& +'(#%)' &)-#'-)

c8&#..( ',#,)& *).#&&) )*%#',(

$BMDVMFMPTWBMPSFTEFMPTáVKPTEFDPNQPOFOUFTFOEFTUJMBEPZDPMBT

9m& 2

a&^ !9m8) 2 '-%#'&, 2&-+#-&& A $9 &#*

www.FreeLibros.me



$BQÎUVMP  1SPDFEJNJFOUPTEFDÃMDVMPFYBDUPQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT

(%(#%(, 2'%'#%'* &#*

9m8* 2

9m8- 2

&#..( 2&#('. &#*

7m^ 2a)^ !7m8) 2&'#')&!7m8* 2&)-#'-)!7m8- 2)*%#',( 

0CTFSWFRVF%DBMD   RVFOPFTJHVBMB%FTQFD &TPPCMJHBBSFDVSSJSBMNÊUPEPuEFDPOWFSHFODJB WFBMBUBCMB  4FEFCFEFUFSNJOBSuUBMRVF 3

;o_ 7m_

9ZheZX 2 _2&

3 _2&

CjZkV

&

9m_

2**%`\bda$] XVaX

3

;o_

[  2

&

P\_  R 29ZheZX

9ZheZX 2%!d

7m_

_2&

9m_

26ci

3

[  YdcYZ [ ′ 

1SVFCBEFUPMFSBODJB

[ ¼  2 _2&

;o_ 7m_ $ 9m_  &

7m_

3

2

\′_ 

_2&

9m_

[  EFCFTFS− 9ZheZX

$ÃMDVMPEFUBTBTEFáVKPWFBMBUBCMB ;o^

9m^ Xdgg 2 &

! 7m^ Xdgg 29m^ Xdgg

7m^ 9m^

XVaX

www.FreeLibros.me

7m^ 9m^

XVaX

  .ÊUPEPuEFDPOWFSHFODJB



5"#-" $¦-$6-04."53*$*"-&41"3"&-&+&.1-0 1"3"/$ .BUSJ[ &#+ −& % %

−*#%% +#%% −& %

% −'#'+ (#'+ −&

% % −.#&, &%#&,

,&!8) ,'!8) ,(!8) ,)!8)

% % 2 '%% %

-PTWBMPSFTJOUFSNFEJPTQBSBFMBMHPSJUNPEF5PNBTTPO K&& 27& 2&#+,!

K'& 2%!

K&' 2+#%− −&−'#..)2(#%%+!

K(& 2−*#%$&#+,2−'#..) %− −&% 2%#% (#%%+

K'' 2

K(' 2−'#'+$(#%%+2−%#,*&K&( 2'#*%-'!

K'( 2,.#,(-)!

K(( 2−(#+*+%

K&) 2+#*&)%nK') 2&'#')&

&OUPODFT MBTUBTBTEFáVKPEFO$TPO

,) 2K&) 2&'#')& ,( 2K'( − K(( ,) 2,.#,(-)− −(#+*+%&'#')&2&')#).' ,' 2.(#*.(!,& 2'-%#'&, $ÃMDVMPEFMBDPNQPTJDJÓOFODBEBFUBQB B 1SJNFSP DBMDVMFMBTUBTBTDPSSFHJEBTEFáVKPEFDPNQPOFOUFTFODBEBFUBQB MJ KDPSS $' MJ K OPDPSS EPOEF

 C m ^!_ 2

a^! _Xdgg 

a^!_Xdgg

8#;#2

9m ^!Y Xdgg BSSJCBEFMBBMJNFOUBDJÓO 9m ^!Y cdXdgg

8#;# 2

7m ^!W Xdgg BCBKPEFMBBMJNFOUBDJÓOZFOMBBMJNFOUBDJÓO 7m ^!W cdXdgg

n n^!_ 2@^!_ m ^!_

&

www.FreeLibros.me



$BQÎUVMP  1SPDFEJNJFOUPTEFDÃMDVMPFYBDUPQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT

5"#-" $0/7&3(&/$*"u1"3"&-&+&.1-0



O$

O$

O$

&)-#'-) '%'#%'* %#,()% (*%

)*%#',( &#('. ((-#-& )*%

1BSB  ;dgθ 2% \^θ '%% IdaZgVcXZ8]ZX` ¶ 1SVFCBEFUPMFSBODJB \′^ θ &(#%-%

(*% ¶ '*+#.

)*% ¶ &*')+)#*

[θ2)*% %#-&[′θ2−&#*(× &%*

4JHVJFOUF  CZmiθ 2%#%%'.* \^θ &..#.+ 1SVFCBEFUPMFSBODJB IdaZgVcXZ8]ZX` ¶ \′^ θ &(#%,*

().#') ¶ '**#,.

''*#%+ ¶ (-&(*#*.

[θ2'')#'+ %#)%[′θ2− (-)%%

8dci^cjZid/ $POUJOVBSB θ 2%#%,%) \^ θ &..#%-( IdaZgVcXZ8]ZX` ¶ 1SVFCBEFUPMFSBODJB

(('#-% ¶

&-#&& ¶

[θ2−%#%%, &#',× &%−*

(('#-% &,#&.,

&-#&& )(&#.+)

9Xdgg 2*).#.. 7mXdgg 2)*%#%-

7mW 9mY 7mW$9mY ;o

&'#')& &-+#-&& %#%+** '%%

D@→ θ 2%#%,%) &..#%%#.&-

9mXdgg 7mXdgg \ _ θ  2

'VODJPOFTUPUBMFT

;o_ & θ

7m_ 9m_

$ÃMDVMPTEFGSBDDJÓONPMQBSBFMFKFNQMP

8#;#Vgg^WVYZaVVa^bZciVX^‹c 8#;#VWV_dYZaVVa^bZciVX^‹c a&!Xdgg a'!Xdgg a(!Xdgg a)!Xdgg m& m' m( m)

c8)

c8*

c8-

&#%++ %#%,* '.-#,& ..#,, .#('% %#.&( %#(+' %#&%* %#%&* %#%%'

&#+), %#&&+ )..#&%' ),+#'&* ,'#',( &,#'%& %#+%* %#).. %#&&. %#%(-

&(#+( %#.*. ',#&+* (,-#&&% *'+#+%% )(&#-&' %#%(( %#(.+ %#-+%#.+%

www.FreeLibros.me

  #BMBODFTEFFOFSHÎBFOGPSNBNBUSJDJBM



$BMDVMFMBUFNQFSBUVSBFODBEBFUBQBDPOVODÃMDVMPEFQVOUPEFCVSCVKB 7BQPSJ[BEPS K $POWFSHFIBDJB5ž$&OUPODFT MBTGSBDDJPOFTNPMFOFMWBQPS TPO n8) 2%#%%'&&#.2%#%')!n8* 2%#%(-*#&'2%#&.*! n8- 2%#.+%%#-&2%#,,n

TVàDJFOUFNFOUFDFSDBOP n& 2%#..,!l]^X]^hXadhZZcdj\]#

-BFUBQBEFBMJNFOUBDJÓO K DPOWFSHFIBDJB5ž$Z$ Z$Z$  &UBQBBSSJCBEFMBFUBQBEFBMJNFOUBDJÓO K DPOWFSHFIBDJBž$Z$Z$  Z$ &MDPOEFOTBEPS K DPOWFSHFIBDJBž$ 3FTVNFOEFDÃMDVMPTEFTQVÊTEFVOBJUFSBDJÓO  

7BQPSJ[BEPS K 

&UBQBEFBMJNFOUBDJÓO K 

&UBQB K

m8) m8* m8n8) n8* n8-

%#%%' %#%(%#.+% %#%') %#&.* %#,,-

%#%&* %#&&. %#-+%#&'. %#))+ %#)()

%#&%* %#).. %#(.+ %#(*, %#+%. %#%(*

I§8

144°

123°

67°

&OFTUFQVOUPVTBSÎBNPTFTUBTUFNQFSBUVSBTQBSBEFUFSNJOBSOVFWPTWBMPSFT,ZFO UPODFT SFQFUJS FM DÃMDVMP NBUSJDJBM Z MB DPOWFSHFODJB  &T PCWJP RVF DPO UBOUP FTGVFS[P TFQSFàFSBVTBSVOTJNVMBEPSEFQSPDFTPTQBSBSFTPMWFSFTUFQSPCMFNB WFBFMQSPCMFNB ( -PTSFTVMUBEPTEFMBUFNQFSBUVSB DPOFMTJNVMBEPSEFQSPDFTPT TVFMFORVFEBSEFO USPEFVOPTQPDPTHSBEPTEFMBTUFNQFSBUVSBTDBMDVMBEBTFOFTUFFKFNQMP EFTQVÊTEFVOB JUFSBDJÓO FYDFQUPQPSMBFUBQB RVFUJFOFVOBUFNQFSBUVSBDBMDVMBEBNVZBMUB QPSRVF MBGSBDDJÓONPMEFIFYBOPFOFMMÎRVJEPFTEFNBTJBEPBMUB5BNCJÊO DPNPFTUFTJTUFNBOP TBUJTGBDFFMEFSSBNFNPMBMDPOTUBOUF FYJTUFNVDIBWBSJBDJÓOFOMBTUBTBTEFáVKP  #"-"/$&4%&&/&3(±"&/'03."."53*$*"-

%FTQVÊTEFMMB[PEFDPOWFSHFODJBEFUFNQFSBUVSB TFQVFEFODPSSFHJSMBTUBTBTEFáVKPEFMÎRVJEPZ WBQPS -KZ7K NFEJBOUFCBMBODFTEFFOFSHÎB WFBMBàHVSB 1BSBMBFUBQBHFOFSBMRVFNVFTUSB MBàHVSB FMCBMBODFEFFOFSHÎBFT 

A _] _ K_=_ 2K_ &= _

&

A _−&] _−& ;_];

_

F_ 



&TUBFDVBDJÓOFTQBSB K /−-BTUBTBTEFáVKPEFMÎRVJEPTTFQVFEFOTVTUJUVJSBQBSUJSEFVO CBMBODFEFNBTBFOUPSOPBMBQBSUFTVQFSJPSEFMBDPMVNOB

www.FreeLibros.me



$BQÎUVMP  1SPDFEJNJFOUPTEFDÃMDVMPFYBDUPQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT

_

A2 K _ _ & 9−

;` 

B

;` 

C

`2&



_−&

A2 K_ 9− _−& `2&

 EPOEF K /− "MTVTUJUVJSMBTFDVBDJPOFT B Z C FOMBFDVBDJÓO 

ZPSEFOBSMPTUÊSNJOPT RVFEB ] _

=_ & K_

&

= _

] _ & K_

_

2;_] ;

F_ 9] _

_

&

;` ] _ & 

;` ] _

] _  `2&



`2&

 1BSBVODPOEFOTBEPSUPUBM DPNP7- % ZII% FMCBMBODFEFFOFSHÎBFT F& K'= ' ;&] ; 2K']& 





&

RVFTFPSEFOBFOMBTJHVJFOUFGPSNB ]& − ='K' 2;];



&

F& 



1BSBFMWBQPSJ[BEPSQBSDJBM K/ FMCBMBODFEFFOFSHÎBFT 

;C];

FC AC−&]C−& 27]7 KC=C 

C



ZMBUBTBEFáVKPUPUBMTFQVFEFDBMDVMBSDPO AC−& 27 KC − ;C 





4FTVTUJUVZFMBFDVBDJÓO  FOMB 

TFPSEFOBOUÊSNJOPTZSFTVMUB =C − ]C−&KC 2;C];



C

FC 7]C−& − ]C − ;C]C−& 



4JMBTFDVBDJPOFT 

  Z  TFMMFWBOBMBGPSNBEFNBUSJ[ TFPCUJFOF

™ % % % % % 8 7 ™ % % % % % 7 8 ™ % % % ™ ™ ™ ™ ™ ™ ™ ™ % % % % ™ % 7 8 % % % % ™ % % 7

7:&

8:& :'

%

%

:' :(

:(

:C−&



K&

9:&

K'

9:'

K(

9:(

™

2

™

:C−&

KC−&

9:C−&

:C

KC

9:C





&TUBNBUSJ[UBNCJÊOUJFOFVOBGPSNBUSJEJBHPOBM DPO"K ZTFQVFEFJOWFSUJSDPOGBDJMJEBEQBSB PCUFOFSMBTUBTBTEFáVKPEFWBQPS-PTDPFàDJFOUFT#&Z$&EFMBFDVBDJÓO  TFPCUJFOFODPO GBDJMJEBEDPNQBSBOEPMBTFDVBDJPOFT 

  Z  DPOMBFDVBDJÓO  1BSBK FTUPT WBMPSFTTPO

www.FreeLibros.me

  #BMBODFTEFFOFSHÎBFOGPSNBNBUSJDJBM





7:& 2%!8 :& 2] & − ='!9:& 2;] ;

F& 

&

B

1BSB K /− 7:_ 2= _ − = _−&!8 :_ 2] _ − = _

&

_

9:_ 2;_] ;

_

F_ 9] _−& − ] _  `2&

 ZQBSBK/ 

_−&

;` ] _ −

7:C 2=C − =C−&!9:C 2;C];

C

;` ] _−& 

C

`2&

FC 7]C−& − ]C − ;C ]C−& 

D

-PTDPFàDJFOUFTEFMBTFDVBDJPOFT  SFRVJFSFODPOPDFSMBTFOUBMQÎBTRVFTBMFOEFDBEBFUBQBZ MPTWBMPSFTEF2-PTWBMPSFTEFMBTFOUBMQÎBTTFQVFEFODBMDVMBSZBRVFUPEBTMBTY ZZUFNQFSBUVSBT TFDPOPDFODPOMPTCBMBODFTEFNBTBZDPOFMMB[PDPOWFSHFOUFEFUFNQFSBUVSB-BTFOUBMQÎBTQBSB MBTNF[DMBTJEFBMFTTPO 8

]_ 2

s m ^!_ ] ^I_ 

B

s n^!_ = ^I_ 

C

^2&

 Z

8

=_ 2 ^2&

 } 5 Z) } 5 TPOMBTFOUBMQÎBTEFMPTDPNQPOFOUFTQVSPT EPOEFI  K  K 

s s ] ^I_ 2 ] ^IgZ[  8e! ,^fI_ − IgZ[  

D



s s = ^ I_2 ] ^IgZ[ λ ^IgZ[  8e!kVeI_ − IgZ[  

E

4FQVFEFOEFUFSNJOBSBQBSUJSEFEBUPT QPSFKFNQMP WFB.BYXFMM  P4NJUI  PDPODB QBDJEBEFTDBMPSÎàDBTZDBMPSFTMBUFOUFTEFFWBQPSBDJÓO &OHFOFSBM MBDPMVNOBFTBEJBCÃUJDB"TÎ 

2KQBSB K /−  2/23   22$



&MTFSWJDJPEFMDPOEFOTBEPSTFQVFEFEFUFSNJOBSDPOCBMBODFTBMSFEFEPSEFMDPOEFOTBEPSUPUBM F& 2K'] 9 − = ' 29 &

A ] 9 − = '   9



 $PNP%Z-%TFFTQFDJàDBO ZI%Z)TFQVFEFODBMDVMBSDPOMBTFDVBDJPOFT 

2TFDBMDVMB DPOGBDJMJEBE1BSBVOBDPMVNOBBEJBCÃUJDBMBDBSHBUÊSNJDBEFMWBQPSJ[BEPSTFDBMDVMBDPOVOCB MBODFHFOFSBMEFFOFSHÎB FC 29]9 7]7 −



C

;`]; − F&  `2&

`



-BJOWFSTJÓOEFMBFDVBDJÓO  QFSNJUFQSPQPOFSOVFWPTWBMPSFTUFOUBUJWPTQBSBMBTUBTBTEF áVKPEFWBQPS-BTUBTBTEFáVKPEFMÎRVJEPTFQPESÃOEFUFSNJOBSFOUPODFTDPOCBMBODFTEFNBTB  DPNPMPTEFMBTFDVBDJPOFT  Z  &TUBTOVFWBTUBTBTEFáVKPEFMÎRVJEPZWBQPSTFDPNQBSBO

www.FreeLibros.me



$BQÎUVMP  1SPDFEJNJFOUPTEFDÃMDVMPFYBDUPQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT

DPOMPTWBMPSFTRVFTFVTBOQBSBMBDPOWFSHFODJBBOUFSJPSEFMPTCBMBODFTEFNBTBZFMMB[PEFUFNQF SBUVSB-BQSVFCBEFDPOWFSHFODJBFTTJ A_!XVaX − A_!Vci 1ε A_!XVaX

n

K_!XVaX − K_!Vci 1ε  K_!XVaX



 QBSBUPEBTMBTFUBQBT FMDÃMDVMPDPOWFSHJÓ1BSBDÃMDVMPTFODPNQVUBEPSB MPBEFDVBEPFTVO EF −P− 4JFMQSPCMFNBOPDPOWFSHF FTOFDFTBSJPVTBSMPTOVFWPTWBMPSFTEF-KZ7KFOFMCBMBODFEF NBTBZFOFMCVDMFEFUFNQFSBUVSB WFBMBàHVSB &MNÊUPEPNÃTTFODJMMPFTQPSTVTUJUVDJÓOEJ SFDUB&TUPFT TFVTBO FOFMTJHVJFOUFUBOUFP MPTWBMPSFTEF-KZ7KRVFTFBDBCBOEFDBMDVMBS $VBOEPTFTBUJTGBDFOMBTFDVBDJPOFT 

FMDÃMDVMPUFSNJOB&TPTFEFCFBRVFFTUÃOSFTVFMUBT UPEBTMBTFDVBDJPOFTEFCBMBODFEFNBTB EFFRVJMJCSJPZEFCBMBODFEFFOFSHÎB-BTPMVDJÓOJOEJDB MBTGSBDDJPOFTNPMBSFTZMBTUBTBTEFáVKPEFMÎRVJEPTZWBQPSFT BTÎDPNPMBUFNQFSBUVSBFODBEB FUBQBZFOMPTQSPEVDUPT &MNÊUPEPEFNBUSJDFTTFBEBQUBDPOGBDJMJEBEBDPOEFOTBEPSFTQBSDJBMFTZBDPMVNOBTDPODP SSJFOUFTMBUFSBMFT WFBMPTQSPCMFNBT$Z$ &MNÊUPEPDPOWFSHFSÃQBSBQSPCMFNBTOPSNBMFT EFEFTUJMBDJÓO4VBNQMJBDJÓOBQSPCMFNBTNÃTDPNQMFKPT DPNPMPTDBTPTEFEFTUJMBDJÓOB[FPUSÓQJDB ZFYUSBDUJWB PDPOBMJNFOUBDJPOFTRVFIJFSWFOBUFNQFSBUVSBTNVZEJGFSFOUFT TBMFEFMBMDBODFEF FTUFMJCSPTJOFNCBSHP FTPTQSPCMFNBTMPTQVFEFSFTPMWFSVOTJNVMBEPSEFQSPDFTPT &ODJFSUPTFOUJEP OPIFNPTEFTDSJUPMBQBSUFNÃTEJGÎDJMEFFTDSJCJSVOQSPHSBNBEFEFTUJMB DJÓO EF WBSJPT DPNQPOFOUFT &T FM EFTBSSPMMP EF VO QBRVFUF EF QSPQJFEBEFT GÎTJDBT RVF BOUJDJQF DPOFYBDUJUVEMBTSFMBDJPOFTEFFRVJMJCSJPZEFFOUBMQÎB #BSOJDLJ $BSMTPO  4BEFRFUBM    4DIBE    4BEBR FU BM   DPNQBSBSPO USFT TJNVMBEPSFT EF QSPDFTPT Z FODPOUSBSPO RVF VOBTEJGFSFODJBTSFMBUJWBNFOUFQFRVFÒBTFOMPTQBSÃNFUSPTZFOMBDPSSFMBDJÓOEFFRVJMJCSJP WBQPSMÎRVJEPQVFEFODBVTBSHSBOEFTFSSPSFTFOMPTSFTVMUBEPT1PSGPSUVOB TFIBIFDIPVOBDBOUJ EBEDPOTJEFSBCMFEFJOWFTUJHBDJÓO WFBMBUBCMB Z'SFEFOTMVOEFUBM Z8BMBT  QBSB EFEVDJSDPSSFMBDJPOFTFYBDUBTEFQSPQJFEBEFTGÎTJDBT4FQVFEFODPNQSBSQSPHSBNBTNVZEFUBMMBEPT EFQSPQJFEBEFTGÎTJDBTZTFJODMVZFOFOMPTTJNVMBEPSFTDPNFSDJBMFTEFQSPDFTPT -B NBZPSÎB EF MBT FNQSFTBT RVF VTBO EFTUJMBDJÓO UJFOFO EJTQPOJCMFT QSPHSBNBT EF DÓNQVUP RVFBQSPWFDIBOQSPDFEJNJFOUPTBWBO[BEPTEFDÃMDVMP7BSJBTFNQSFTBTEFQSPHSBNBTZEFEJTFÒP WFOEFOFTPTQSPHSBNBT&MJOHFOJFSPOPSNBMVTBFTBTSVUJOBTZOPUJFOFRVFIBDFSMPTHSBOEFTFT GVFS[PTOFDFTBSJPTQBSBFTDSJCJSTVQSPQJPQSPHSBNB4JOFNCBSHP QVFEFTFSNVZÙUJMDPNQSFOEFS MPTQFSàMFTFTQFSBEPTZMPTCBMBODFTCÃTJDPTEFNBTBZFOFSHÎBQBSBJOUFSQSFUBSMPTSFTVMUBEPTEF DÓNQVUPZEFUFSNJOBSDVÃOEPFTPTSFTVMUBEPTTPOTÓMPCBTVSB"TÎ FTJNQPSUBOUFDPNQSFOEFSMPT QSJODJQJPTEFMPTDÃMDVMPTEFEFTUJMBDJÓO BVODVBOEPOPTFFOUJFOEBDPNQMFUBNFOUFMPTEFUBMMFTEFM QSPHSBNBEFDÃMDVMP  3&46.&/m0#+&5*704

&OFTUFDBQÎUVMPIFNPTEFTBSSPMMBEPNÊUPEPTQBSBDBMDVMBSEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT-PT PCKFUJWPTEFFTUFDBQÎUVMPTPOMPTTJHVJFOUFT  6TBSVONÊUPEPNBUSJDJBMQBSBSFTPMWFSCBMBODFTEFNBTBEFWBSJPTDPNQPOFOUFT  6TBSFMNÊUPEP EFDPOWFSHFODJBZDÃMDVMPTEFQVOUPEFCVSCVKBQBSBEFUFSNJOBSOVFWBTUFN QFSBUVSBTFODBEBFUBQB  6TBSVONÊUPEPNBUSJDJBMQBSBSFTPMWFSMPTCBMBODFTEFFOFSHÎBQBSBOVFWPTáVKPT

www.FreeLibros.me

5BSFB



3&'&3&/$*"4

#BSOJDLJ 4% i)PX(PPEBSF:PVS%BUB u$IFN&OH1SPHSFTT  

 KVOJPEF  $BSMTPO &$ i%POU(BNCMFXJUI1IZTJDBM1SPQFSUJFTGPS4JNVMBUJPOTu $IFN&OH1SPHSFTT  

 0DU  'SFEFOTMVOE " +(NFIMJOHZ13BTNVTTFO 7BQPS-JRVJE&RVJMJCSJB6TJOH6/*'"$"(SPVQ $POUSJCVUJPO.FUIPE &MTFWJFS "NTUFSEBN  )PMMBOE %% 'VOEBNFOUBMTPG.VMUJDPNQPOFOU%JTUJMMBUJPO .D(SBX)JMM /FX:PSL  ,JOH $+ 4FQBSBUJPO1SPDFTTFT ‰&E .D(SBX)JMM /FX:PSL  -BQJEVT -%JHJUBM$PNQVUBUJPOGPS$IFNJDBM&OHJOFFST .D(SBX)JMM /FX:PSL  .BYXFMM +# %BUB#PPLPO)ZESPDBSCPOT 7BO/PTUSBOE 1SJODFUPO /+  1PMJOH #& +.1SBVTOJU[Z+10$POOFMM 5IF1SPQFSUJFTPG(BTFTBOE-JRVJET ‰&E .D(SBX )JMM /FX:PSL  4BEFR + )"%VBSUFZ384FSUI i"OPNBMPVT3FTVMUTGSPN1SPDFTT4JNVMBUPSTu $IFN&OH &EVDBUJPO  

 JOWJFSOPEF  4DIBE 3$ i.BLFUIF.PTUPG1SPDFTT4JNVMBUJPOu $IFN&OH1SPHSFTT  

 FOFSPEF   4FJEFS 8% +%4FBEFSZ%3-FXJO 1SPDFTT%FTJHO1SJODJQMFT 8JMFZ /FX:PSL  4NJUI #% %FTJHOPG&RVJMJCSJVN4UBHF1SPDFTTFT .D(SBX)JMM /FX:PSL  8BMBT 4. 1IBTF&RVJMJCSJBJO$IFNJDBM&OHJOFFSJOH #VUUFSXPSUI #PTUPO  5"3&"

" 1SPCMFNBTQBSBEJTDVTJÓO " &OFMNÊUPEPNBUSJDJBMTVQVTJNPTRVF,, 5 Q y$ÓNPQPESÎBDBNCJBSFMEJBHSBNBEF áVKPEFMBàHVSB TJ,, 5 Q YJ

" 4JFTWÃMJEPFMEFSSBNFNPMBMDPOTUBOUF yDÓNPTFTJNQMJàDBSÃMBàHVSB " %FTBSSPMMFVOBUBCMBEFSFMBDJPOFTDMBWFQBSBFTUFDBQÎUVMP " &OVOQSPHSBNBEFTJNVMBDJÓOEFEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT MPTMB[PTFTUÃOBOJEB EPT&MMB[PFYUFSOPFTEFGSBDDJPOFTNPMBSFT BDPOUJOVBDJÓOFTUÃFMEFMBTUBTBTEFáVKP ZFM NÃTJOUFSOPFTEFUFNQFSBUVSB  -BTGSBDDJPOFTNPMTPOFMMB[PFYUFSOPQPSRVF B .VDIPTQSPCMFNBTEFEFTUJMBDJÓOTFQVFEFOSFTPMWFSTJOFTUFMB[P C $POGSFDVFODJB BMDBNCJBSGSBDDJPOFTNPMBSFTOPTFOPUBVOHSBOFGFDUPTPCSFMPTWBMP SFTEF, D -BTGSBDDJPOFTNPMBSFTUJFOFOHSBOJNQBDUPTPCSFMPTWBMPSFTEF,TÓMPQBSBTJTUFNBT DPODPNQPSUBNJFOUPDPNQMFKPEFFRVJMJCSJP E 5PEPMPBOUFSJPS  &MMB[PEFMBUFNQFSBUVSBTFIBDFBOUFTRVFFMCVDMFEFUBTBEFáVKPQPSRVF B -BTUFNQFSBUVSBTOPQVFEFOTFSDPOTUBOUFTFOMBEFTUJMBDJÓO C $POGSFDVFODJB MPTáVKPTTPONVZQSÓYJNPTBTFSDPOTUBOUFTFODBEBTFDDJÓOEFMBDP MVNOB D 4FQVFEFIBDFSVOBNVZCVFOBQSPQPTJDJÓOUFOUBUJWBEFUBTBTEFáVKP E 5PEPMPBOUFSJPS  6OBCVFOBQSPQPTJDJÓOUFOUBUJWBQBSBUBTBTEFáVKPFT B 4VQPOFSEFSSBNFNPMBMDPOTUBOUF

www.FreeLibros.me



$BQÎUVMP  1SPDFEJNJFOUPTEFDÃMDVMPFYBDUPQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT

C 4VQPOFSUBTBTEFáVKPEFMÎRVJEPZWBQPSDPOTUBOUFTFOUPEBMBDPMVNOB D 6TBSVODÃMDVMPEFQVOUPEFCVSCVKBFOMBQBSUFTVQFSJPSZFOFMGPOEPEFMBDPMVNOB  1BSBUFOFSVOCVFOWBMPSUFOUBUJWPQBSBMBTUFNQFSBUVSBT B 4VQÓOHBTFEFSSBNFNPMBMDPOTUBOUF C ¼TFTFDVBMRVJFSUFNQFSBUVSBBSCJUSBSJB D ¼TFTFVODÃMDVMPEFQVOUPEFCVSCVKBFOMBQBSUFTVQFSJPSZFOFMGPOEPEFMBDPMVNOB  -PTCBMBODFTEFNBTBTFSFTVFMWFOGPSNBOEPVOBNBUSJ[RVFBDPOUJOVBDJÓOTFJOWJFSUF-B NBUSJ[QFSNJUFBVOPUFOFSMBBMJNFOUBDJÓOFO B 4ÓMPVOMVHBSEFMBDPMVNOB C %PTMVHBSFTFOMBDPMVNOB D $VBMRVJFSFUBQBFOMBDPMVNOB QFSPOPFMDPOEFOTBEPSZOPFMWBQPSJ[BEPS E $VBMRVJFSFUBQBFOMBDPMVNOB ZUBNCJÊOFMWBQPSJ[BEPSZFMDPOEFOTBEPS $ $  $ $

%FTWJBDJPOFT %FTBSSPMMFMBSVUJOBEFDPOWFSHFODJBQBSBVODÃMDVMPEFQVOUPEFCVSCVKB 6TFFMQSPDFEJNJFOUPEFDPOWFSHFODJBEF/FXUPOZEFEV[DBMBFDVBDJÓO   4VQPOHBRVFIBZVOBDPSSJFOUFMBUFSBMEFMÎRVJEP DVZBDPNQPTJDJÓOFTYKZTVáVKPFT4K RVF TBMFEFMBFUBQBK FOMBàHVSB B %FEV[DBMBTFDVBDJPOFTEFCBMBODFEFNBTB   B 

QBSBFTUBDPMVNOBNPEJàDBEB C %FEV[DBOVFWBTFDVBDJPOFTQBSBFMNÊUPEPuEFDPOWFSHFODJB*OEJRVFDÓNPDBNCJBSÃO MBTFDVBDJPOFT 

  Z B  D %FEV[DBOVFWBTFDVBDJPOFTEFCBMBODFEFFOFSHÎB%FEV[DBOVFWPTDPFàDJFOUFTQBSBMB FDVBDJÓO C  $ %FEV[DB MB FDVBDJÓO EF CBMBODF EF NBTB QBSB FM NÊUPEP NBUSJDJBM  TJ IBZ VO DPOEFOTBEPS QBSDJBMFOMVHBSEFVODPOEFOTBEPSUPUBM4VTUJUVZBMBTFDVBDJPOFTEFMB  BMB   $ %FEV[DBMBFDVBDJÓOEFCBMBODFEFNBTBQBSBFMNÊUPEPNBUSJDJBMTJIBZVOWBQPSJ[BEPSUPUBM 4VHFSFODJB-MBNFDPOUBDUP/BMBFUBQBJOGFSJPSEFMBDPMVNOB % 1SPCMFNBT  -BTSFTQVFTUBTEFQSPCMFNBTDPOVOBTUFSJTDPTFFODVFOUSBOFOMBQBSUFGJOBMEFMMJCSP % 6OBBMJNFOUBDJÓODPOUJFOFNPMEFNFUBOP NPMEFOQFOUBOPZNPMEF OIFYBOP-BUFNQFSBUVSBFTž$$BMDVMFMBQSFTJÓOEFQVOUPEFCVSCVKB6TFMBHSÃàDBEF %F1SJFTUFS % 6OBNF[DMBMÎRVJEBFTUÃGPSNBEBQPSNPMEFFUBOP NPMEFOQFOUBOPZNPMEF OIFQUBOP Bž$ZBQSFTJÓOBMUB"MCBKBSMFOUBNFOUFMBQSFTJÓOyBRVÊQSFTJÓODPNFO[BSÃ MBNF[DMBBIFSWJS 6TFMBHSÃàDBEF%F1SJFTUFS %  4VQPOHBRVFTFEJTQPOFEFOIFYBOP OIFQUBOPZOPDUBOPEFUBMNBOFSBRVFTFQVFEFDBN CJBSMBGSBDDJÓONPMEFTVNF[DMBBDVBMRVJFSWBMPSRVFTFEFTFF4JMBQSFTJÓOEFMTJTUFNBFT L1B  B y$VÃMFTMBNÃYJNBUFNQFSBUVSBEFCVSCVKBQPTJCMF C y$VÃMFTMBNÎOJNBUFNQFSBUVSBEFCVSCVKBQPTJCMF 6TFMBTHSÃàDBTEF%F1SJFTUFS %  6OBNF[DMBFTUÃGPSNBEBQPSOCVUBOP OQFOUBOPZOIFYBOP ZFTUÃBž'ZQTJB&M MÎRVJEPZFMWBQPSFTUÃOFOFRVJMJCSJP4JFMMÎRVJEPDPOUJFOFGSBDDJÓONPMEFOCVUBOP  DBMDVMFMBTGSBDDJPOFTNPMBSFTEFMMÎRVJEPZFMWBQPS6TFMBTHSÃàDBTEF%F1SJFTUFS QFSPUFOHB DVJEBEPDPOTVTVOJEBEFT/PUB&TUFQSPCMFNBOPFTQBSBQSVFCBZFSSPS

www.FreeLibros.me

5BSFB



%  $BMDVMFMBUFNQFSBUVSBEFQVOUPEFCVSCVKBZMBTGSBDDJPOFTNPMBSFTFOFMQVOUPEFCVSCVKB  QBSBVOBNF[DMBBL1BRVFDPOUJFOFNPMEFFUJMFOP NPMEFFUBOPZ NPMEFQSPQBOP6TFMBHSÃàDBEF%F1SJFTUFS %  $BMDVMFMBUFNQFSBUVSBEFQVOUPEFCVSCVKBZMBTGSBDDJPOFTNPMBSFTFOFTFVOUP QBSBVOB NF[DMB BBUN GPSNBEBQPSNPMEFOCVUBOP NPMEFOQFOUBOPZNPM EFOIFYBOP6TFMBHSÃàDBEF%F1SJFTUFS % 1BSBMBQSJNFSBUFOUBUJWBEFMFKFNQMP EFUFSNJOFMBNBUSJ[EFDPNQPOFOUFTQBSBOQFOUB OP ZBDPOUJOVBDJÓOVTFFMBMHPSJUNPEF5IPNBTQBSBDBMDVMBSMBTUBTBTEFáVKPEFOQFOUBOP MÎRVJEPRVFTBMFOEFDBEBFUBQB$PNQBSFTVTáVKPTEFOQFOUBOPDPOMPTWBMPSFTRVFBQBSF DFOFOFMFKFNQMP % 1BSBFMQSJNFSUBOUFPEFMFKFNQMPEFUFSNJOFMBNBUSJ[EFDPNQPOFOUFTQBSBFMOPDUBOP ZEFTQVÊTVTFFMBMHPSJUNPEF5IPNBTQBSBFODPOUSBSMBTUBTBTEFáVKPEFOPDUBOPMÎRVJEP RVFEFKBODBEBFUBQB$PNQBSFTVTUBTBTEFáVKPEFOPDUBOPDPOMPTWBMPSFTSFQPSUBEPTFOFM FKFNQMP % 4FWBBTFQBSBSVOBNF[DMBEFFUBOP QSPQBOP OCVUBOPZOQFOUBOPFOVOBDPMVNOBEFEFTUJMB DJÓORVFUSBCBKBBBUN-BDPMVNOBUJFOFVODPOEFOTBEPSUPUBMZVOWBQPSJ[BEPSQBSDJBM-B UBTBEFáVKPEFBMJNFOUBDJÓOFTLHNPMIZFTVOMÎRVJEPTBUVSBEPRVFDPOUJFOFNPMEF FUBOP NPMEFQSPQBOP NPMEFOCVUBOPZNPMEFOQFOUBOP-BDPMVNOB UJFOFFUBQBTEFFRVJMJCSJPNÃTFMWBQPSJ[BEPSQBSDJBM RVFFTVODPOUBDUPEFFRVJMJCSJP-BBMJ NFOUBDJÓOFTUÃFOMBTFHVOEBFUBQBBCBKPEFMDPOEFOTBEPSUPUBM-BSFMBDJÓOEFSFáVKPFT-% -BUBTBEFáVKPEFEFTUJMBEPFT%LHNPMI%FTBSSPMMFFMCBMBODFEFNBTBZMBNBUSJ[ EFFRVJMJCSJP FDVBDJÓO DPOWBMPSFTOVNÊSJDPTQBSBDBEBFMFNFOUP "K #K $KZ%K )ÃHBMP QBSBTVQSJNFSWBMPSQSPQVFTUP5KUFNQFSBUVSBEFQVOUPEFCVSCVKBEFMBBMJNFOUBDJÓO VTF MBNJTNBUFNQFSBUVSBFOUPEBTMBTFUBQBT MPTWBMPSFTEF,TFUPNBOEFMBHSÃàDBEF%F1SJFTUFS -PTWBMPSFTEF-Z7TPODPOEFSSBNFNPMBMDPOTUBOUF'PSNFMBNBUSJ[TÓMPQBSBFMQSPQBOP ' 1SPCMFNBTRVFSFRVJFSFOPUSPTSFDVSTPT '  6OBDPMVNOBEFEFTUJMBDJÓODPOEPTFUBQBTNÃTVOWBQPSJ[BEPSQBSDJBMZVODPOEFOTBEPSQBS DJBM TFQBSB CFODFOP  UPMVFOP Z YJMFOP -B UBTB EF BMJNFOUBDJÓO FT  LHNPMI FT VO WBQPS TBUVSBEPRVFTFJOUSPEVDFFOMBFUBQBEFMGPOEPEFMBDPMVNOB-BTDPNQPTJDJPOFT GSBDDJPOFT NPMBSFT EFMBBMJNFOUBDJÓOTPO[# [5Z[9&MSFáVKPFTVOMÎRVJEPTBUVSBEP ZQQTJB4FEFTFBUFOFSVOBUBTBEFáVKPEFEFTUJMBEPJHVBMB%LHNPMI4VQPOHBRVF ,J17JQ 17QSFTJÓOEFWBQPS /0TVQPOHBWPMBUJMJEBESFMBUJWBDPOTUBOUF QFSPTÎEFSSB NFNPMBMDPOTUBOUF6TFFMNÊUPEPEFNBUSJDFTQBSBSFTPMWFSMPTCBMBODFTEFNBTBZFMNÊUPEP uQBSBDPOWFSHFODJBEFUFNQFSBUVSB$PNPQSJNFSWBMPSQSPQVFTUPEFMBUFNQFSBUVSB TVQPOHB RVFUPEBTMBTFUBQBTFTUÃOFOMBUFNQFSBUVSBEFMQVOUPEFSPDÎPEFMBBMJNFOUBDJÓO4ÓMPIBHB VOBJUFSBDJÓO7FBFOFMQSPCMFNB$FMNBOFKPEFMDPOEFOTBEPSQBSDJBM ( 1SPCMFNBTQBSBDPNQVUBEPSB ( 6TFVOTJNVMBEPSEFQSPDFTPTQBSBSFTPMWFSQPSDPNQMFUPFMFKFNQMP/PTVQPOHBEFSSB NFNPMBMDPOTUBOUF$PNQBSFUFNQFSBUVSBTZGSBDDJPOFTNPMFODBEBFUBQB DPOMPTWBMPSFT PCUFOJEPTFOFMFKFNQMP EFTQVÊTEFVOBUFOUBUJWB ( 6OBDPMVNOBPSEJOBSJBEFEFTUJMBDJÓOTFQBSBFUBOP QSPQBOPZOCVUBOP-BUBTBEFBMJNFO UBDJÓOFTLHNPMIZFTVOMÎRVJEPTBUVSBEPBBUN-BTGSBDDJPOFTNPMBSFTFOMBBMJ NFOUBDJÓOTPOFUBOP QSPQBOPZOCVUBOP-BDPMVNOBUJFOFFUBQBTEF FRVJMJCSJPZMBBMJNFOUBDJÓOFOUSBFOMBFUBQB DPOUBOEPEFBSSJCBQBSBBCBKP -BBMJNFO UBDJÓOFOUSBBSSJCBEFMBFUBQB-BQSFTJÓOEFMBDPMVNOBFTBUNZTFQVFEFDPOTJEFSBS

www.FreeLibros.me



$BQÎUVMP  1SPDFEJNJFOUPTEFDÃMDVMPFYBDUPQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFT

DPOTUBOUF-BDPMVNOBUJFOFVODPOEFOTBEPSUPUBMZVOWBQPSJ[BEPSUJQPNBSNJUB-BSFMBDJÓO EFSFáVKPFYUFSOPFT-%ZMBUBTBEFáVKPEFEFTUJMBEPTFBKVTUBFO%LHNPMI 6TFVOTJNVMBEPSEFQSPDFTPTQBSBFTUFTJTUFNB ZDPOUFTUFMPTJHVJFOUF  y2VÊQSPHSBNBEFFRVJMJCSJPWBQPSMÎRVJEPVTÓ  &YQMJRVFQPSRVÊFTDPHJÓFTFQBRVFUF  "OPUFMPTWBMPSFTTJHVJFOUFT  5FNQFSBUVSBEFMDPOEFOTBEPS@@@@@ž$  5FNQFSBUVSBEFMWBQPSJ[BEPS@@@@@@ž$  'SBDDJPOFTNPMFOFMQSPEVDUPEFTUJMBEP@@@@@@@@@@@@@@@@@@@@  'SBDDJPOFTNPMFOMPTGPOEPTQSPEVDJEPT@@@@@@@@@@@@@@@@@@@  -BFUBQBEFBMJNFOUBDJÓOJOEJDBEByGVFMBÓQUJNB 4Î/P  4JOPMPGVF MBFUBQBEFBMJNFOUBDJÓOEFCFFTUBSB NÃTDFSDBEFMDPOEFOTBEPSPC NÃT DFSDBEFMWBQPSJ[BEPS  /PUB)BHBMBDBOUJEBENÎOJNBEFTJNVMBDJPOFTQBSBDPOUFTUBSFTUBTQSFHVOUBT/PPQUJNJDF  $VBOEPTFVTBMBFUBQBEFBMJNFOUBDJÓOJOEJDBEB yDVÃMQMBUPQSPEVDFFMNÃYJNPEJÃNFUSP EFDPMVNOB FONFUSPT DPOQMBUPTQFSGPSBEPT 1MBUP@@@@@@@@@%JÃNFUSP@@@@@@@@@@ 

W>

=

A

X>

=

A

=

A

'*(63" &426&."4%&."1"4%&$637"4%&3&4*%60 $6"/%0)":6/ ";&¶53010%&16/50%&--*$*¶/.±/*.0 %0)&35::."-0/&   3&*.13&40$0/"6503*;"$*¶/%&.$(3"8)*-- $01:3*()5 .$(3"8)*--  %&45*-"$*¶/&953"$5*7"

-BEFTUJMBDJÓOEFFYUSBDDJÓOTFVTBQBSBTFQBSBSB[FÓUSPQPTZNF[DMBTDPOQVOUPTEFFCVMMJDJÓODFS DBOPT&OMBEFTUJMBDJÓOFYUSBDUJWBTFBHSFHBVOTPMWFOUFBMBDPMVNOBEFEFTUJMBDJÓO&MTPMWFOUFTF TFMFDDJPOBQBSBRVFVOPEFMPTDPNQPOFOUFT # QBTFBÊMFOGPSNBTFMFDUJWB$PNPTFTVFMFFTDPHFS BMTPMWFOUFQBSBRVFUFOHBVOQVOUPEFFCVMMJDJÓOBQSFDJBCMFNFOUFNBZPSRVFFMEFMPTDPNQPOFO :iVcda &#%

%#-

%#+

%#)

%#'

%

% 6\jV

%#'

%#)

%#+

%#-

&#% 7ZcXZcd

'*(63" ."1"$"-$6-"%0%&$637"%&3&4*%601"3"&-4*45&." &5"/0-"(6"#&/$&/0 %0)&35::."-0/&  -04$6"%304 /&(30440/";&¶530104#*/"3*04 &-53*¦/(6-0/&(30&46/";&¶53010 5&3/"3*0)&5&30(­/&0:-"-±/&"%&16/50:3":"3&13&4&/5"-" &/70-7&/5&%&40-6#*-*%"%1"3"-"4%04$"1"4-±26*%"43&*.13&40 $0/"6503*;"$*¶/%&.$(3"8)*-- $01:3*()5 .$(3"8)*--

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBNÊUPEPTDPNQMFKPTEFEFTUJMBDJÓO

UFTRVFTFFTUÃOTFQBSBOEP FMDPNQPOFOUFBUSBÎEP # UJFOFWPMBUJMJEBESFEVDJEB&OUPODFT FMPUSP DPNQPOFOUF " TFWVFMWFSFMBUJWBNFOUFNÃTWPMÃUJMZFTTFODJMMPTBDBSMPFOFMEFTUJMBEP4FSFRVJFSF VOBDPMVNOBBQBSUFQBSBTFQBSBSBMTPMWFOUFZBMDPNQPOFOUF#-BTDVSWBTEFSFTJEVP EFTQVÊTEF BHSFHBSFMTPMWFOUF TFNVFTUSBOFOMBàHVSB TFQBSBDJÓOEFDPNQPOFOUFTFCVMMJDJPOFTDFSDBOBT  ZFOMB$ TFQBSBDJÓOEFB[FÓUSPQPT  &OMBàHVSBTFNVFTUSBVOEJBHSBNBEFáVKPDBSBDUFSÎTUJDPEFMBTFQBSBDJÓOEFVOBNF[DMB CJOBSJB4JTFFTUÃTFQBSBOEPVOB[FÓUSPQP MBBMJNFOUBDJÓOEFCFFTUBSDFSDBOBBMBDPODFOUSBDJÓO B[FPUSÓQJDBFOUPODFT VOBDPMVNOBEFEFTUJMBDJÓOCJOBSJB RVFOPTFNVFTUSB TVFMFBOUFDFEFSBM TJTUFNBEFEFTUJMBDJÓOFYUSBDUJWB&OMBDPMVNOBTFBHSFHBFMTPMWFOUFWBSJBTFUBQBTBSSJCBEFMB BMJNFOUBDJÓO ZVOBTQPDBTFUBQBTBCBKPEFMBQBSUFTVQFSJPSEFMBDPMVNOB&OMBTFDDJÓOTVQFSJPS  FMTPMWFOUF SFMBUJWBNFOUFOPWPMÃUJM TFFMJNJOBZTFQSPEVDF"QVSPDPNPEFTUJMBEP&OMBTFDDJÓO JOUFSNFEJBFTUÃOQSFTFOUFTHSBOEFTDBOUJEBEFTEFTPMWFOUFZMPTDPNQPOFOUFT"Z#TFTFQBSBOVOP EFPUSP4FBDPTUVNCSBVTBS   PIBTUBWFDFTNÃTTPMWFOUFRVFMBBMJNFOUBDJÓOFOUPODFT  DPOGSFDVFODJB MBDPODFOUSBDJÓOEFTPMWFOUFFOMBTFDDJÓOJOUFSNFEJBFTNVZBMUB0CTFSWFRVFMBTF QBSBDJÓOEF"Z#EFCFTFSDPNQMFUBFOMBTFDDJÓOJOUFSNFEJB QPSRVFUPEP#RVFMMFHVFBMBTFDDJÓO TVQFSJPSOPTFSÃTFQBSBEP EFCJEPBRVFIBZNVZQPDPTPMWFOUFQSFTFOUF ZTBMESÃDPOTFDVFOUFNFO UFFOFMEFTUJMBEP-BTFDDJÓOJOGFSJPSBHPUBBM"EFMBNF[DMB QPSMPRVFTÓMPTBMFOFMTPMWFOUFZ# QPSFMGPOEPEFMBDPMVNOB &MEJBHSBNBEFMBDVSWBEFSFTJEVPQBSBMBEFTUJMBDJÓOFYUSBDUJWBEFFUBOPMZBHVB DPOFUJMFOHMJ DPMDPNPTPMWFOUF TFWFFOMBàHVSB-BTDVSWBTDPNJFO[BOFOFMB[FÓUSPQPCJOBSJP FUBOPM ZBHVB

DPOMPRVFFTUBHSÃàDBEFSFTJEVPFTQBSFDJEBBMBàHVSBD$PNPUPEBTMBTDVSWBT EFSFTJEVPUJFOFOMBNJTNBGPSNBHFOFSBM FOFTUFTJTUFNBOPIBZGSPOUFSBEFEFTUJMBDJÓO TVHJFSPBM MFDUPSRVFDPNQBSFMBGPSNBEFMBTDVSWBTEFSFTJEVPFOMBàHVSBDPOMBTEFMBàHVSB EPOEF BQBSFDFVOBGSPOUFSBEFEFTUJMBDJÓO 4FBHSFHBTPMWFOUFFTFODJBMNFOUFQVSPBVOáVKPEFLHNPMI MBCPSBUPSJPFOFMBQÊOEJDFEFMDBQÎUVMP &MTPMWFOUFZMBBMJNFOUBDJÓOTFQVFEFODPNCJOBSDPNP BMJNFOUBDJÓONF[DMBEB .  EFUFSNJOBEBDPOMBSFHMBEFMBQBMBODB

RVFTFTFQBSBFOUPODFTFOMBT DPSSJFOUFT%Z# DPNPNVFTUSBMBàHVSB4FOFDFTJUBOTJNVMBDJPOFTEFUBMMBEBTQBSBEFUFSNJOBSTJMB

Producto Producto Recirculación de solvente Alimentación Enfriador

Relleno de solvente

'*(63" %*"(3"."%&'-6+0%&6/"%&45*-"$*¶/&953"$5*7"

www.FreeLibros.me

  %FTUJMBDJÓOFYUSBDUJWB



UBTBEFáVKPEFMTPMWFOUFZMBSFMBDJÓOEFSFáVKPTPOTVàDJFOUFNFOUFHSBOEFT"MBVNFOUBSFMáVKPEF TPMWFOUF FMQVOUP.TFNPWFSÃ FOMBDVSWB IBDJBFMWÊSUJDFEFMTPMWFOUF-BDPSSJFOUFCJOBSJB#TF TFQBSBDPOGBDJMJEBEFOMBDPMVNOB"VORVFTFQVFEFVTBSFTUFTJTUFNBQBSBSPNQFSFMB[FÓUSPQP FUBOPMBHVB FTNÃTFDPOÓNJDBMBEFTUJMBDJÓOB[FPUSÓQJDB WFBMBTFDDJÓO -BTDVSWBTEFSFTJEVP EF%B#TFEFUJFOFOBNCBTFO4-BEFTUJMBDJÓOFYUSBDUJWBGVODJPOBQPSRVFFMTPMWFOUFTFBÒBEFBMB DPMVNOBWBSJBTFUBQBTBSSJCBEFMBEFBMJNFOUBDJÓO6OBOÃMJTJTDPNQMFUPEFMBEFTUJMBDJÓOFYUSBDUJWB TBMF EFM BMDBODF EF FTUB JOUSPEVDDJÓO %PIFSUZ Z .BMPOF   EFTDSJCFO JOGPSNBDJÓO EFUBMMBEB BDFSDBEFMVTPEFNBQBTEFDVSWBEFSFTJEVPQBSBEJTFÒBSTJTUFNBTEFEFTUJMBDJÓOFYUSBDUJWB -BNF[DMBEFTPMWFOUFZ#TFNBOEBBMBDPMVNOBEPOEFMPTFMFNFOUPTTFTFQBSBO4JTFTFMFD DJPOBFMTPMWFOUFFOGPSNBDPSSFDUB MBTFHVOEBDPMVNOBQVFEFTFSCBTUBOUFDPSUBQPSRVFFMDPNQP OFOUF#FTBQSFDJBCMFNFOUFNÃTWPMÃUJMRVFFMTPMWFOUF&MTPMWFOUFSFDVQFSBEPTFQVFEFFOGSJBSZ HVBSEBSQBSBWPMWFSMPBVTBSFOMBDPMVNOBEFEFTUJMBDJÓOFYUSBDUJWB0CTFSWFRVFFMTPMWFOUFEFCF FOGSJBSTFBOUFTEFFOUSBSBMBDPMVNOBQPSRVFTVQVOUPEFFCVMMJDJÓOFTBQSFDJBCMFNFOUFNBZPS RVFMBUFNQFSBUVSBEFPQFSBDJÓOEFMBDPMVNOB -BDPMVNOBFTEFEFTUJMBDJÓOTJNQMFZQVFEFEJTFÒBSTFDPOMPTNÊUPEPTEFTDSJUPTFOFMDBQÎ UVMP-BDPMVNOBFTCBTUBOUFNÃTDPNQMFKB QFSPDPOGSFDVFODJBTFQVFEFBEBQUBSFMNÊUPEP EFNBUSJ[EFQVOUPEFCVSCVKBRVFTFEFTDSJCJÓFOFMDBQÎUVMP$PNPFMTJTUFNBFTOPJEFBMZMPT WBMPSFTEF,EFQFOEFOEFMBDPODFOUSBDJÓOEFMTPMWFOUF TFSFRVJFSFVODJSDVJUPEFDPODFOUSBDJÓO FOFMEJBHSBNBEFáVKPRVFNVFTUSBMBàHVSB1PSGPSUVOB TFQVFEFQSPQPOFSVOCVFOWBMPS QBSBMBDPODFOUSBDJÓOEFTPMWFOUF ZBRVFTFSÃDBTJDPOTUBOUFFOMBTFDDJÓOJOUFSNFEJBZUBNCJÊO FOMBJOGFSJPS FYDFQUVBOEPFOFMWBQPSJ[BEPS&OMBQBSUFTVQFSJPSEFMBDPMVNOB MBDPODFOUSBDJÓO EFMTPMWFOUFEFDSFDFSÃDPONVDIBSBQJEF[IBTUBDFSP&TUBTDPODFOUSBDJPOFTEFTPMWFOUFRVFEBSÃO SFMBUJWBNFOUFJOBMUFSBEBTGSFOUFBUFNQFSBUVSBTZUBTBTEFáVKP-PTWBMPSFT,TFQVFEFODBMDVMBS

¶/

0

.

¶/ $*

%#+

"$

H

%#&

%#.

%#'

%#-

%#(

%#,

%#)

0"/

%#*

B

&5

-

.0

%#+

'3

$*

%#,

"$

;

'3

%#-

- %#* &5*&/ %#) (-*$ 0 %#( %#'

%#.

%#&

9

%#&

%#'

%#(

7 %#)

%#*

%#+

%#,

%#-

%#.

'3"$$*¶/.0-"(6"

'*(63" $637"4%&3&4*%601"3"&-4*45&."%&"(6"&5"/0- &5*-&/(-*$0- &/%&45*-"$*¶/&953"$5*7"1"3"30.1&3&-";&¶53010 &5"/0-"(6"$637"4(&/&3"%"4103"41&/1-6464"/%0 /35-$0.0%"504%&&26*-*#3*07"103-±26*%04&"(3&("30/-"4 -±/&"4'.4:#.% %&#"-"/$&%&."4"

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBNÊUPEPTDPNQMFKPTEFEFTUJMBDJÓO

DPOMBFDVBDJÓO 

EFUFSNJOBOEPMPTDPFàDJFOUFTEFBDUJWJEBEDPOMBDPSSFMBDJÓOEFFRVJMJCSJP WBQPSMÎRVJEPBEFDVBEB-BGPSNBNÃTGÃDJMEFIBDFSFTUPTDÃMDVMPTFTDPOTJNVMBEPSFTEFQSPDFTPT WFBFMBQÊOEJDFEFMDBQÎUVMP  &OMBàHVSB 4FBEFS  TFNVFTUSBOMPTQFSàMFTEFDPODFOUSBDJÓOQBSBMBEFTUJMBDJÓO FYUSBDUJWBEFOIFQUBOPZUPMVFOPVTBOEPGFOPMDPNPTPMWFOUF-PTQFSàMFTGVFSPODBMDVMBEPTSJHVSP TBNFOUFVTBOEPVONÊUPEPEFDPSSFDDJÓOTJNVMUÃOFBZMPTDPFàDJFOUFTEFBDUJWJEBETFDBMDVMBSPODPO MBFDVBDJÓOEF8JMTPO-BBMJNFOUBDJÓOGVFVOBNF[DMBEFMCNPMIEFOIFQUBOPZMCNPMI EFUPMVFOP RVFFOUSBODPNPMÎRVJEPBž'FOMBFUBQB&MTPMWFOUFSFDJSDVMBEPFOUSBFOMBFUBQB BVOáVKPUPUBMEFMCNPMI)BZVOUPUBMEFDPOUBDUPTEFFRVJMJCSJPJODMVZFOEPFMWBQPSJ [BEPSQBSDJBM&MGFOPM EFBMUPQVOUPEFFCVMMJDJÓO BUSBFBMUPMVFOPQPSRVFBNCPTTPODPNQVFTUPT BSPNÃUJDPT&MIFQUBOPTFWVFMWFFOUPODFTNÃTWPMÃUJMZTBMFFOFMEFTUJMBEP DPNQPOFOUF"FOMB àHVSB 0CTFSWFFOMBàHVSBRVFMBDPODFOUSBDJÓOEFGFOPMEJTNJOVZFDPONVDIBSBQJEF[ BSSJCBEFMBFUBQBNJFOUSBTRVFBVNFOUBMBEFOIFQUBOP%FMBFUBQBBMBMBDPODFOUSBDJÓO EFGFOPMFTBQSPYJNBEBNFOUFDPOTUBOUFZFMUPMVFOPTFTFQBSBEFMIFQUBOP%FMBTFUBQBTB MB DPODFOUSBDJÓOEFGFOPMFTDPOTUBOUFQFSPBVOWBMPSNFOPS&TUFDBNCJPEFDPODFOUSBDJÓOEFMTPMWFO UF GFOPM TVDFEFQPSRVFMBBMJNFOUBDJÓOFOUSBDPNPMÎRVJEP4FQVFEFPCUFOFSVOBDPODFOUSBDJÓO DPOTUBOUFEFTPMWFOUFTJTFFWBQPSBMBBMJNFOUBDJÓO PBHSFHÃOEPMFBMHPEFTPMWFOUFSFDJSDVMBEP&M IFQUBOPTFBHPUBFOMBNF[DMBFOUSFMBTFUBQBTZ&OFMWBQPSJ[BEPS FMTPMWFOUFFTOPWPMÃUJM FO DPNQBSBDJÓODPOFMUPMVFOP&OUPODFT FMWBQPSBMGPOEPFTNVDIPNÃTDPODFOUSBEPFOUPMVFOPRVF FOGFOPM&MSFTVMUBEPFTVOHSBOJODSFNFOUPFOMBDPODFOUSBDJÓOEFGFOPMFOMBFUBQBRVFTFWF EFMBàHVSB3PCJOTPOZ(JMMJMBOE 

4JJSPMBZ#BSOJDLJ  Z%PIFSUZZ.BMPOF   NVFTUSBOQFSàMFTEFDPODFOUSBDJÓOQBSBPUSPTTJTUFNBTEFEFTUJMBDJÓOFYUSBDUJWB -BTDPODFOUSBDJPOFTDBTJDPOTUBOUFTEFGFOPM TPMWFOUF BSSJCBZBCBKPEFMBFUBQBEFBMJNFO UBDJÓO àHVSB QFSNJUFOEFTBSSPMMBSNÊUPEPTBQSPYJNBEPTEFDÃMDVMP ,OJDMF  4FQVFEF VTBSVOEJBHSBNBEF.D$BCF5IJFMFQTFVEPCJOBSJPQBSBMBTFQBSBDJÓOEFIFQUBOPZUPMVFOP-B DVSWBEFiFRVJMJCSJPuSFQSFTFOUBMPTEBUPTZYQBSBFMIFQUBOPZUPMVFOPBDPODFOUSBDJÓODPOTUBOUFEF GFOPM-BDVSWBEFFRVJMJCSJPUFOESÃVOBEJTDPOUJOVJEBEFOMBFUBQBEFBMJNFOUBDJÓO1BSBMBTFUBQBT RVFFTUÃOBSSJCBEFMBEFBMJNFOUBDJÓOEFMTPMWFOUF TFQVFEFVTBSVOEJBHSBNBCJOBSJPOPSNBMEF .D$BCF5IJFMFQBSBIFQUBOPGFOPM,OJDLMF  UBNCJÊOEFTDSJCFMBNPEJàDBDJÓOEFMNÊUPEP EF 'FOTLF6OEFSXPPE(JMMJMBOE WBSJBOEP MB WPMBUJMJEBE SFMBUJWB QBSB SFQSFTFOUBS FM FRVJMJCSJP EF IFQUBOPUPMVFOPDPOMBDPODFOUSBDJÓOEFGFOPMFOMBFUBQBEFBMJNFOUBDJÓO -BSB[ÓOEFMHSBOBVNFOUPFOMBDPODFOUSBDJÓOEFTPMWFOUFFOFMWBQPSJ[BEPSTFWJTVBMJ[BDPO GBDJMJEBEBMJNBHJOBSVODBTPFYUSFNP FOFMRVFOPTFWBQPSJ[BTPMWFOUFFOFMWBQPSJ[BEPS&OUPO DFT FMWBQPSBMGPOEPFT FOFTFODJB FMDPNQPOFOUF#QVSP-BUBTBEFáVKPEFMÎRVJEPFOMBDPMVNOB TFQVFEFEFTDPNQPOFSDPNPTJHVF 

A 2H 7a†f K 



TJFOEP4MBUBTBEFáVKPDPOTUBOUFEFTPMWFOUF#MÎRFTMBUBTBEFáVKPEFMDPNQPOFOUF# RVFQFSNB m OFDFFOFMMÎRVJEP FOFMWBQPSJ[BEPSZ7 FTMBUBTBEFáVKPEFMWBQPSRVFDPOTJTUFQSJODJQBMNFOUFEF #-BUBTBEFáVKPEFGPOEPTTPOMBTDPSSJFOUFTRVFQFSNBOFDFOMÎRVJEBT 

'POEPT4 #MÎR



-BGSBDDJÓONPMBSEF#FOFMMÎRVJEPFOMBDPMVNOBTFQVFEFDBMDVMBSDPO 

m 7!Xda 2

7 a†f  K H 7 a†f  K



www.FreeLibros.me



  %FTUJMBDJÓOFYUSBDUJWB



Fracción molar en fase líquida

Heptano

Fenol

Heptano

Fenol

'*(63" 1&3'*-&4$"-$6-"%04 %&$0.104*$*¶/1"3"-"%&45*-"$*¶/ &953"$5*7"%&50-6&/0:/)&15"/0 50."%0%&4&"%&3  3&*.13&40 $0/"6503*;"$*¶/%&1&33:4$)&.*$"- &/(*/&&34)"/%#00, ‰&% $01:3*()5  .$(3"8)*--

Tolueno

Etapas

ZMBGSBDDJÓONPMBSEF#FOMPTGPOEPTFT 

m 7![dcYdh 2

7 a†f H 7 a†f





1BSBMBTUBTBTEFáVKPOPSNBMFTFTUPSFTVMUBFOY# DPMY# GPOEPT"VODVBOEPFMTPMWFOUFTFBCBTUBOUF WPMÃUJM DPNPFOMBàHVSB MBDPODFOUSBDJÓOEFUPMVFOP DPNQPOFOUF# CBKBFOFMWBQPSJ[BEPS -BTFMFDDJÓOEFMTPMWFOUFFTEFFYUSFNBJNQPSUBODJB&MQSPDFTPFTTJNJMBSBMEFTFMFDDJPOBSVO TPMWFOUFQBSBFYUSBDDJÓOMÎRVJEPMÎRVJEPRVFTFEFTDSJCJSÃFOFMDBQÎUVMP1PSEFàOJDJÓO FMTPM WFOUFOPEFCFGPSNBSVOB[FÓUSPQPDPOBMHVOPEFMPTDPNQPOFOUFT àHVSB$ 4JMPGPSNB FM QSPDFTPTFUSBOTGPSNBFOEFTUJMBDJÓOB[FPUSÓQJDBRVFTFEFTDSJCFFOMBTJHVJFOUFTFDDJÓO&OHFOFSBM  TFTFMFDDJPOBVOTPMWFOUFRVFTFQBSF[DBNÃTBMBDMBWFQFTBEBQBSBRVFEJTNJOVZBMBWPMBUJMJEBEEF

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBNÊUPEPTDPNQMFKPTEFEFTUJMBDJÓO

ÊTUB&YJTUFOFYDFQDJPOFTBFTUBSFHMBQPSFKFNQMP FOFMTJTUFNBOCVUBOP−CVUFOPDPOGVSGVSBM TFEJTNJOVZFMBWPMBUJMJEBEEFMCVUFOPRVFFTNÃTWPMÃUJM 4IJOTLFZ  "ZVEBOMBTMJTUBTEF FYUSBDUBOUFT 7BO8JOLMF  QBSBEFTUJMBDJÓOFYUSBDUJWB FOMBEFUFSNJOBDJÓOEFVOBFTUSVDUVSB HFOFSBMRVFBVNFOUFDPOFàDBDJBMBWPMBUJMJEBEEFMBTDMBWFT4FQVFEFOVTBSTBMFTDPNPiTPMWFOUFu  FOFTQFDJBMDVBOEPIBZRVFFMJNJOBSQFRVFÒBTDBOUJEBEFTEFBHVB 'VSUFS  5BNCJÊOBZVEB FMBOÃMJTJTEFMBDVSWBEFSFTJEVPQBSBBTFHVSBSRVFFMTPMWFOUFOPGPSNFB[FÓUSPQPTBEJDJPOBMFT #JFHMFSFUBM %PIFSUZZ.BMPOF   4FQVFEFBZVEBSBMBTFMFDDJÓOEFMTPMWFOUFTJTFUJFOFOFODVFOUBMBTQPMBSJEBEFTEFMPTDPN QVFTUPTRVFTFIBOEFTFQBSBS&OMBUBCMBTFNVFTUSBVOBMJTUBCSFWFEFDMBTFTEFDPNQVFTUPT PSEFOBEPTQPSQPMBSJEBEDSFDJFOUF4JTFWBOBTFQBSBSEPTDPNQVFTUPTEFQPMBSJEBEEJGFSFOUF TF QVFEFTFMFDDJPOBSVOTPMWFOUFRVFBUSBJHBFMNFOPTQPMBS PFMNÃTQPMBSEFMPTEPT1PSFKFNQMP  TVQPOHBNPTRVFTFUSBUBEFTFQBSBBDFUPOB DFUPOBRVFIJFSWFBž$ EFNFUBOPM BMDPIPMRVF IJFSWFBž$ &TUFTJTUFNBGPSNBVOB[FÓUSPQP1PESÎBNPTBHSFHBSVOIJESPDBSCVSPRVFBUSBJHB BMBBDFUPOB QFSPTJTFBHSFHBSBFMIJESPDBSCVSPTVàDJFOUF FMNFUBOPMTFWPMWFSÎBNÃTWPMÃUJM6OB BMUFSOBUJWBTFODJMMBFTBHSFHBSBHVB RVFBUSBFFMNFUBOPMZIBDFRVFMBBDFUPOBTFBNÃTWPMÃUJM&M NFUBOPMZFMBHVBTFTFQBSBOEFTQVÊTFOMBDPMVNOB&OFTUFFKFNQMPUBNCJÊOQPESÎBNPTBHSFHBS VOBMDPIPMEFNBZPSQFTPNPMFDVMBS DPNPCVUBOPM QBSBBUSBFSBMNFUBOPM $VBOEP TF RVJFSF TFQBSBS EPT IJESPDBSCVSPT  NJFOUSBT NBZPS TFB MB EJGFSFODJB FO MB DBOUJEBE EFEPCMFTFOMBDFT VOTPMWFOUFQPMBSGVODJPOBSÃNFKPSQBSBDBNCJBSMBWPMBUJMJEBE1PSFKFNQMP FM GVSGVSBMEJTNJOVZFMBWPMBUJMJEBEEFMPTCVUFOPT FODPNQBSBDJÓODPOMBEFMPTCVUBOPT&MGVSGVSBMFT VOBMDPIPMDÎDMJDPRVFTFVTBFOMVHBSEFBHVBQPSRVFMPTIJESPDBSCVSPTTPONJTDJCMFTFOGVSGVSBM6O BOÃMJTJTNÃTEFUBMMBEPEFMBTFMFDDJÓOEFTPMWFOUFJOEJDBRVFMPTQVFOUFTEFIJESÓHFOPTPONÃTJNQPS UBOUFTRVFMBQPMBSJEBE #FSH 4NJUI   5"#-" $-"4&4%&$0.16&450410310-"3*%"%&4$3&$*&/5&4        

)JESPDBSCVSPT ­UFSFT "MEFIÎEPT $FUPOBT ­TUFSFT "MDPIPMFT (MJDPMFT "HVB

6OBWF[FODPOUSBEBVOBFTUSVDUVSBHFOFSBM TFQVFEFOWFSJàDBSIPNÓMPHPTEFQFTPNPMFDVMBS DSFDJFOUFQBSBEFUFSNJOBSDVBMUJFOFVOQVOUPEFFCVMMJDJÓOMPTVàDJFOUFNFOUFBMUPQBSBQPEFSSFDV QFSBSTFDPOGBDJMJEBEFOMBDPMVNOB4JOFNCBSHP VOQVOUPEFFCVMMJDJÓOEFNBTJBEPFMFWBEPOPFT DPOWFOJFOUFQPSRVFMBDPMVNOBEFSFDVQFSBDJÓOEFTPMWFOUFUFOESÎBRVFPQFSBSBVOBUFNQFSBUVSB EFNBTJBEPBMUB&MTPMWFOUFEFCFTFSUPUBMNFOUFNJTDJCMFDPOBNCPTDPNQPOFOUFTFOUPEPFMJOUFS WBMPEFDPNQPTJDJPOFTEFMBEFTUJMBDJÓO 4F QSFàFSF VTBS VO TPMWFOUF OP UÓYJDP  OP JOáBNBCMF  OP DPSSPTJWP F JOFSUF "EFNÃT  EFCF DPOTFHVJSTFDPOGBDJMJEBEZEFCFTFSCBSBUP ZBRVFMPTDPTUPTEFSFMMFOPFJOWFOUBSJPEFTPMWFOUF QVFEFOTFSSFMBUJWBNFOUFBMUPT&OFTUBEFDJTJÓOUBNCJÊOEFCFUFOFSTFFODVFOUBMPTFGFDUPTTPCSFFM BNCJFOUFZMPTDPTUPTFOFMDJDMPEFEVSBDJÓOEFWBSJPTTPMWFOUFT "MMFOZ4IPOOBSE  $PNPEF DPTUVNCSF FMEJTFÒBEPSEFCFIBDFSDPNQSPNJTPTQBSBMBTFMFDDJÓOEFVOTPMWFOUF6ODPNQSPNJTP

www.FreeLibros.me

  %FTUJMBDJÓOB[FPUSÓQJDBDPOTPMWFOUFBHSFHBEP



GSFDVFOUFFTVTBSVOTPMWFOUFRVFTFVTFFOPUSPMVHBSEFMBQMBOUB PCJFOVOTVCQSPEVDUPEFVOB SFBDDJÓO BVORVFQPSPUSPMBEPQVFEFOPTFSFMTPMWFOUFÓQUJNP 1BSB TFQBSBDJPOFT EF JTÓNFSPT  MB EFTUJMBDJÓO FYUSBDUJWB TVFMF GBMMBS QPSRVF FM TPMWFOUF UJFOF FMNJTNPFGFDUPTPCSFMPTJTÓNFSPT1PSFKFNQMP #FSH  JOGPSNÓRVFFMNFKPSQPSUBEPSQBSB TFQBSBSNZQYJMFOPBVNFOUBCBMBWPMBUJMJEBESFMBUJWBEFB6OBBMUFSOBUJWBGSFOUFBMB EFTUJMBDJÓOFYUSBDUJWBOPSNBMFTVTBSVOTPMWFOUFRVFEFQSFGFSFODJB ZFOGPSNBSFWFSTJCMF SFBDDJPOF DPOVOPEFMPTJTÓNFSPT %PIFSUZZ.BMPOF  &MFTRVFNBEFMQSPDFTPTFSÃTJNJMBSBMEFMBàHV SB TJFOEPFMQSPEVDUP"FMJTÓNFSPMJHFSPZFMJTÓNFSPQFTBEPFMQSPEVDUP#-BSFBDDJÓOEJSFDUB TFFGFDUÙBFOMBQSJNFSBDPMVNOBZFMQSPEVDUPEFMBSFBDDJÓOTFBMJNFOUBBMBTFHVOEBDPMVNOB&O MBDPMVNOBTFFGFDUÙBMBSFBDDJÓOJOWFSTBZFMTPMWFOUFSFBDUJWPTFSFDJSDVMBBMBDPMVNOB&TUF QSPDFEJNJFOUPFTCBTUBOUFQBSFDJEPBMBSFBDDJÓODPOEFTUJMBDJÓORVFTFEFTDSJCJSÃFOMBTFDDJÓO  %&45*-"$*¶/";&053¶1*$"$0/40-7&/5&"(3&("%0

$VBOEPTFGPSNBVOB[FÓUSPQPIPNPHÊOFP PMBNF[DMBUJFOFQVOUPTEFFCVMMJDJÓONVZDFSDBOPT  OPFTQPTJCMFVTBSMPTQSPDFEJNJFOUPTEFTDSJUPTFOMBTFDDJÓO4JOFNCBSHP TFQVFEFBÒBEJSVO TPMWFOUF PQPSUBEPS RVFGPSNFVOB[FÓUSPQPCJOBSJPPUFSOBSJPZVTBSMPQBSBTFQBSBSMBNF[DMB &MUSVDPFTUÃFOFTDPHFSVOTPMWFOUFRVFGPSNFVOB[FÓUSPQPIFUFSPHÊOFP FOUPODFTTPOÙUJMFTMPT QSPDFEJNJFOUPTEFMBTFDDJÓO

PGÃDJMEFTFQBSBSDPOPUSPTNÊUPEPT DPNPFYUSBDDJÓONFEJBOUF VOMBWBEPDPOBHVB$PNPBIPSBIBZUSFTDPNQPOFOUFT FTQPTJCMFUFOFSVOPPNÃTB[FÓUSPQPTCJ OBSJPT PVOB[FÓUSPQPUFSOBSJP&MEJBHSBNBEFáVKPEFQFOEFEFMDPNQPSUBNJFOUPEFMTJTUFNBFO FRVJMJCSJPRVFTFQVFEFJOWFTUJHBSDPODVSWBTEFEFTUJMBDJÓOZDVSWBTEFSFTJEVP TFDDJÓO "RVÎ TFEFTDSJCJSÃOBMHVOPTFKFNQMPTUÎQJDPT -BàHVSBNVFTUSBVOEJBHSBNBEFáVKPTJNQMJàDBEP OPTFJOEJDBFMFYUFOTPVTPEFJOUFS DBNCJPTEFDBMPS QBSBTFQBSBSCVUBEJFOPTZCVUJMFOPT VTBOEPBNPOJBDPMÎRVJEPDPNPQPSUBEPS Recirculación de azeótropo

Separador Alimentación de C4

Alternativa Recirculación de NH3

Columna de agotamiento

Columna de destilación azeotrópica Vaporizador intermedio

Butileno Butadieno

'*(63" 4&1"3"$*¶/%&#65"%*&/0:#65*-&/04 64"/%0".0/*"$0$0.0 1035"%03 10''&/#&3(&3&5"-  

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBNÊUPEPTDPNQMFKPTEFEFTUJMBDJÓO

1PGGFOCFSHFSFUBM  0CTFSWFFMVTPEFMWBQPSJ[BEPSJOUFSNFEJPFOMBDPMVNOBEFEFTUJMBDJÓO B[FPUSÓQJDBQBSBNJOJNJ[BSMBQPMJNFSJ[BDJÓO"ž$ FMB[FÓUSPQPFTIPNPHÊOFP&MBNPOJBDPTF QVFEFSFDVQFSBSQPSFOGSJBNJFOUPQPSRVFBUFNQFSBUVSBTNFOPSFTBž$TFGPSNBOEPTGBTFTMÎRVJ EBT%VSBOUFMB4FHVOEB(VFSSB.VOEJBM FOMBTQMBOUBTJOEVTUSJBMFTRVFTFVTBSPOB−ž$ MBGBTF EFBNPOJBDPDPOUFOÎBFOQFTPEFCVUJMFOP&TUFBNPOJBDPTFSFDJSDVMBBMBDPMVNOBB[FPUSÓQJDB  TFBDPNPSFáVKPPFOMBFUBQB-BGBTFTVQFSJPSTFBMJNFOUBBMBDPMVNOBEFBHPUBNJFOUPZDPOUJF OFEFBNPOJBDP FOQFTP&MB[FÓUSPQPQSPEVDJEPFOMBDPMVNOBEFBHPUBNJFOUPTFSFDJSDVMBBM TFQBSBEPS&TUFFKFNQMPJMVTUSBMPTTJHVJFOUFTQVOUPTHFOFSBMFT &MB[FÓUSPQPGPSNBEPTFFOGSÎB  DPOGSFDVFODJB QBSBPCUFOFSEPTGBTFTZPQBSBPQUJNJ[BSMBPQFSBDJÓOEFMTFEJNFOUBEPSMÎRVJEP MÎRVJEP MBTDPSSJFOUFTRVFTFPCUJFOFOFOVOTFEJNFOUBEPSDBTJOVODBTPOQVSBTZEFCFOTFSQV SJàDBEBTQPTUFSJPSNFOUF&TUPTFWFFOMBDPMVNOBEFBHPUBNJFOUPEFMBàHVSB &MQSPEVDUP CVUJMFOP TFQVFEFSFDVQFSBS DPOGSFDVFODJB EFMTPMWFOUF /) FOVOBDPMVNOBEFBHPUBNJFOUP  FOMVHBSEFVOBDPMVNOBDPNQMFUBEFEFTUJMBDJÓO QPSRVFTFSFDJSDVMBFMB[FÓUSPQP 0USPTJTUFNBDPOVOTPMPB[FÓUSPQPCJOBSJPFTFMRVFTFWFFOMBàHVSB 4NJUI  &OMB DPMVNOBB[FPUSÓQJDB FMDPNQPOFOUF"ZFMQPSUBEPSGPSNBOVOB[FÓUSPQPEFQVOUPEFFCVMMJDJÓO NÎOJNPRVFTFSFDVQFSBDPNPEFTUJMBEP&MPUSPDPNQPOFOUF # TFSFDVQFSBDPNPQSPEVDUPQVSP

Relleno de agua Extracción con lavado de agua

Recirculación de agua Alimentación

Columna azeotrópica

Recirculación de solvente

Relleno de solvente

'*(63" %&45*-"$*¶/";&053¶1*$"$0/6/";&¶53010#*/"3*0%&16/50%& --*$*¶/.±/*.04&64"-"7"%0%&"(6"1"3"3&$61&3"3&-40-7&/5&%&4.*5)  

www.FreeLibros.me

  %FTUJMBDJÓOB[FPUSÓQJDBDPOTPMWFOUFBHSFHBEP



EFGPOEPT&OFTUFDBTP FMB[FÓUSPQPGPSNBEPFTIPNPHÊOFPZTFVTBVOMBWBEPDPOBHVB FYUSBD DJÓOEPOEFTFVTBBHVB QBSBSFDVQFSBSFMTPMWFOUFEFMDPNQPOFOUFEFTFBEP DPOFMDVBMGPSNBVO B[FÓUSPQP&MDPNQVFTUP"QVSPFTFMQSPEVDUPEFMBDPMVNOBEFMBWBEPDPOBHVB4FSFRVJFSFVOB DPMVNOBTJNQMFEFEFTUJMBDJÓOQBSBSFDVQFSBSFMTPMWFOUFEFMBHVB&OUSFMPTTJTUFNBTRVÎNJDPTRVF VTBOEJBHSBNBTEFáVKPQBSFDJEPTBÊTUFFTUÃOMBTFQBSBDJÓOEFDJDMPIFYBOP " EFCFODFOP # VTBO EPBDFUPOBDPNPTPMWFOUFZMBFMJNJOBDJÓOEFJNQVSF[BTEFMCFODFOP DPONFUBOPMDPNPTPMWFOUF 6OUFSDFSFKFNQMPCBTUBOUFDPNÙOFTMBTFQBSBDJÓOEFMB[FÓUSPQPEFFUBOPMBHVBVTBOEPVO IJESPDBSCVSPDPNPQPSUBEPS&MCFODFOPFSBFMQPSUBEPSNÃTDPNÙO MBDVSWBEFSFTJEVPTFWFFOMB àHVSB

QFSPEFCJEPBTVUPYJDJEBE TFIBTVTUJUVJEPDPOÊUFSEJFUÎMJDP OQFOUBOPPOIFYBOP 6OB[FÓUSPQPUFSOBSJPIFUFSPHÊOFPTBMFDPNPEFTUJMBEPEFMBDPMVNOBEFEFTUJMBDJÓOB[FPUSÓQJDB6O EJBHSBNBEFáVKPUÎQJDPQBSBFTUFTJTUFNBTFWFFOMBàHVSB #MBDL 3PCJOTPOZ(JMMJMBOE  4FBEFS 4IJOTLFZ 4NJUI %PIFSUZZ.BMPOF 8JEBHEPZ4FJEFS   -B BMJNFOUBDJÓO B MB DPMVNOB EF EFTUJMBDJÓO B[FPUSÓQJDB FT FM QSPEVDUP EFTUJMBEP EF VOB DPMVNOB CJOBSJBDPOFUBOPMBHVB RVFTFFODVFOUSBDFSDBOBBMBDPNQPTJDJÓOB[FPUSÓQJDB-BDPNQPTJDJÓOEFM B[FÓUSPQPUFSOBSJPWBSÎBMJHFSBNFOUF EFBDVFSEPDPOFMQPSUBEPSRVFTFFTDPKB1PSFKFNQMP DVBOEP FMQPSUBEPSFTOIFYBOP FMB[FÓUSPQPDPOUJFOFEFIFYBOP EFFUBOPMZEFBHVB UPEPT FOQFTP 4IJOTLFZ  -BSFMBDJÓOBHVBFUBOPMFOFMB[FÓUSPQPUFSOBSJPEFCFTFSNBZPSRVFMBDP SSFTQPOEJFOUFFOMBBMJNFOUBDJÓOQBSBRVFTFQVFEBFMJNJOBSUPEBFMBHVBDPOFMB[FÓUSPQPZTBDBSFM FYDFTPEFFUBOPMDPNPQSPEVDUPQVSPEFGPOEPT-BDBQBTVQFSJPSFOFMTFQBSBEPSDPOUJFOFEF IFYBOP EFFUBOPMZEFBHVB UPEPTFOQFTP NJFOUSBTRVFMBDBQBJOGFSJPSDPOUJFOF EFIFYBOP EFFUBOPMZEFBHVB UBNCJÊOFOFOQFTP-BDBQBTVQFSJPSEFMTFQBSBEPS TFSFáVKBBMBDPMVNOBEFEFTUJMBDJÓOB[FPUSÓQJDB NJFOUSBTRVFMBDBQBJOGFSJPSTFNBOEBBVOBDPMVN OBEFBHPUBNJFOUPQBSBFMJNJOBSFMBHVB -PTDÃMDVMPTQBSBDVBMRVJFSBEFMPTTJTUFNBTEFEFTUJMBDJÓOB[FPUSÓQJDBTPOCBTUBOUFNÃTDPN QMFKPTRVFQBSBMBEFTUJMBDJÓOTJNQMF PIBTUBQBSBMBEFTUJMBDJÓOFYUSBDUJWB-BDPNQMFKJEBETFEFCF Solvente de relleno

Separador

Reflujo de hidrocarburo

Capa de agua

Etanol, 70 a 90% en peso

Agotador

Agua

Etanol

'*(63" %&45*-"$*¶/";&053¶1*$"5&3/"3*"1"3"4&1"3"3&5"/0-%& "(6" $0/1035"%03%&)*%30$"3#630

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBNÊUPEPTDPNQMFKPTEFEFTUJMBDJÓO

BMDPNQPSUBNJFOUPFOFRVJMJCSJP RVFPCWJBNFOUFFTOPJEFBM ZBMBQPTJCMFGPSNBDJÓOEFUSFTGBTFT EPTMÎRVJEBTZVOBEFWBQPS EFOUSPEFMBDPMVNOB-BDVSWBEFSFTJEVPRVFNVFTUSBMBàHVSB EFNVFTUSBDPODMBSJEBEMBDPNQMFKJEBEEFFTPTTJTUFNBT1SPLPQBLJTZ4FJEFS Z8JEBHP Z4FJEFS  SFTFÒBOMPTQSPDFEJNJFOUPTEFDÃMDVMPQBSBEFTUJMBDJÓOB[FPUSÓQJDB #MBDL 

)PGGNBO 

1SPLPQBLJTZ4FJEFS 

3PCJOTPOZ(JMMJMBOE 

4FB EFS 

4NJUI  Z8JEBHPZ4FJEFS  IBOQSFTFOUBEPSFTVMUBEPTEFTJNVMBDJPOFTQBSB FTUPTTJTUFNBT-PTSFTVMUBEPTEF4FBEFSQBSBMBEFTIJESBUBDJÓOEFMFUBOPMDPOOQFOUBOPDPNPTPM WFOUFTFHSBàDBOFOMBàHVSB&MTJTUFNBRVFTFVTÓFTQBSFDJEPBMEJBHSBNBEFáVKPEFMBàHVSB -BBMJNFOUBDJÓOBMBDPMVNOBDPOUFOÎBGSBDDJÓONPMBSEFFUBOPM-BDPMVNOBUSBCBKÓB VOBL1BQBSBQFSNJUJSMBDPOEFOTBDJÓOEFMEFTUJMBEPDPOBHVBEFFOGSJBNJFOUPDPOFUBQBT  VOWBQPSJ[BEPSQBSDJBMZVODPOEFOTBEPSUPUBM-BUFSDFSBFUBQBBCBKPEFMDPOEFOTBEPSGVFMBFUBQB EFBMJNFOUBDJÓO0CTFSWFRVFMPTQFSàMFTEFMDPOEFOTBEPSTPOEJGFSFOUFTBMPTRVFTFWJFSPOFOFM DBQÎUVMP&MQFOUBOPQBSFDF TVQFSàDJBMNFOUF TFSVOBDMBWFMJHFSB QFSPOBEBEFÊMBQBSFDFFOMPT GPOEPT&OTVMVHBS VOBQFRVFÒBDBOUJEBEEFBHVBTBMFFOMPTGPOEPTKVOUPDPOFMFUBOPM $POGSFDVFODJB FTNÃTEJGÎDJMTFMFDDJPOBSVOTPMWFOUFQBSBMBEFTUJMBDJÓOB[FPUSÓQJDBRVFQBSB MBEFTUJMBDJÓOFYUSBDUJWB&OHFOFSBMIBZNFOPTTPMWFOUFTRVFGPSNFOB[FÓUSPQPTRVFIJFSWBOBVOB UFNQFSBUVSB TVàDJFOUFNFOUF CBKB QBSB RVF TV FMJNJOBDJÓO EFM EFTUJMBEP TFB TFODJMMB  P CJFO RVF

Etanol Pentano

Fracción mol en vapor

Agua

V Etapa

'*(63" 1&3'*-&4%&$0.104*$*¶/1"3"6/"$0-6./"%& %&45*-"$*¶/";&053¶1*$"%0/%&4&4&1"3""(6":&5"/0- $0/ 1035"%03%&/1&/5"/0 4&"%&3  

www.FreeLibros.me

  %FTUJMBDJÓODPOSFBDDJÓORVÎNJDB



IJFSWBO B VOB UFNQFSBUVSB TVàDJFOUFNFOUF BMUB QBSB RVF TF QVFEBO FMJNJOBS FO MPT GPOEPT 4PO ÙUJMFTMPTBOÃMJTJTEFMBDVSWBEFEFTUJMBDJÓOZDVSWBEFSFTJEVPQBSBDMBTJàDBSMPTTPMWFOUFTQSPCBCMFT  ZQBSBEFTBSSPMMBSOVFWPTQSPDFTPT #JFHMFSFUBM %PIFSUZZ.BMPOF 8JEBHPZ4FJEFS   "EFNÃT FMB[FÓUSPQPCJOBSJPPUFSOBSJPRVFTFGPSNFEFCFTFSGÃDJMEFTFQBSBS&OMBQSÃD UJDB FTUFSFRVJTJUPTFTBUJTGBDFDPOB[FÓUSPQPTIFUFSPHÊOFPTZDPOB[FÓUSPQPTRVFTFBOGÃDJMFTEF TFQBSBSNFEJBOUFVOMBWBEPDPOBHVB&MQPSUBEPSRVFTFFTDPKBUBNCJÊOEFCFTBUJTGBDFSMPTSFRVJ TJUPTEFOPTFSUÓYJDP OPTFSDPSSPTJWP UFOFSJOFSDJBRVÎNJDB RVFTFDPOTJHBDPOGBDJMJEBE DPOCBKP DPTUPZRVFTFBOBNJHBCMFTBMBNCJFOUF%FCJEPBMBEJàDVMUBEEFFODPOUSBSTPMWFOUFTBEFDVBEPT  MPTTJTUFNBTEFEFTUJMBDJÓOB[FPUSÓQJDBDPOTPMWFOUFTFYDMVTJWPTTPOQBUFOUBCMFT  %&45*-"$*¶/$0/3&"$$*¶/26±.*$"

&OPDBTJPOFT MBTDPMVNOBTEFEFTUJMBDJÓOTFVTBODPNPSFBDUPSFTRVÎNJDPT-BWFOUBKBEFFTUFNÊUPEP FTRVFQVFEFOFGFDUVBSTFBMNJTNPUJFNQPMBEFTUJMBDJÓOZMBSFBDDJÓOFOFMNJTNPSFDJQJFOUFZMPTQSP EVDUPTTFQVFEFOFMJNJOBSQBSBJNQVMTBSVOBSFBDDJÓOSFWFSTJCMFIBTUBTVUFSNJOBDJÓO-BBQMJDBDJÓO JOEVTUSJBMNÃTGSFDVFOUFFTMBGPSNBDJÓOEFÊTUFSFTDPOVOÃDJEPDBSCPYÎMJDPZVOBMDPIPM1PSFKFNQMP  MBGBCSJDBDJÓOEFBDFUBUPEFNFUJMPQPSEFTUJMBDJÓOSFBDUJWBGVFVOHSBOÊYJUPDPOFMRVFOPQVEJFSPO DPNQFUJSMPTQSPDFTPTDPOWFODJPOBMFT #JFHMFSFUBM  -BEFTUJMBDJÓOSFBDUJWBGVFQBUFOUBEBQPS #BLIBVTFO ZIBTJEPPCKFUPEFWBSJBTQBUFOUFTEFTEFFOUPODFT WFB4JJSPMBZ#BSOJDLJ  Z %PIFSUZZ.BMPOF ZMBTSFGFSFODJBTBIÎDJUBEBT -BSFBDDJÓOFOVOBDPMVNOBEFEFTUJMBDJÓOQVF EFUBNCJÊOTFSJOEFTFBCMFDVBOEPTFEFTDPNQPOFVOPEFMPTQSPEVDUPTRVFTFEFTFBO -BEFTUJMBDJÓODPOSFBDDJÓOFTÙUJMQBSBSFBDDJPOFTSFWFSTJCMFT$PNPFKFNQMP UFOESÎBNPTSF BDDJPOFTDPNPMBTTJHVJFOUFT 628 628 9 6 728 9

-PTPCKFUJWPTEFMBEFTUJMBDJÓOTPOTFQBSBSFMPMPTQSPEVDUPTEFMPMPTSFBDUJWPTQBSBJNQVMTBSBMBT SFBDDJPOFTIBDJBMBEFSFDIBZSFDVQFSBSVOPPNÃTQSPEVDUPTQVSJàDBEPT %FQFOEJFOEPEFMBTQSPQJFEBEFTEFMTJTUFNBFOFRVJMJCSJP FTQPTJCMFVTBSEJTUJOUBTDPOàHVSB DJPOFTEFEFTUJMBDJÓO DPNPNVFTUSBMBàHVSB&OMBàHVSB"TFSFQSFTFOUBFMDBTPFORVFFM SFBDUJWPFTNFOPTWPMÃUJMRVFFMQSPEVDUP #FMDL  4JTFGPSNBOWBSJPTQSPEVDUPT OPTFJOUFOUB TFQBSBSMPTFOFTUFTJTUFNB-BQVSHBFTQBSBFWJUBSMBBDVNVMBDJÓOEFJNQVSF[BTPQSPEVDUPTOP WPMÃUJMFTEFSFBDDJPOFTTFDVOEBSJBT4JMBBMJNFOUBDJÓOFTNÃTWPMÃUJMRVFFMQSPEVDUPRVFTFEFTFB  TFQVFEFFOUPODFTVTBSFMBSSFHMPEFMBàHVSB# #FMDL  &TUBDPMVNOBFTUÃ FOFTFODJB B SFáVKPUPUBM TBMWPQPSVOBQFRVFÒBQVSHB RVFQPESÎBOFDFTJUBSTFQBSBFMJNJOBSWPMÃUJMFTPHBTFT -BTàHVSBT$ %Z&NVFTUSBOTJTUFNBTFOEPOEFTFGPSNBOEPTQSPEVDUPTÊTUPTTF TFQBSBOFOUSFTÎZEFMPTSFBDUJWPTFOMBDPMVNOBEFEFTUJMBDJÓO&OMBàHVSB$ FMPMPTSFBDUJWPT UJFOFOWPMBUJMJEBEJOUFSNFEJBFOUSFMBEFMPTEPTQSPEVDUPT&OUPODFT MPTSFBDUJWPTQFSNBOFDFSÃO FOMBQBSUFNFEJBEFMBDPMVNOBIBTUBDPOTVNJSTF NJFOUSBTRVFMPTQSPEVDUPTTFTBDBOEFNBOFSB DPOUJOVB JNQVMTBOEPBMBSFBDDJÓOIBDJBMBEFSFDIB4JMPTSFBDUJWPTOPUJFOFOWPMBUJMJEBEJOUFSNF EJB BMHVOPTEFFMMPTBQBSFDFSÃOFODBEBDPSSJFOUFEFQSPEVDUP 4V[VLJFUBM  -PTFTRVFNBT BMUFSOBUJWPTRVFNVFTUSBOFOMBTàHVSBT%Z& 4V[VLJFUBM 4JJSPMBZ#BSOJDLJ  DPOGSFDVFODJBTFSÃODPOWFOJFOUFTQBSBMBSFBDDJÓO " #$ %

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBNÊUPEPTDPNQMFKPTEFEFTUJMBDJÓO

Purga

Producto volátil

Producto

Purga

Volátiles

No volátiles

'*(63" &426&."41"3"%&45*-"$*¶/$0/3&"$$*¶/26±.*$"" 130%6$5070-¦5*- -"3&"$$*¶/&4"$# 130%6$50/070-¦5*- -"3&"$$*¶/&4"%$ %04130%6$504  -"43&"$$*0/&440/"$ %0" #$ % % & 3&"$$*¶/" #$ % 4*&/%0# :%/070-¦5*-&4 &OFTBTEPTàHVSBT MBTFTQFDJFT"Z$TPOSFMBUJWBNFOUFWPMÃUJMFT NJFOUSBTRVFMBTFTQFDJFT#Z %TPOSFMBUJWBNFOUFOPWPMÃUJMFT$PNPMPTSFBDUJWPTTFBMJNFOUBOFOMPTFYUSFNPTPQVFTUPTEFMB DPMVNOB IBZVOBSFHJÓONVDIPNBZPSEPOEFFTUÃOQSFTFOUFTMPTEPTSFBDUJWPT&OUPODFT FMUJFNQP EFSFTJEFODJBQBSBMBSFBDDJÓOTFSÃNBZPSFOMBTàHVSBT%Z&RVFFOMBàHVSB$ QPSMPRVF TFFTQFSBOSFOEJNJFOUPTNBZPSFT-PTTJTUFNBTEFMBTàHVSBT$Z%TFIBOVTBEPQBSBSFBDDJP OFTEFFTUFSJàDBDJÓO DPNP ¦DJEPBDÊUJDP FUBOPM BDFUBUPEFFUJMP BHVB 4V[VLJFUBM 

Z

www.FreeLibros.me

  %FTUJMBDJÓODPOSFBDDJÓORVÎNJDB



¦DJEPBDÊUJDP NFUBOPM BDFUBUPEFNFUJMP BHVB 4JJSPMBZ#BSOJDLJ  NVFTUSBOVONBQBEFDVSWBEFSFTJEVPDPODVBUSPDPNQPOFOUFTQBSBMB QSPEVDDJÓOEFBDFUBUPEFNFUJMP6TBSPOVOBNPEJàDBDJÓOEFMBàHVSB& EPOEFTFBMJNFOUBVO DBUBMJ[BEPSMÎRVJEPOPWPMÃUJMFOUSFMBTBMJNFOUBDJPOFTEFÃDJEPBDÊUJDP # ZNFUBOPM " .VFTUSBO MPTQFSàMFTEFMPTDVBUSPDPNQPOFOUFTZEFMDBUBMJ[BEPS $VBOEPFOMBDPMVNOBTFFGFDUÙBVOBSFBDDJÓO FTOFDFTBSJPNPEJàDBSMBTFDVBDJPOFTEFCBMBO DFEFNBTBZFOFSHÎBQBSBJODMVJSMPTUÊSNJOPTEFMBSFBDDJÓO-BFDVBDJÓOHFOFSBMEFCBMBODFEF NBTBQBSBMBFUBQBK FDVBDJÓO TFQVFEFNPEJàDBSDPNPTJHVF 

K_n_ A_m_ ¶K_ ¶&n_ ¶& ¶A _ &m_ & 2;_o_ g_



BRVÎ FMUÊSNJOPEFSFBDDJÓOSKFTQPTJUJWPTJFMDPNQPOFOUFFTVOQSPEVDUPEFMBSFBDDJÓO1BSBVTBS MBFDVBDJÓO  TFEFCFVTBSMBFDVBDJÓOEFWFMPDJEBEBEFDVBEBQBSBMBSFBDDJÓO DPNPSK&O HFOFSBM MBWFMPDJEBEEFMBSFBDDJÓOEFQFOEFSÃUBOUPEFMBUFNQFSBUVSBDPNPEFMBTDPNQPTJDJPOFT EFMPTMÎRVJEPT $VBOEPMPTCBMBODFTEFNBTBFTUÃOFOGPSNBNBUSJDJBM FMUÊSNJOPEFMBSFBDDJÓOTFQVFEFJODMVJS DÓNPEBNFOUFDPOMBBMJNFOUBDJÓOFOFMUÊSNJOP% FDVBDJPOFT  Z  $POFMMPTFDPOTFSWBMB GPSNBUSJEJBHPOBMEFMCBMBODFEFNBTB QFSPFMUÊSNJOP%EFQFOEFEFMBDPODFOUSBDJÓOEFMMÎRVJEPZ MBUFNQFSBUVSBEFMBFUBQB&TOFDFTBSJPNPEJàDBSMPTQSPDFEJNJFOUPTEFDPOWFSHFODJBQBSBSFTPMWFS FMDPOKVOUPSFTVMUBOUFEFFDVBDJPOFT QPSRVFQVFEFTFSRVFMPTQSPDFEJNJFOUPTEFTDSJUPTFOFMDBQÎUV MPOPDPOWFSKBO-BTFDVBDJPOFTTFIBOWVFMUPBMUBNFOUFOPMJOFBMFTEFCJEPBMUÊSNJOPEFWFMPDJEBE EFSFBDDJÓO&OHFOFSBM MPTTJNVMBEPSFTEFQSPDFTPTNPEFSOPTQVFEFODPOWFSHFSFOQSPCMFNBTEF EFTUJMBDJÓOSFBDUJWB BVORVFQPESÎBTFSOFDFTBSJPDBNCJBSMBTQSPQJFEBEFTEFDPOWFSHFODJB &OMBàHVSB 4V[VLJFUBM  BQBSFDFVOBNVFTUSBEFQFSàMFTEFDPNQPTJDJÓOZUFN QFSBUVSBQBSBMBFTUFSJàDBDJÓOEFÃDJEPBDÊUJDPZFUBOPMDPOFMTJTUFNBEFEFTUJMBDJÓOEFMBàHVSB $-BDPMVNOBEFEFTUJMBDJÓOTFOVNFSBDPOFUBQBT JODMVZFOEPBMDPOEFOTBEPSUPUBM /P  ZFMWBQPSJ[BEPSQBSDJBM /P -BSFBDDJÓOQVFEFFGFDUVBSTFFODBEBFUBQBEFMBDPMVNOB FOFM DPOEFOTBEPSZFMWBQPSJ[BEPS-BBMJNFOUBDJÓOTFJOUSPEVDFFOMBFUBQBDPNPMÎRVJEPTBUVSBEPZ FTUÃGPSNBEBQSJODJQBMNFOUFQPSÃDJEPBDÊUJDPZFUBOPMDPOVOBQFRVFÒBDBOUJEBEEFBHVB4FVTB VOBSFMBDJÓOEFSFáVKPJHVBMB&MQSPEVDUPEFTUJMBEPDPOUJFOFMBNBZPSQBSUFEFMBDFUBUPEFFUJMP QSPEVDJEPFOMBSFBDDJÓO BEFNÃTEFFUBOPMZVOBQFRVFÒBDBOUJEBEEFBHVB5PEPFMÃDJEPBDÊUJDP OPSFBDDJPOBEPBQBSFDFFOMPTGPOEPTKVOUPDPOMBNBZPSQBSUFEFMBHVBZVOBGSBDDJÓOJNQPSUBOUF EFMFUBOPM&TPCWJPRVFMBSFBDDJÓOOPFTDPNQMFUB 6OUJQPEJTUJOUPEFEFTUJMBDJÓODPOSFBDDJÓOFTMBiEFTUJMBDJÓODBUBMÎUJDBu 1BSLJOTPO  &O FTUFQSPDFTP TFBQJMBOQBTUJMMBTEFDBUBMJ[BEPS FTGFSBTPDJMJOESPT FOMBDPMVNOB&TBTQBTUJMMBT TJSWFOBEFNÃTDPNPFNQBRVFEFDPMVNOB WFBFMDBQÎUVMP &TUFQSPDFTPTFVTÓQBSBQSPEVDDJÓO DPNFSDJBMEFÊUFSNFUÎMJDPUFSCVUÎMJDP .5#& EFNFUIZMUFSUCVUZMFUIFS DPOMBSFBDDJÓOFOGBTFMÎ RVJEBFOUSFJTPCVUJMFOPZNFUBOPM&MDBMPSHFOFSBEPQPSMBSFBDDJÓOFYPUÊSNJDBTFVTBQBSBPCUFOFS HSBOQBSUFEFMDBMPSOFDFTBSJPQBSBMBEFTUJMBDJÓO%FTEFRVFTFQSPIJCJÓFMVTPEF.5#&DPNPBEJ UJWPEFHBTPMJOB EFCJEPBQSPCMFNBTEFDPOUBNJOBDJÓOPSJHJOBEPTFOUBORVFTEFBMNBDFOBNJFOUP DPOGVHBT FTUBTVOJEBEFTTFIBODFSSBEP&OUSFPUSBTBQMJDBDJPOFTEFMBEFTUJMBDJÓODBUBMÎUJDBFTUÃO MBEFTVMGVSBDJÓOEFMBHBTPMJOB MBTFQBSBDJÓOEFCVUFOPEFVOBDPSSJFOUFEF$NF[DMBEPTZMB FTUFSJàDBDJÓOEFÃDJEPTHSBTPT "VORVFNVDIPTTJTUFNBTEFSFBDDJÓOOPUJFOFOMBTDBSBDUFSÎTUJDBTDPSSFDUBTEFFRVJMJCSJPEF SFBDDJÓOPEFFRVJMJCSJPWBQPSMÎRVJEP DVBOEPTFDVFOUBDPOFMMBT FTUBUÊDOJDBFTVONÊUPEPJOEVT USJBMNVZWBMJPTP

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBNÊUPEPTDPNQMFKPTEFEFTUJMBDJÓO

Alimentación Ácido acético Etanol Agua Acetato de etilo

Composición del líquido (fracción mol)

Temperatura [°C]

'*(63" 1&3'*-&4%&$0.104*$*¶/:5&.1&3"563"1"3"-"3&"$$*¶/¦$*%0"$­5*$0 &5"/0-"$&5"50%&&5*-0 "(6"%&46;6,*&5"- 

$01:3*()53&*.13&40 $0/"6503*;"$*¶/%&+063/"-0'$)&.*$"-&/(*/&&3*/(0'+"1"/  3&46.&/m0#+&5*704

&OFTUFDBQÎUVMPEFTDSJCJNPTMPTTJTUFNBTEFEFTUJMBDJÓOB[FPUSÓQJDBZFYUSBDUJWB ZMBEFTUJMBDJÓODPO SFBDDJÓORVÎNJDBTJNVMUÃOFB"MàOBMEFFTUFDBQÎUVMPEFCFVTUFEBMDBO[BSMPTTJHVJFOUFTPCKFUJWPT  "OBMJ[BSTJTUFNBTEFEFTUJMBDJÓOCJOBSJBVTBOEPPUSPTFTRVFNBTEFTFQBSBDJÓOQBSBSPNQFSFM B[FÓUSPQP  3FTPMWFS QSPCMFNBT EF EFTUJMBDJÓO B[FPUSÓQJDB CJOBSJB IFUFSPHÊOFB  JODMVZFOEP FM TFDBEP EF TPMWFOUFTPSHÃOJDPTDPOEJBHSBNBTEF.D$BCF5IJFMF  &YQMJDBSZBOBMJ[BSMBEFTUJMBDJÓOQPSBSSBTUSFDPOWBQPS  6TBSEJBHSBNBTEF.D$BCF5IJFMFPTJNVMBEPSFTEFQSPDFTPQBSBSFTPMWFSQSPCMFNBTEPOEFTF VTBOEPTQSFTJPOFTQBSBTFQBSBSBMPTB[FÓUSPQPT  %FUFSNJOBSMPTQPTJCMFTQSPEVDUPTEFVOBEFTUJMBDJÓOUFSOBSJBVTBOEPDVSWBTEFSFTJEVP  &YQMJDBSFMPCKFUJWPEFMBEFTUJMBDJÓOFYUSBDUJWB TFMFDDJPOBSVOTPMWFOUFBEFDVBEP FYQMJDBSMPT QFSàMFTFTQFSBEPTEFDPODFOUSBDJÓOZIBDFSMPTDÃMDVMPTDPOVOTJNVMBEPSEFQSPDFTPT  6TBSVOEJBHSBNBEFDVSWBEFSFTJEVPQBSBEFUFSNJOBSMPTQSPEVDUPTFTQFSBEPTEFVOBEFTUJMB DJÓOB[FPUSÓQJDBDPOVOTPMWFOUFBHSFHBEP  &YQMJDBSFOGPSNBDVBMJUBUJWBFMPCKFUPEFFGFDUVBSVOBSFBDDJÓOFOVOBDPMVNOBEFEFTUJMBDJÓOZ EFTDSJCJSMBTWFOUBKBTZEFTWFOUBKBTEFMBTEJTUJOUBTDPOàHVSBDJPOFTEFDPMVNOB 3&'&3&/$*"4

"MMFO %5Z%34IPOOBSE (SFFO&OHJOFFSJOH&OWJSPONFOUBMMZ$POTDJPVT%FTJHOPG$IFNJ DBM1SPDFTTFT 1SFOUJDF)BMM153 6QQFS4BEEMF3JWFS /FX+FSTFZ  #FMDL -) i$POUJOVPVT3FBDUJPOTJO%JTUJMMBUJPO&RVJQNFOUu "*$I&+     #FSH - i4FMFDUJOHUIF"HFOUGPS%JTUJMMBUJPO1SPDFTTFTu $IFN&OH1SPHS  

 4FQU 

www.FreeLibros.me

3FGFSFODJBT



#JFHMFS -5 *&(SPTTNBOOZ"88FTUFSCFSH 4ZTUFNBUJD.FUIPETPG$IFNJDBM1SPDFTT %FTJHO 1SFOUJDF)BMM153 6QQFS4BEEMF3JWFS /FX+FSTFZ  #MBDL $ i%JTUJMMBUJPO.PEFMJOHPG&UIBOPM3FDPWFSZBOE%FIZESBUJPO1SPDFTTFTGPS&UIB OPMBOE(BTPIPMu $IFN&OH1SPHS  

 4FQU  $IBNCFST +. i&YUSBDUJWF%JTUJMMBUJPO %FTJHOBOE"QQMJDBUJPOu $IFN&OH1SPHS     %PIFSUZ .Z..BMPOF $PODFQUVBM%FTJHOPG%JTUJMMBUJPO4ZTUFNT .D(SBX)JMM /FX:PSL  %SFX +8 i4PMWFOU3FDPWFSZu FO1"4DIXFJU[FS &E

)BOECPPLPG4FQBSBUJPO5FDIOJRVFT GPS$IFNJDBM&OHJOFFST B&E .D(SBX)JMM /FX:PSL  4FDDJÓO &MMFSCF 38 i4UFBN%JTUJMMBUJPO4USJQQJOHu FO1"4DIXFJU[FS &E

)BOECPPLPG4FQBSBUJPO 5FDIOJRVFTGPS$IFNJDBM&OHJOFFST B&E .D(SBX)JMM /FX:PSL  4FDDJÓO 'SBOL 5$ i#SFBL"[FPUSPQFTXJUI1SFTTVSF4FOTJUJWF%JTUJMMBUJPOu $IFN&OH1SPH    BCSJMEF  'VSUFS 8' i1SPEVDUJPOPG'VFM(SBEF&UIBOPMCZ&YUSBDUJWF%JTUJMMBUJPO&NQMPZJOHUIF4BMU &GGFDUu 4FQ1VSJGJD.FUIPET     )FOHTUFCFDL 3+ %JTUJMMBUJPO1SJODJQMFTBOE%FTJHO 3FJOIPME /FX:PSL  )PGGNBO &+ "[FPUSPQJDBOE&YUSBDUJWF%JTUJMMBUJPO *OUFSTDJFODF /FX:PSL  ,OJDLMF  ) /  i&YUSBDUJWF %JTUJMMBUJPOu  "*$I& .PEVMBS *OTUSVDUJPO  4FSJF # 4UBHFXJTF BOE .BTT5SBOTGFS0QFSBUJPOT7PM.VMUJDPNQPOFOU%JTUJMMBUJPO "*$I& /FX:PSL  1ÃHT -VEXJH && "QQM1SPD%FT B&E 7PM (VMG1VCMJTIJOH$P )PVTUPO  -VZCFO 8- i"[FPUSPQJD5PXFS%FTJHOCZ(SBQIu )ZESPDBSCPO1SPDFTTJOH  

 &OF   /FMTPO 1" i$PVOUFSDVSSFOU&RVJMJCSJVN4UBHF4FQBSBUJPOXJUI3FBDUJPOu "*$I&+     1BSLJOTPO ( i%JTUJMMBUJPO/FX8SJOLMFTGPSBO"HF0ME5FDIOPMPHZu $IFN&OH1SPH     KVMJPEF  1FSSZ  3 ) Z % 8 (SFFO &ET

 $IFNJDBM &OHJOFFST )BOECPPL  B FE  .D(SBX)JMM  /FX :PSL  1PGGFOCFSHFS / -))PSTMFZ )4/VUUJOHZ&$#SJUUPO i4FQBSBUJPOPG#VUBEJFOFCZ"[FP USPQJD%JTUJMMBUJPOXJUI"NNPOJBu 5SBOT"NFS*OTU$IFN&OH     1SPLPQBLJT (+Z8%4FJEFS i%ZOBNJD4JNVMBUJPOPG"[FPUSPQJD%JTUJMMBUJPO5PXFSTu "*$I& +     3PCJOTPO  $ 4 Z & 3 (JMMJMBOE  &MFNFOUT PG 'SBDUJPOBM %JTUJMMBUJPO  B &E  .D(SBX)JMM  /FX :PSL  $BQ 4FBEFS +% i%JTUJMMBUJPOu FO1FSSZ 3)Z%8(SFFO &ET

$IFNJDBM&OHJOFFST)BOECPPL  B&E .D(SBX)JMM /FX:PSL  4FDDJÓO 4IJOTLFZ '( %JTUJMMBUJPO$POUSPM 'PS1SPEVDUJWJUZBOE&OFSHZ$POTFSWBUJPO B&E .D(SBX)JMM  /FX:PSL  $BQTZ 4JJSPMB  + + Z 4 % #BSOJDLJ  i&OIBODFE %JTUJMMBUJPOu  FO 1FSSZ  3 ) Z % 8 (SFFO &ET

 1FSSZT$IFNJDBM&OHJOFFST)BOECPPL B&E .D(SBX)JMM /FX:PSL 1ÃHTB  4NJUI #% %FTJHOPG&RVJMJCSJVN4UBHF1SPDFTTFT .D(SBX)JMM /FX:PSL  $BQ 4V[VLJ * ):BHJ ),PNBUTVZ.)JSBUB i$BMDVMBUJPOPG.VMUJDPNQPOFOU%JTUJMMBUJPO"DDPN QBOJFECZB$IFNJDBM3FBDUJPOu +$IFN&OH+BQBO     7BO8JOLMF . %JTUJMMBUJPO .D(SBX)JMM /FX:PSL  8BOLBU  1 $  i(SBQIJDBM .VMUJDPNQPOFOU %JTUJMMBUJPOu  "*$I& .PEVMBS *OTUSVDUJPO  4FSJF # 4UBHFXJTF BOE .BTT 5SBOTGFS 0QFSBUJPOT 7PM  .VMUJDPNQPOFOU %JTUJMMBUJPO  "*$I&  /FX :PSL   1ÃHT

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBNÊUPEPTDPNQMFKPTEFEFTUJMBDJÓO

8JEBHP  4 Z 8 % 4FJEFS  i"[FPUSPQJD %JTUJMMBUJPOu  "*$I& +PVSOBM       8PPEMBOE  -3 i4UFBN%JTUJMMBUJPOu FO%+%F3FO[P &E

6OJU0QFSBUJPOTGPS5SFBUNFOUPG)B[BSEPVT *OEVTUSJBM8BTUFT /PZFT%BUB$PSQ 1BSL3JEHF /FX+FSTFZ  1ÃHT 8PPET %3 1SPDFTT%FTJHOBOE&OHJOFFSJOH1SBDUJDF 1SFOUJDF)BMM153 &OHMFXPPE$MJGGT  /FX+FSTFZ  5"3&"

" 1SPCMFNBTQBSBEJTDVTJÓO " $PNQBSFMPTTJTUFNBTRVFNVFTUSBOMBTàHVSBT" #Z$y$VÃMFTTPOMBTWFOUBKBTZ EFTWFOUBKBTEFDBEBTJTUFNB " &YQMJRVFMBTEJGFSFODJBTFOUSFMBEFTUJMBDJÓOFYUSBDUJWBZMBEFTUJMBDJÓOB[FPUSÓQJDBy$VÃMFT TPOMBTWFOUBKBTZEFTWFOUBKBTEFDBEBQSPDFEJNJFOUP " y1PSRVÊTFSFRVJFSFVOFOGSJBEPSFOMBàHVSB y1VFEFBQSPWFDIBSTFFTUBFOFSHÎBFOFM QSPDFTP " &YQMJRVFFMPCKFUPEFMTFEJNFOUBEPSMÎRVJEPMÎRVJEPFOMBTàHVSBT" Z " &YQMJRVFQPSRVÊMPTCBMBODFTFYUFSOPTEFNBTBTPOJHVBMFTQBSBMBTàHVSBT"Z " y1PSRVÊIBZBEJDJPOFTEFTPMWFOUFEFSFMMFOPFOMBTàHVSBT Z " &YQMJRVFQPSRVÊFMQFSàMEFDPNQPTJDJÓOEFQFOUBOPUJFOFVONÃYJNPFOMBàHVSB " &YQMJRVFDPOTVTQSPQJBTQBMBCSBT MBTWFOUBKBTEFFGFDUVBSBMNJTNPUJFNQPVOBSFBDDJÓOZMB EFTUJMBDJÓO " $VBOEP TF IBDF VOB EFTUJMBDJÓO DPO SFBDDJÓO  MB DPMVNOB TF EFCF EJTFÒBS DPNP SFBDUPS Z DPNPDPMVNOBEFEFTUJMBDJÓOBMNJTNPUJFNQPy&ORVÊBTQFDUPTQVFEFOEJGFSJSFTUBTDPMVN OBTSFTQFDUPBMBTDPMVNOBTEFEFTUJMBDJÓOOPSNBM " &OHFOFSBM OPDPOWJFOFUFOFSSFBDDJPOFTFOMBTDPMVNOBTEFEFTUJMBDJÓO4JTFFTUÃFGFDUVBOEP VOBSFBDDJÓO yRVÊTFQVFEFIBDFSQBSBNJOJNJ[BSMB " &MBCPSFTVQSPQJBUBCMBEFSFMBDJPOFTDMBWFQBSBFTUFDBQÎUVMP " 4JTFFWBQPSBVOBNF[DMBMÎRVJEBEFOCVUBOPMZBHVBRVFDPOUFOHBEFOCVUBOPM yDVÃMFT MBDPNQPTJDJÓOEFMWBQPS  WFBMBàHVSB 3FQJUBFMQSPCMFNBQBSBNF[DMBTRVFDPOUFOHBO  ZNPMEFOCVUBOPM&YQMJRVFRVÊFTUÃTVDFEJFOEP " 4FRVJFSFVTBSEFTUJMBDJÓOFYUSBDUJWB àHVSB QBSBTFQBSBSFUBOPMEFBHVB DPOFUJMFOHMJDPM DPNPTPMWFOUF6OQSPEVDUPTFSÃFUBOPMZFMQSPEVDUP#TFSÃBHVB-BTFUBQBTTFDVFOUBOB QBSUJSEFMDPOEFOTBEPSZFMWBQPSJ[BEPSFT/&MQMBUPEFBMJNFOUBDJÓOQBSBSFDJSDVMBDJÓO EFTPMWFOUFFOMBDPMVNOBFT/4-BTFUBQBTEFBMJNFOUBDJÓOTPO/'FOMBDPMVNOBZ/' FOMBDPMVNOB&TDPKBMBTPMVDJÓOÓQUJNBQBSBMPTFMFNFOUPTNFODJPOBEPT   4JIBZEFNBTJBEPTPMWFOUFFOFMQSPEVDUPBHVB B "VNFOUBS-%FOMBDPMVNOB C "VNFOUBSFMWBMPSEF/4 D "VNFOUBSMBDBOUJEBEEFFUBQBTFOMBTFDDJÓOEFBHPUBNJFOUPEFMBDPMVNOB E "VNFOUBSMBDBOUJEBEEFFUBQBTFOMBTFDDJÓOEFBHPUBNJFOUPEFMBDPMVNOB F "VNFOUBSMBDBOUJEBEEFFUBQBTFOMBTFDDJÓOEFFOSJRVFDJNJFOUPEFMBDPMVNOB   4JIBZEFNBTJBEBBHVBFOFMFUBOPMQSPEVDUP FOUPODFTTFBHSFHBTPMWFOUFGSFTDP TJOSFDJSDV MBSTPMWFOUF  B "VNFOUBS-%FOMBDPMVNOB C "VNFOUBSFMáVKPEFTPMWFOUF D "VNFOUBSFMWBMPSEF/4 E "VNFOUBSMBDBOUJEBEEFFUBQBTFOMBTFDDJÓOEFBHPUBNJFOUPEFMBDPMVNOB

www.FreeLibros.me

5BSFB



  4JIBZEFNBTJBEBBHVBFOFMQSPEVDUPFUBOPMDVBOEPTFVTBSFDJSDVMBDJÓOEFTPMWFOUF QFSPOP MBIBCÎBDVBOEPTFVTBCBTPMWFOUFGSFTDPFOUPODFTJOEJRVFTJTFEFCF B "VNFOUBS-%FOMBDPMVNOB C "VNFOUBSFMWBMPSEF/4 D "VNFOUBSMBDBOUJEBEEFFUBQBTFOMBTFDDJÓOEFBHPUBNJFOUPEFMBDPMVNOB E 3FEVDJSFMBHVBFOMBTDPMBTEFMBDPMVNOB   4JIBZEFNBTJBEPFUBOPMFOFMQSPEVDUPBHVB B "VNFOUBS-%FOMBDPMVNOB C "VNFOUBSFMWBMPSEF/4 D "VNFOUBSMBDBOUJEBEEFFUBQBTFOMBTFDDJÓOEFBHPUBNJFOUPEFMBDPMVNOB E 3FEVDJSFMBHVBFOMPTGPOEPTEFMBDPMVNOB F "VNFOUBSMBDBOUJEBEEFFUBQBTFOMBTFDDJÓOEFFOSJRVFDJNJFOUPEFMBDPMVNOB   4JIBZEFNBTJBEPTPMWFOUFFOFMFUBOPMQSPEVDUP B "VNFOUBS-%FOMBDPMVNOB C "VNFOUBSFMWBMPSEF/' D "VNFOUBSMBDBOUJEBEEFFUBQBTFOMBTFDDJÓOEFBHPUBNJFOUPEFMBDPMVNOB E 3FEVDJSFMBHVBFOMPTGPOEPTEFMBDPMVNOB $ %FEVDDJPOFT $ %FEV[DBMBFDVBDJÓO  QBSBFMTJTUFNBB[FPUSÓQJDPIFUFSPHÊOFPCJOBSJPDPOEPTDPMVNOBT $ 1BSBVOB[FÓUSPQPIFUFSPHÊOFPCJOBSJP USBDFFMBSSFHMPEFMBDPMVNOBTJMBDPNQPTJDJÓOEF MBBMJNFOUBDJÓOFTNFOPSRVFMBDPODFOUSBDJÓOEFMB[FÓUSPQP [Y 5SBDFFMEJBHSBNBEF .D$BCF5IJFMFQBSBFTUFTJTUFNB $ 1BSBVOBTFQBSBDJÓOB[FPUSÓQJDBCJOBSJBIFUFSPHÊOFB MBBMJNFOUBDJÓOQVFEFTFSJOUSPEVDJEB FOFMTFQBSBEPSMÎRVJEPMÎRVJEP&OFTUFDBTP TFFNQMFBOEPTDPMVNOBTEFBHPUBNJFOUP B #PTRVFKFMBEJTQPTJDJÓOEFDPMVNOBT C %JCVKFFMEJBHSBNB.D$BCF5IJFMFQBSBFTUFTJTUFNB D $PNQBSFFTUFTJTUFNBDPOFMEFMBàHVSB"ZFMQSPCMFNB$ $ 5SBDFFMEJBHSBNBEF.D$BCF5IJFMFQBSBVOTJTUFNBDPOEPTQSFTJPOFT QBSFDJEPBMEFMB àHVSB $ &TGÃDJMEFEVDJSVOBFDVBDJÓOQBSB PSHXFOXQBSFDJEBBMBFDVBDJÓO  IÃHBMP$PNQBSFFM FRVJMJCSJPDBMDVMBEPFOFMBHVBDPOMPTEBUPTEFFRVJMJCSJPQBSBCVUBOPMBHVBEFMQSPCMFNB %)BHBDPNFOUBSJPTTPCSFFMBKVTUF-PTEBUPTEFQSFTJÓOEFWBQPSFTUÃOFO1FSSZZ(SFFO  6TFMPTEBUPTEFMQSPCMFNB%DPNPEBUPTEFTPMVCJMJEBE $ %FEV[DBMBFDVBDJÓO   % 1SPCMFNBT  -BTSFTQVFTUBTEFQSPCMFNBTDPOVOBTUFSJTDPTFFODVFOUSBOFOMBÙMUJNBQBSUFEFMMJCSP % 6OBDPMVNOBEFEFTUJMBDJÓOFTUÃTFQBSBOEPJTPQSPQBOPMZBHVBBL1B/FDFTJUBNPTRVF MBGSBDDJÓONPMBSEFJTPQSPQBOPMTFBYQ MPRVFOPQVFEFMPHSBSMBDPMVNOBEFEFTUJMB DJÓO4JOFNCBSHP TJMBDPMVNOBMMFHBBZ DPOVOTFQBSBEPSEFNFNCSBOBTFQVFEF PCUFOFSVOQSPEVDUPDPOYQ"MHPEFFTUFNBUFSJBMTFSFHSFTBDPNPSFáVKPMÎRVJEPTBUV SBEP Y -BBMJNFOUBDJÓOJOJDJBMBMBDPMVNOBFT'LHNPMIZUJFOFNPMEF JTPQSPQBOPM&TUBBMJNFOUBDJÓOFTVOWBQPSTBUVSBEP-BDPSSJFOUFSFDJSDVMBEBFTVOMÎRVJEP TBUVSBEPRVFUJFOFGSBDDJÓONPMEFJTPQSPQBOPM4FEFTFBRVFY#-BDPMVNOBVTB WBQPS EJSFDUP  TBUVSBEP  RVF FT EF BHVB QVSB 4F BKVTUB MB SFMBDJÓO EF SFáVKP JOUFSOP FO MB TFDDJÓOTVQFSJPSB-7$BMDVMFMPTEPTMVHBSFTÓQUJNPTEFMQMBUPEFBMJNFOUBDJÓOZMB DBOUJEBEUPUBMEFFUBQBT1VFEFVTUFETVQPOFSRVFEFSSBNFNPMBMDPOTUBOUF-BDPMVNOBFT

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBNÊUPEPTDPNQMFKPTEFEFTUJMBDJÓO

QBSFDJEBBMBEFMBàHVSB$ QFSPTFVTÓVODBMFOUBNJFOUPDPOWBQPSEJSFDUP-PTEBUPTEF FRVJMJCSJPJTPQSPQBOPMBHVBTFFODVFOUSBOFO1FSSZZ(SFFO  1ÃH "DPOUJOVB DJÓOTFQSFTFOUBOMPTWBMPSFTQBSBJTPQSPQBOPM m

#%%)*

#%%+.

#%&',

#%(*,

#%+,-

#&((.

#&+*&

#('%)

n

#%-&*

#&)%*

#'&-*

#(+.'

#)+),

#*%(+

#*&*(

#*)*+

m

#(,*'

#),'%

#*&.,

#*.)*

#,--%

#-%'%

#.(%(

#.++%

n

#*+&*

#*-+%

#+%((

#+((%

#,*)+

#,+-%

#.%&%

#.*'*

%  &OMBUBCMBTFQSFTFOUBOEBUPTEFFRVJMJCSJPWBQPSMÎRVJEPQBSBBHVBOCVUBOPM4FEFTFB EFTUJMBSLHNPMIEFVOBNF[DMBGPSNBEBQPSNPMEFBHVBZEFWBQPS FOVO TJTUFNBEFEFTUJMBDJÓOB[FPUSÓQJDBFOEPTDPMVNOBT4FEFTFBRVFMPTQSPEVDUPTTFBOVOBGBTF EFCVUBOPMRVFDPOUFOHBGSBDDJÓONPMBSEFBHVBZVOBGBTFEFBHVBRVFDPOUFOHBVOB GSBDDJÓONPMEFBHVBEF-BQSFTJÓOFTL1B&MSFáVKPFTVOMÎRVJEPTBUVSBEP6TF -7   -7 NÎO FO MB DPMVNOB RVF QSPEVDF CVUBOPM DBTJ QVSP "NCBT DPMVNOBT UJFOFO WBQPSJ[BEPSFTQBSDJBMFT 7# FOMBDPMVNOBRVFQSPEVDFFMBHVB 5"#-" %"504%&-&26*-*#3*07"103-±26*%01"3" "(6":/#65"/0-""5. '3"$$*¶/.0-"3%&"(6" -ÎRVJEP7BQPSUž$-ÎRVJEP7BQPSUž$ % (#. )#, *#* ,#% '*#, ',#* '.#' (%#* ).#+ *%#+ **#' *+#) *,#&

% '+#, '.#. ('#( (*#' +'#. +)#& +*#* ++#' ,(#+ ,)#% ,*#% ,*#' ,)#-

&&, &&&#* &&%#+ &%.#+ &%-#.,#. .,#' .+#, .+#( .(#* .(#) .'#. .'#. .'#.

*,#( .,#* .-#% .-#' .-#* .-#+ .-#..#' ..#) ..#, ..#..#. &%%

,*#% ,*#' ,*#+ ,*#,,#* ,-#) -%#-)#( --#) .'#. .*#& .-#& &%%

.'#.'#, .(#% .'#.(#) .(#) .(#, .*#) .+#.-#( .-#) ..#) &%%

'VFOUF$VFUBM  NPMEFBHVB%BUPTQBSBBHVBBTFUPNB SPOEF1FSSZZ(SFFO  

B $BMDVMFMBTUBTBTEFáVKPEFMPTQSPEVDUPT C $BMDVMFMBVCJDBDJÓOÓQUJNBEFMBBMJNFOUBDJÓOZMBDBOUJEBEEFFUBQBTFOMBTDPMVNOBT /PUB5SBDFEPTEJBHSBNBTEF.D$BCF5IJFMF % &O MB UBCMB  TF FODVFOUSBO MPT EBUPT EF FRVJMJCSJP WBQPSMÎRVJEP QBSB BHVB Z OCVUBOPM UFOHBFODVFOUBRVFFTUÃOFONPMEFBHVB 4FDVFOUBDPOVOPTTJTUFNBTEFEFTUJMBDJÓO JOTUBOUÃOFBRVFTFQBSBOLHNPMIEFEPTNF[DMBTEJTUJOUBTEFBHVBZOCVUBOPM

www.FreeLibros.me

5BSFB



B -BBMJNFOUBDJÓODPOUJFOFNPMEFBHVB ZFMWBQPSEFQSPEVDUPDPOUJFOFNPMEF BHVB$BMDVMF- Y 7Z5UBNC C -BBMJNFOUBDJÓODPOUJFOFNPMEFBHVBZEFMBBMJNFOUBDJÓOFTUÃFWBQPSBEB $BMDVMF- Y 7 ZZ5UBNC % 6OBNF[DMBEFEPTGBTFTMÎRVJEBTRVFDPOUJFOFONPMEFBHVBZNPMEFOCVUBOPM  FOQSPNFEJP TFEFKBTFEJNFOUBSQBSBQFSNJUJSMBGPSNBDJÓOEFMBTEPTGBTFTMÎRVJEBTy$VÃMFT TPOMBTDPNQPTJDJPOFTZáVKPTEFFTUBTEPTGBTFT -PTEBUPTEFMFRVJMJCSJPWBQPSMÎRVJEPTF FODVFOUSBOFOMBUBCMB'LHNPMI % 6OBBMJNFOUBDJÓOFOGPSNBEFWBQPSTBUVSBEPDPOUJFOFNPMEFBHVBZNPMEF CVUBOPM-BUBTBEFBMJNFOUBDJÓOFTLHNPMI-BBMJNFOUBDJÓOTFDPOEFOTBZTFNBOEB BVOTFQBSBEPSMÎRVJEPMÎRVJEP-BDBQBBDVPTBTFSFUJSBZFTFMQSPEVDUPBDVPTP 8ZMBDBQB TVQFSJPS EFCVUBOPMTFNBOEBBVOBDPMVNOBEFBHPUBNJFOUPRVFUJFOFVOWBQPSJ[BEPSQBS DJBM-PTGPOEPTEFFTUBDPMVNOBEFBHPUBNJFOUPTPOFMCVUBOPMQSPEVDUPRVFEFCFDPOUFOFS NPMEFBHVB-PTEBUPTEFFRVJMJCSJPFTUÃOFOMBUBCMB$BMDVMF B -PTáVKPT8Z# m C 4J7 # DBMDVMFMBDBOUJEBEEFFUBQBTEFFRVJMJCSJP FTDBMPOBOEPEFTEFFMGPOEPIBDJB BSSJCB  m D %FUFSNJOF 7 # NÎOQBSBFTUBTFQBSBDJÓO % 4F EFTFB TFQBSB OCVUBOPM Z BHVB FO VOB DPMVNOB DPOUJOVB EF BHPUBNJFOUP -PT EBUPT EF FRVJMJCSJPFTUÃOFOMBUBCMB-BDPMVNOBUJFOFVOWBQPSJ[BEPSQBSDJBM&MWBQPSEFTUJMBEP EFMBDPMVNOBTFNBOEBBVODPOEFOTBEPSUPUBMZBVOTFQBSBEPSMÎRVJEPMÎRVJEP EPOEFTF TFQBSBGPSNBOEPEPTGBTFTMÎRVJEBT-BTEPTGBTFTTFSFUJSBOZTPOEPTQSPEVDUPTEFTUJMBEPT OPIBZSFáVKP -BBMJNFOUBDJÓOBMBDPMVNOBFTLHNPMIEFVOBNF[DMBRVFDPOUJFOF NPMEFOCVUBOPM-BBMJNFOUBDJÓOFTVOMÎRVJEPTBUVSBEP&MQSPEVDUPEFGPOEPTDPO UJFOFEFBHVB-BSFMBDJÓOEFWBQPSBMGPOEPFT4VQPOHBEFSSBNFNPMBMDPOTUBOUF B $BMDVMFMBDPNQPTJDJÓOEFMEFTUJMBEP FOGSBDDJPOFTNPMBSFT ZMBDBOUJEBEEFFUBQBTOFDF TBSJBT C $BMDVMF#ZMBUBTBEFáVKPEFMWBQPSEFTUJMBEP D $BMDVMFMBTUBTBTEFáVKPEFMPTEPTQSPEVDUPTEFTUJMBEPTMÎRVJEPT % -BBOJMJOBZFMBHVBTPOQBSDJBMNFOUFNJTDJCMFTZGPSNBOVOB[FÓUSPQPIFUFSPHÊOFP"Q NN)H MBTDPODFOUSBDJPOFTB[FPUSÓQJDBTTPOFMWBQPSUJFOFGSBDDJÓONPMBSEFBOJMJOB MB GBTFBDVPTBMÎRVJEBDPOUJFOFGSBDDJÓONPMBSEFBOJMJOBZMBGBTFPSHÃOJDBMÎRVJEBDPOUJFOF GSBDDJÓONPMBSEFBOJMJOB&TUJNFMBWPMBUJMJEBESFMBUJWBEFMBHVBDPOSFTQFDUPBMBBOJMJOB FOMBGBTFPSHÃOJDB/PUB5FOHBDVJEBEPZVTFGSBDDJPOFTNPMBSFTEFMDPNQPOFOUFDPSSFDUP %  6OB BMJNFOUBDJÓO EF   LHI EF ÊUFS EJJTPQSPQÎMJDP $)0  DPOUJFOF  FO QFTP EF BHVB4FEFTFBRVFFMQSPEVDUPÊUFSEJJTPQSPQÎMJDPDPOUFOHBFOQFTPEFBHVB-BBMJNFO  UBDJÓOFTVOMÎRVJEPTBUVSBEP6TFFMTJTUFNBEFMBàHVSBRVFUSBCBKBBL1B6TF-%  -% NÎO%FUFSNJOF -% NÎO -% FUBQBÓQUJNBEFBMJNFOUBDJÓOZDBOUJEBEUPUBMEFFUBQBT OFDFTBSJBT4VQPOHBRVFFTWÃMJEPFMEFSSBNFNPMBMDPOTUBOUF"DPOUJOVBDJÓOTFQSFTFOUBOMPT TJHVJFOUFTEBUPTEFMB[FÓUSPQPÊUFSEJTPQSPQÎMJDPBHVB 5SBOT"*$I&     Z TFQBSBEPSDBQBTVQFSJPSYDBQBJOGFSJPSYBL1BZž$ 5PEBTMBTDPNQPTJDJPOFTTPOGSBDDJPOFTFOQFTPEFÊUFSEJJTPQSPQÎMJDP &TUJNF BHVBÊUFSFOÊUFSDPOFTUPTEBUPT VOJEBEFTGSBDDJPOFTNPMBSFT 4VQPOHBRVFFTUBWPMB UJMJEBESFMBUJWBFTDPOTUBOUF % 4F VTB VOB DPMVNOB EF FOSJRVFDJNJFOUP QBSB TFDBS  LHNPMI EF ÊUFS EJJTPQSPQÎMJDP RVF DPOUJFOFGSBDDJÓONPMBSEFBHVB&TUBBMJNFOUBDJÓOFOUSBDPNPWBQPSTBUVSBEP4FGPSNB VOB[FÓUSPQPIFUFSPHÊOFP%FTQVÊTEFDPOEFOTBSFOVODPOEFOTBEPSUPUBMZEFTFQBSBSMBT

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBNÊUPEPTDPNQMFKPTEFEFTUJMBDJÓO

EPTDBQBTMÎRVJEBT TFSFUJSBMBDBQBBDVPTBDPNPQSPEVDUPZMBDBQBEFÊUFSEJJTPQSPQÎMJDPTF SFHSFTBDPNPSFáVKP4FUSBCBKBDPOVOBSFMBDJÓOEFSFáVKPFYUFSOPRVFFTWFDFTMBSFMBDJÓO NÎOJNBEFSFáVKPFYUFSOP-BPQFSBDJÓOFTBBUN$BMDVMFMBSFMBDJÓONÎOJNBEFSFáVKP FYUFSOP MB-%SFBM MBUBTBEFáVKPEFEFTUJMBEPZMBGSBDDJÓONPMBSEFBHVB MBUBTBEFáVKPEF GPOEPTZTVGSBDDJÓONPMBSEFBHVBZMBDBOUJEBEEFFUBQBTEFFRVJMJCSJPOFDFTBSJBT OÙNFSP FUBQBTVQFSJPS 6TFVOEJBHSBNBBNQMJBEPEF.D$BCF5IJFMFQBSBEFUFSNJOBSMBDBOUJEBEEF FUBQBT4FQVFEFOVTBSEBUPTEFMBDPNQPTJDJÓOB[FPUSÓQJDB QSPCMFNB% QBSBDBMDVMBSMBT GSBDDJPOFTNPMBSFTEFBHVBFOMBTEPTDBQBT FOFMTFQBSBEPSZMBWPMBUJMJEBESFMBUJWBEFMBHVB DPOSFTQFDUPBMÊUFSBCBKBTDPODFOUSBDJPOFTEFBHVB-BTGSBDDJPOFTFOQFTPEFCFODPOWFSUJSTF QSJNFSPBGSBDDJPOFTNPMBSFT %  $POVOTJTUFNBEFEFTUJMBDJÓODPOBSSBTUSFEFWBQPSEFBHVBEFVOBTPMBFUBQB TFSFDVQFSB OEFDBOPBQBSUJSEFVOBQFRVFÒBDBOUJEBEEFTVTUBODJBTPSHÃOJDBTOPWPMÃUJMFT-BQSFTJÓO FTNN)H4JFMEFTUJMBEPSUSBCBKBDPOQSFTFODJBEFBHVBMÎRVJEBZMBDBQBPSHÃOJDBFOÊM DPOUJFOFNPMEFOEFDBOP EFUFSNJOF B -BUFNQFSBUVSBEFMEFTUJMBEPS C -BTNPMFTEFBHVBFWBQPSBEBQPSNPMEFOEFDBOPFWBQPSBEP -BQSFTJÓOEFWBQPSEFMEFDBOPTFFODVFOUSBFOFMFKFNQMP-BTQSFTJPOFTEFWBQPSEF BHVBTPO 5FOž$Z17FONN)H  1FSSZZ(SFFO   I

.*#*

.+#%

.+#*

.,#%

.,#*

.-#%

.-#*

..#%

..#*

EK +)*#+, +*,#+' ++.#,* +-'#%, +.)#*, ,%,#', ,'%#&* ,((#') ,)+#*'

% 4FIBDFVOBEFTUJMBDJÓODPOUJOVBEFPDUBOPMQPSBSSBTUSFDPOWBQPSEFBHVBFOVOBFUBQB -BVOJEBEUSBCBKBBNN)H-BEFTUJMBDJÓODPOWBQPSEFBHVBTFIBDFFOQSFTFODJBEF BHVBMÎRVJEB&MWBQPSEFTUJMBEPTFDPOEFOTBZTFGPSNBOEPTDBQBTMÎRVJEBTJONJTDJCMFT-B DPSSJFOUFFOUSBOUFEFDPNQVFTUPPSHÃOJDPDPOUJFOFNPMEFPDUBOPMZFMSFTUPTPODPN QVFTUPTOPWPMÃUJMFT-BUBTBEFáVKPEFMBBMJNFOUBDJÓOFTLHNPMI%FTFBNPTSFDVQFSBS FMEFMPDUBOPM  &OFMQSPCMFNB%TFFODVFOUSBOMPTEBUPTEFQSFTJÓOEFWBQPSEFMBHVB&TPTEBUPTTF QVFEFOBKVTUBSBMBGPSNBEFMBFDVBDJÓOEF"OUPJOFDPO$-BQSFTJÓOEFWBQPSEF PDUBOPMTFDBMDVMBUBNCJÊODPOMBFDVBDJÓOEF"OUPJOF MPH 17 "−# 5 $

%POEF" #Z$ 4FB17MBQSFTJÓOEFWBQPSFONN)HZ5MBUFNQFSBUVSBFOHSBEPT$FMTJVT B $BMDVMFMBUFNQFSBUVSBEFPQFSBDJÓOEFMEFTUJMBEPS C $BMDVMFMBGSBDDJÓONPMBSEFPDUBOPMFOFMWBQPSRVFTBMFEFMEFTUJMBEPS D $BMDVMFMBTNPMFTEFPDUBOPMSFDVQFSBEBTZMBTEFBHVBDPOEFOTBEBFOFMQSPEVDUPEFTUJMBEP % &TCBTUBOUFEJSFDUBMBHFOFSBDJÓOEFDVSWBTEFEFTUJMBDJÓOQBSBTJTUFNBTDPOWPMBUJMJEBESFMB UJWBDPOTUBOUFZFTVOBFYQFSJFODJBFYDFMFOUFQBSBBQSFOEJ[BKF(FOFSFDVSWBTEFEFTUJMBDJÓO FOMBàHVSBQBSBCFODFOP "

UPMVFOP # ZDVNFOP $

DPO "#  ##Z $# -BPQFSBDJÓOFTBSFáVKPUPUBM B  -B GSBDDJÓO NPMBS EF " FO FM WBQPSJ[BEPS FT   Z MB GSBDDJÓO NPMBS EF # FT  C  -BGSBDDJÓONPMBSEF"FOFMWBQPSJ[BEPSFTZMBGSBDDJÓONPMBSEF#FT D -BGSBDDJÓONPMBSEF"FOFMWBQPSJ[BEPSFT ZMBGSBDDJÓONPMBSEF#FT

www.FreeLibros.me

5BSFB



3FDVFSEFRVFMBTVNBEFMBTGSBDDJPOFTNPMBSFTEF" #Z$FOFMWBQPSJ[BEPSFT -BTPMVDJÓOTFWFFOMBàHVSB % -BHFOFSBDJÓOEFDVSWBTEFSFTJEVPQBSBTJTUFNBTDPOWPMBUJMJEBESFMBUJWBDPOTUBOUFFTCBT UBOUFEJSFDUBZFTVOBFYDFMFOUFFYQFSJFODJBEFBQSFOEJ[BKF(FOFSFDVSWBTEFSFTJEVPQBSBFM TJTUFNBEFCFODFOP "

UPMVFOP #

DVNFOP $

DPO "#  ##Z $# B -BGSBDDJÓONPMBSEF"FOMBSFUPSUBFTZMBGSBDDJÓONPMBSEF#FT$PNQBSF FTUFSFTVMUBEPDPOMBTDVSWBTEFEFTUJMBDJÓOEFMBàHVSB C -BGSBDDJÓONPMBSEF"FOMBSFUPSUBFTZMBEF#FT 3FDVFSEFRVFMBTVNBEFMBTGSBDDJPOFTNPMBSFTEF" #Z$FOMBSFUPSUBFT % 4FEFTFBVTBSVOTJTUFNBDPOEPTQSFTJPOFT QBSFDJEPBMEFMBàHVSB QBSBTFQBSBSVOB BMJNFOUBDJÓOGPSNBEBQPSNPMEFCFODFOPZNPMEFFUBOPM-BUBTBEFBMJNFO UBDJÓOFTLHNPMIZFTVOMÎRVJEPTBUVSBEP-BTDPMVNOBT USBCBKBSÃOBL1BZB L1B4FEFTFBRVFFMQSPEVDUPEFFUBOPMUFOHBNPMEFFUBOPMZRVFFMQSPEVDUP EFCFODFOPUFOHBNPMEFCFODFOP4VQPOHBRVFMPTEPTQSPEVDUPTEFTUJMBEPTFTUÃOB DPODFOUSBDJPOFTB[FPUSÓQJDBT B 5SBDFFMEJBHSBNBEFáVKPQBSBFTUFQSPDFTP*EFOUJàRVFMBTDPSSJFOUFTQBSBRVFDPSSFTQPO EBODPOTVTDÃMDVMPT C $BMDVMFMPTáVKPTEFMPTQSPEVDUPTFUBOPMZCFODFOP D $BMDVMFMPTáVKPTEFMBTEPTDPSSJFOUFTEFTUJMBEBTRVFTFBMJNFOUBOBMBPUSBDPMVNOB %BUPT 4FBEFS  &MB[FÓUSPQPFTIPNPHÊOFP"L1B MBUFNQFSBUVSBB[FPUSÓQJDB FTž$ZDPOUJFOFGSBDDJÓONPMBSEFFUBOPM"L1B MBUFNQFSBUVSBB[FPUSÓQJDBFT ž$ZDPOUJFOFGSBDDJÓONPMBSEFFUBOPM&MFUBOPMFTNÃTWPMÃUJMBGSBDDJPOFTNPMBSFT NFOPSFTRVFMBDPNQPTJDJÓOB[FPUSÓQJDB % 4FEFTFBTFQBSBSVOBBMJNFOUBDJÓOGPSNBEBQPSNPMEFFUBOPMZNPMEFCFO DFOPVTBOEPVOTJTUFNBEFEFTUJMBDJÓODPOEPTQSFTJPOFT TJNJMBSBMEFBMàHVSB-BUBTB EFBMJNFOUBDJÓOFTLHNPMI-BTEPTDPMVNOBTGVODJPOBOBL1BZBL1B-PT EBUPTEFMPTB[FÓUSPQPTBQBSFDFOFOFMQSPCMFNB%%FTFBNPTVOQSPEVDUPEFFUBOPM  1& RVFDPOUFOHBNPMEFFUBOPMZVOQSPEVDUPCFODFOP 1# RVFDPOUFOHBNPM EFCFODFOP4VQPOHBRVFMPTQSPEVDUPTEFTUJMBEPTTFBQSPYJNBOIBTUBGSBDDJÓONPMBSEF MBDPNQPTJDJÓOB[FPUSÓQJDB QPSFKFNQMP Y%EFMBDPMVNOBBL1BFTP  B 5SBDFFMEJBHSBNBEFQSPDFTP JOEJRVFMBQSFTJÓOZMPTQSPEVDUPT ZMPTEJBHSBNBTBQSPYJ NBEPTEF.D$BCF5IJFMF C %FUFSNJOFMBUBTBEFáVKPEFMFUBOPMQSPEVDUP 1& ZMBUBTBEFáVKPEFMQSPEVDUPCFODF OP 1# D %FUFSNJOFMBTUBTBTEFáVKPEFMPTEPTEFTUJMBEPT % 6OTJTUFNBEFEFTUJMBDJÓOFYUSBDUJWBTFQBSBFUBOPMEFBHVB VTBOEPFUJMFOHMJDPMDPNPTPM WFOUF-BDPSSJFOUFEFSFMMFOPEFTPMWFOUFFTFUJMFOHMJDPMQVSP&MEJBHSBNBEFáVKPFTFMRVF NVFTUSBMBàHVSB-BUBTBEFáVKPEFMBBMJNFOUBDJÓOFTLHNPMI-BBMJNFOUBDJÓO DPOUJFOFGSBDDJÓONPMBSEFFUBOPMZGSBDDJÓONPMBSEFBHVB4FEFTFBRVFFMQSP EVDUPFUBOPM EFTUJMBEPEFMBDPMVNOB DPOUFOHBEFFUBOPMZEFFUJMFOHMJDPM  FOGSBDDJPOFTNPMBSFT ZFMSFTUPTFBBHVB&MQSPEVDUPBHVB EFTUJMBEPEFMBDPMVNOB EFCF UFOFSEFBHVBZEFFUJMFOHMJDPM GSBDDJPOFTNPMBSFTZFMSFTUPTFBFUBOPM % 1BSBFMTJTUFNBEFEFTUJMBDJÓOFYUSBDUJWBRVFNVFTUSBMBàHVSBMBBMJNFOUBDJÓOMÎRVJEB TBUVSBEBDPOUJFOFNPMEFOIFQUBOPZNPMEFUPMVFOP-BUBTBEFáVKPEFBMJNFO UBDJÓOFTLHNPMI&MTPMWFOUFFTGFOPM DPOVOáVKPEFSFDJSDVMBDJÓOEFTPMWFOUFEF LHNPMI%FTFBNPTRVFFMOIFQUBOPQSPEVDUP QSPEVDUP" DPOUFOHBNPMEFOIFQ UBOPZRVFFMUPMVFOPQSPEVDUP QSPEVDUP# DPOUFOHBNPMEFUPMVFOP$PNPQSJNFSB

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBNÊUPEPTDPNQMFKPTEFEFTUJMBDJÓO

BQSPYJNBDJÓO TVQPOHBRVFFMGFOPMTFTFQBSBQFSGFDUBNFOUFZRVFFMTPMWFOUFEFSFMMFOPFT LHNPMI$BMDVMFMBTUBTBTEFáVKPEFOIFQUBOPQSPEVDUPZEFUPMVFOPQSPEVDUP % 6OTJTUFNBEFEFTUJMBDJÓOFYUSBDUJWBTFQBSBFUBOPMEFBHVB DPOFUJMFOHMJDPMDPNPTPMWFOUF-B DPSSJFOUFEFTPMWFOUFEFSFMMFOPFTEFFUJMFOHMJDPMQVSP&MEJBHSBNBTFWFFOMBàHVSB DPO FUBOPMDPNPQSPEVDUP"ZBHVBDPNPQSPEVDUP#-BUBTBEFáVKPEFBMJNFOUBDJÓOFTLH NPMI RVFDPOUJFOFOEFFUBOPMZEFBHVB FOGSBDDJPOFTNPMBSFT%FTFBNPTRVF FMFUBOPMQSPEVDUP EFTUJMBEPEFMBDPMVNOB DPOUFOHBEFFUBOPM EFFUJMFOHMJDPM  FOGSBDDJPOFTNPMBSFTZFMSFTUPEFBHVB&MBHVBQSPEVDUP EFTUJMBEPEFMBDPMVNOB EFCF DPOUFOFSEFBHVBZEFFUJMFOHMJDPM FOGSBDDJPOFTNPMBSFTZFMSFTUPEFFUBOPM % %FTFBNPTVTBSOIFYBOPDPNPQPSUBEPSQBSBTFQBSBSVOBBMJNFOUBDJÓOGPSNBEBQPS EFFUBOPMZEFBHVB FOQFTP ZPCUFOFSFUBOPMZBHVB4FVTBSÃFMTJTUFNBEFMBàHVSB -BBMJNFOUBDJÓOFOUSBB LHIZFTVOMÎRVJEPTBUVSBEP&MFUBOPMQSPEVDUPDPOUJF OFEFFUBOPM EFIFYBOP FOQFTPZVOBUSB[BEFBHVB&MQSPEVDUPEFBHVB EFCFDPOUFOFSEFBHVBZEFFUBOPM FOQFTPZVOBUSB[BEFIFYBOP)BHBCB MBODFTFYUFSOPTEFNBTBZDBMDVMFMBTUBTBTEFáVKPEFMTPMWFOUFEFSFMMFOP OIFYBOP

FUBOPM QSPEVDUPZBHVBQSPEVDUP TVQPOHBRVFUSB[B   /PUB$VJEFMPTQVOUPTEFDJNBMFTBMVTBSGSBDDJPOFTFOQFTPZFOQFTP % 4FEFTFBTFQBSBSLHNPMIEFVOBNF[DMBEFNFUJMFUJMDFUPOBZBHVBFOFMTJTUFNBEFMB àHVSB-BBMJNFOUBDJÓOBMBDPMVNOBDPOUJFOFNPMEFBHVB-BDPMVNOBFTUÃB QTJBZQSPEVDFGPOEPTRVFTPOFTFODJBMNFOUFBHVBQVSB&MEFTUJMBEPEFMBDPMVNOBFTUÃVO QPDPBSSJCBEFMNPMB[FPUSÓQJDP RVFFTEFBHVB Y%EFBHVB &TUFEFTUJMBEPTF BMJNFOUBBMBDPMVNOBRVFFTUÃBQTJB-BDPMVNOBQSPEVDFGPOEPTRVFFOFTFODJBTPO NFUJMFUJMDFUPOBQVSBZVOEFTUJMBEPDPOY%GSBDDJÓONPMBSEFBHVB RVFFTVOQPDPNF OPSRVFMBDPNQPTJDJÓOB[FPUSÓQJDB BHVBBQTJB -BPQFSBDJÓOFTFOFTUBEPFTUBCMF  $BMDVMF# # % %ZMBBMJNFOUBDJÓOUPUBMBMBDPMVNOB % 6OBDPMVNOBEFEFTUJMBDJÓOTFQBSBBHVBZOCVUBOPMBVOBBUNÓTGFSBEFQSFTJÓO-PTEBUPTEF FRVJMJCSJPFTUÃOFOMBUBCMB&MTJTUFNBEFEFTUJMBDJÓOFTTJNJMBSBMEFMBàHVSBZUJFOFVO WBQPSJ[BEPSQBSDJBM VODPOEFOTBEPSUPUBMZVOTFEJNFOUBEPSMÎRVJEPMÎRVJEP-BDBQBJOGFSJPS EFMTFEJNFOUBEPS SJDBFOBHVB DPOYX TFTBDBDPNPQSPEVDUPEFTUJMBEP-BDBQBTVQF SJPS YX SFHSFTBBMBDPMVNOBDPNPSFáVKPMÎRVJEPTBUVSBEP-BBMJNFOUBDJÓODPOUJFOF NPMEFBHVB FTVOWBQPSTBUVSBEPZFOUSBBLHNPMI-PTGPOEPTDPOUJFOFO m EFBHVB FOGSBDDJÓONPMBS6TFVOBSFMBDJÓOEFWBQPSBMGPOEPEF7 #4VQPOHBWÃMJEP FMEFSSBNFNPMBMDPOTUBOUF&TDBMPOFMBTFUBQBTEFMGPOEPIBDJBBSSJCB$BMDVMFMBVCJDBDJÓO ÓQUJNBEFMBBMJNFOUBDJÓOZMBDBOUJEBEUPUBMEFFUBQBTEFFRVJMJCSJPOFDFTBSJBT % &TUBNPTTFQBSBOEPVOBBMJNFOUBDJÓOEFWBQPSTBUVSBEPRVFDPOUJFOFNPMEFBHVB ZNPMEFOCVUBOPMFOVOBDPMVNOBEFFOSJRVFDJNJFOUP-BUBTBEFBMJNFOUBDJÓOFT LHNPMI&MWBQPSEFMBQBSUFTVQFSJPSEFMBDPMVNOBWBBVODPOEFOTBEPS ZEFTQVÊT BVOTFQBSBEPSMÎRVJEPMÎRVJEP-BDBQBBDVPTBTFSFUJSBDPNPQSPEVDUPEFTUJMBEPZMBDBQB PSHÃOJDBSFHSFTBDPNPSFáVKP4FEFTFBRVFMBDPNQPTJDJÓOEFMPTGPOEPTTFBNPMEF BHVB-PTEBUPTEFMFRVJMJCSJPFTUÃOFOMBUBCMB$BMDVMF B &MWBMPSEFMBSFMBDJÓOEFSFáVKPFYUFSOP -% C -BDBOUJEBEEFFUBQBTEFFRVJMJCSJPOFDFTBSJBT D -BGSBDDJÓONPMEFBHVB Z FOFMWBQPSRVFTBMFEFMBFUBQB % &TUBNPTTFQBSBOEPVOBNF[DMBEFOCVUBOPMZBHVB-BUBTBEFBMJNFOUBDJÓOFTLHNPMI -B BMJNFOUBDJÓO FT VO MÎRVJEP TBUVSBEP DPO  NPM EF BHVB -B BMJNFOUBDJÓO FOUSB B VOWBQPSJ[BEPSEFUJQPSFUPSUBRVFFTVODPOUBDUPEFFRVJMJCSJP-PTGPOEPTEFMBNBSNJUB TBMFOFOGPSNBDPOUJOVBZUJFOFONPMEFBHVB&MWBQPSEFMBSFUPSUBTFNBOEBBVO

www.FreeLibros.me

5BSFB



DPOEFOTBEPSUPUBMZEFTQVÊTBVOBTFOUBEPSMÎRVJEPMÎRVJEP&MEFTUJMBEPFTMBDBQBEFBHVB EFMTFEJNFOUBEPS EFBHVB -BPQFSBDJÓOFTBBUN-PTEBUPTEFFRVJMJCSJPWBQPS MÎRVJEPQBSBBHVBZOCVUBOPMBBUN BQBSFDFOFOMBUBCMB B $BMDVMF%Z# C $BMDVMF- UBTBEFSFáVKPMÎRVJEP Z7 áVKPEFWBQPSEFMBSFUPSUBBMDPOEFOTBEPS  -BGPSNBNÃTGÃDJMEFBUBDBSFTUFQSPCMFNBFTEFTEFFMQSJODJQJP&TUPFT TVQPOFSFRVJMJCSJP FOMBSFUPSUBZIBDFSCBMBODFTEFNBTBDPOMBTGSBDDJPOFTNPMDPOPDJEBTEFMBTDBQBTMÎRVJEBT FOFRVJMJCSJP FOFMEFDBOUBEPS & 1SPCMFNBTNÃTDPNQMJDBEPT & %FTFBNPTTFQBSBSBHVBEFOJUSPNFUBOP $)/0 -BQSJNFSBBMJNFOUBDJÓO BMBDPMVNOB  UJFOFNPMEFBHVBZFTWBQPSTBUVSBEPRVFFOUSBBLHNPMEÎB-BTFHVOEBBMJNFOUB DJÓO BMBDPMVNOB DPOUJFOFNPMEFBHVBZFTVOMÎRVJEPTBUVSBEPRVFFOUSBBLH NPMEÎB4FVTBSÃVOTJTUFNBEFEPTDPMVNOBTDPOVOTFQBSBEPSMÎRVJEPMÎRVJEP-PTGPOEPTEF MBDPMVNOBDPOUJFOFONPMEFBHVBVTBS -7 FOFTUBDPMVNOB-PTGPOEPTEFMB mm DPMVNOBDPOUJFOFONPMEFBHVB6TF -7 FOFTUBDPMVNOB-PTEBUPTEFFRVJMJCSJP BQBSFDFOFOMBUBCMB B $BMDVMFMBDBOUJEBEEFFUBQBTZFMMVHBSÓQUJNPEFBMJNFOUBDJÓOFODBEBDPMVNOB C $BMDVMF-7FOMBDPMVNOB&YQMJRVFTVSFTVMUBEP & -PTEBUPTEFFRVJMJCSJPWBQPSMÎRVJEPQBSBBHVBZOCVUBOPM BBUNBQBSFDFOFOMBUBCMB -BBMJNFOUBDJÓOGSFTDBDPOUJFOFLHNPMIEFVOMÎRVJEPTBUVSBEPRVFDPOUJFOF NPMEFBHVB-BBMJNFOUBDJÓOGSFTDBTFNF[DMBDPOMBSFDJSDVMBDJÓOEFMTFQBSBEPS QBSBGPSNBS MBBMJNFOUBDJÓOUPUBM'5RVFFOUSBBVOBDPMVNOBEFBHPUBNJFOUPEPOEFTFPCUJFOFFMCVUBOPM QSPEVDUP WFBMBàHVSB 4VQPOHBRVFFTUBBMJNFOUBDJÓOUPUBMFTVOMÎRVJEPTBUVSBEP&MCV UBOPMQSPEVDUPDPOUJFOFNPMEFBHVB&MBHVBQSPEVDUPTFPCUJFOFFOPUSBDPMVNOBEF BHPUBNJFOUPZDPOUJFOFNPMEFBHVB&OMBDPMVNOBEFCVUBOPM MBSFMBDJÓOEFWBQPS BMGPOEPFT&OMBDPMVNOBEFBHVB MBSFMBDJÓOEFWBQPSBMGPOEPFT4VQPOHB EFSSBNFNPMBMDPOTUBOUF-PTEPTWBQPSJ[BEPSFTTPOQBSDJBMFT-BTEPTDPSSJFOUFTEFSFáVKP FOUSBODPNPMÎRVJEPTTBUVSBEPT-BPQFSBDJÓOFTBBUN$PNPFTUFQSPCMFNBFTEJGÎDJM MB MJTUBTJHVJFOUFMPHVJBSÃIBTUBMMFHBSBMBTPMVDJÓO 5"#-"  %"504 %& &26*-*#3*0 1"3" "(6"/*530.&5"/0""5. -ÎRVJEP

,#. &+#' '(#' (&#' (.#' )*#% **#' +(#,(#% ,,#%

7BQPS

-ÎRVJEP

7BQPS

()#% )*#% ).#, *%#% *%#' *%#' *%#' *%#' *%#' *%#'

-&#) --#% .&#) .'#* .(#* .*#& .*#. .,#* .,#.-#+

*%#& *%#' *%#( *&#( *'#. **#. *,#* +*#+-#) ,.#'

'VFOUF $IVZDPMT   NPMEFBHVB 

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBNÊUPEPTDPNQMFKPTEFEFTUJMBDJÓO

B $BMDVMFMBTUBTBTEFáVKPEFMPTEPTQSPEVDUPT VTFCBMBODFTEFNBTBFYUFSOPT  C $BMDVMFMBUBTBEFáVKPEFWBQPSFOMBDPMVNOBEFCVUBOPMZEFTQVÊTMBUBTBEFáVKPEF MÎRVJEP '5 UBNCJÊOFOMBDPMVNOBEFCVUBOPM D $BMDVMF[5DPOFMCBMBODFEFNBTBFOMBUFNF[DMBEPSBEFMBBMJNFOUBDJÓOGSFTDBZFMSFáVKP E 5SBDFMBHSÃàDBEFMBMÎOFBJOGFSJPSEFPQFSBDJÓOZDBMDVMFFMWBMPSEFMBGSBDDJÓONPMFOFM WBQPSRVFTBMFEFMBDPMVNOBEFCVUBOPMZMBDBOUJEBEEFFUBQBTEFFRVJMJCSJP F 6TFVOBHSÃàDBBNQMJBEBEF.D$BCF5IJFMFQBSBEFUFSNJOBSMBGSBDDJÓONPMFOFMWBQPS RVFTBMFEFMBDPMVNOBEFBHVBZMBDBOUJEBEOFDFTBSJBEFFUBQBTEFFRVJMJCSJP

G ;I !o I

;!o l

%#*,( %#.,*

Columna de butanol

Columna de agua

0.02, fracción mol de agua Butanol producto

0.995, fracción mol de agua Agua producto

& 4FEFTFBQSPEVDJSBHVBQVSBIJSWJFOEPWBQPSEFOEFDBOPDPOFMMB WFBMBàHVSB &TVOUJQP EFEFTUJMBDJÓOJOWFSTBQPSBSSBTUSFEFWBQPS&MBHVBEFNBSDPOUJFOFBQSPYJNBEBNFOUF c8&%

n-decano agua nagua

;

Sal + agua

Recirculación

c8&%

agua + sal vapor de n-decano

www.FreeLibros.me

desecho

5BSFB



FOQFTPEFTBM RVFQVFEFTVQPOFSTFFT/B$M-BBMJNFOUBDJÓOFTLHEFBHVBEFNBSI -B UFNQFSBUVSB EF BMJNFOUBDJÓO FT ž$ &M BHVB TF DBMJFOUB DPO WBQPS QVSP TBUVSBEP EF OEFDBOPBNN)H-BNBZPSQBSUFEFMWBQPSEFOEFDBOPTFDPOEFOTB NJFOUSBTRVFFM SFTUPQBTBFOFMEFTUJMBEPDPOFMWBQPSEFBHVB-BQSFTJÓOFTNN)H4FEFTFBSFDVQFSBS FMEFBHVBDPNPDPOEFOTBEP B $BMDVMFMBUFNQFSBUVSBBQSPYJNBEBFOFMEFTUJMBEPS C $BMDVMFMBTNPMFTEFOEFDBOPBSSBTUSBEBTQPSFMWBQPS QPSIPSB %BUPT1SFTJÓOEFWBQPSEFMOEFDBOPFOFMFKFNQMPQSFTJÓOEFWBQPSEFMBHVBFOFMQSP CMFNB%1.BHVB1./B$M1.$-BTBMOPFTWPMÃUJM&MBHVBZ FMOEFDBOPTPOJONJTDJCMFT&M/B$MTÓMPTFEJTVFMWFFOBHVB ' 1SPCMFNBTRVFSFRVJFSFOPUSPTSFDVSTPT ' 6OBQBSBUPEFEFTUJMBDJÓOEFVOBFUBQBTFWBBVTBSQBSBSFDVQFSBSOOPOBOP $) EFDPN QVFTUPTPSHÃOJDPTOPWPMÃUJMFT-BPQFSBDJÓOFTBBUN NN)H ZFMEFTUJMBEPSUSBCBKBSÃ DPOQSFTFODJBEFBHVBMÎRVJEB4JMPTGPOEPTEFMEFTUJMBEPSEFCFODPOUFOFSNPMEFOPOB OPFOMBGBTFPSHÃOJDB TJFOEPFMSFTUPOPWPMÃUJMFT

EFUFSNJOF B -BUFNQFSBUVSBEFMBEFTUJMBDJÓO C -BTNPMFTEFBHVBFWBQPSBEBQPSNPMEFOPOBOPFWBQPSBEP D -BTNPMFTEFBHVBDPOEFOTBEBQPSNPMEFOPOBOPFWBQPSBEPQBSBVOMÎRVJEPRVFFOUSBB MBUFNQFSBUVSBEFMEFTUJMBEPS E 3FQJUBMBTQBSUFTBZC TJMPTGPOEPTEFMEFTUJMBEPSEFCFODPOUFOFSNPMEFOPOBOP -PTEBUPTTFQVFEFODPOTVMUBSFO1FSSZZ(SFFO   ' 4FEFTFBSFDVQFSBSOOPOBOP $)

VODPNQPOFOUFEFMBHBTPMJOB EFVOBNF[DMBEFBDFJUFT WPMÃUJMFT HSBTBZTÓMJEPT4FIBSÃFOVOTJTUFNBEFEFTUJMBDJÓOQPSBSSBTUSFDPOWBQPSFOFTUBEP FTUBCMFZEFVOBTPMBFUBQB RVFUSBCBKFFOQSFTFODJBEFBHVBMÎRVJEBZBVOBQSFTJÓOUPUBMEF L1B-BBMJNFOUBDJÓODPOUJFOFNPMEFOOPOBOPZTFEFTFBSFDVQFSBSEFM OOPOBOPFOFMEFTUJMBEP-BBMJNFOUBDJÓOFOUSBBMBUFNQFSBUVSBEFMWBQPSJ[BEPSBVOáVKP EFLHNPMI$BMDVMF B -BGSBDDJÓONPMEFOOPOBOPFOMBDBQBPSHÃOJDBEFMPTGPOEPT C -BUFNQFSBUVSBEFMEFTUJMBEPS D -PTLHNPMEFOPOBOPIFOFMEFTUJMBEP E -PTLHNPMEFBHVBIFOFMEFTUJMBEP F -PTLHNPMEFBHVBIFOMPTGPOEPT 4VQPOHBRVFFMBHVBZFMOOPOBOPTPOUPUBMNFOUFJONJTDJCMFT-PTEBUPTEFQSFTJÓOEFWBQPS QBSBFMBHVBFTUÃOFOFMQSPCMFNB%6TFMBHSÃàDBEF%F1SJFTUFSPMBMFZEF3BPVMUQBSB PCUFOFS,D 5 QUPU &OUPODFT QPSH,DYD PSHQUPU-PTWBMPSFTEFDBMPSMBUFOUFTFFODVFOUSBOFO FMMJCSPEF1FSSZ PFOGVFOUFTTJNJMBSFT ( 1SPCMFNBTQBSBDPNQVUBEPSB ( 3FTVFMWBFMQSPCMFNB%DPOVOTJNVMBEPSEFQSPDFTPT /PUB4FQVFEFIBDFSEFWBSJBTNBOFSBTTJTFVTB"TQFO1MVT B 6TF3"%'3"$DPO/ DPOEFOTBEPSUPUBMZWBQPSJ[BEPSQBSDJBM DPOMBBMJNFOUBDJÓO BMWBQPSJ[BEPS3FDJSDVMFMBGBTFPSHÃOJDBEFMEFDBOUBEPSBMBDPMVNOBDPNPTFHVOEBBMJ NFOUBDJÓO FOFMWBQPSJ[BEPS*OUSPEV[DBFMáVKPEFDPMBTZ-%$PNJFODFDPO-%  ZEJTNJOVZBFOGBDUPSFTEFIBTUB RVFFTDBTJDFSP  C 3FTVÊMWBMPDPNPQSPCMFNBEFUBOUFPT DPO'-"4) VODBMFOUBEPS )&"5&3 ZVOEF DBOUBEPS %&$"/5&3 3FHSFTFMBDBQBPSHÃOJDBEFMEFDBOUBEPS SFáVKP DPNPTFHVOEB

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBNÊUPEPTDPNQMFKPTEFEFTUJMBDJÓO

BMJNFOUBDJÓOBMBFWBQPSBDJÓOJOTUBOUÃOFB7BSÎF7'FOFMUBNCPS IBTUBMMFHBSBMBGSBD DJÓONPMRVFTFEFTFBFOMPTGPOEPT D )BZPUSPTNÊUPEPTRVFTFQVFEFOTFHVJS "1­/%*$&"-$"1±56-0 4*.6-"$*¶/%&4*45&."4 $0.1-&+04%&%&45*-"$*¶/

&OFTUFBQÊOEJDFTFDPOUJOÙBOMBTJOTUSVDDJPOFTEFMPTBQÊOEJDFTBMPTDBQÎUVMPTZ"VORVFTF NFODJPOBFMTJNVMBEPS"TQFO1MVT TFQVFEFOVTBSPUSPTTJNVMBEPSFTEFQSPDFTP-PTUSFTQSPCMF NBTEFFTUFBQÊOEJDFUFOESÃODPSSJFOUFTEFSFDJSDVMBDJÓOFODPMVNOBTEFEFTUJMBDJÓO-PTQSPDFEJ NJFOUPTRVFTFQSFTFOUBOBRVÎQBSBPCUFOFSDPOWFSHFODJBTPO UPEPT GPSNBTEFBSSBTUSFDPOWBQPS $PNPOPTPOMPTÙOJDPTNÊUPEPTRVFTFQVFEFOBQMJDBS MFFODBSFDFNPTFYQFSJNFOUBSDPOPUSPT NÊUPEPT 4J QFSTJTUFO QSPCMFNBT BM DPSSFS FM TJNVMBEPS  WFB FM BQÊOEJDF (VÎB EF MPDBMJ[BDJÓO EF GBMMBTFOMBTTFQBSBDJPOFT QBSB"TQFO1MVT RVFTFFODVFOUSBEFTQVÊTEFMDBQÎUVMP -BCPSBUPSJP 1BSUF"%FTUJMBDJÓOBEPTQSFTJPOFTQBSBTFQBSBSB[FÓUSPQPT1BSBTFQBSBSB[FÓ USPQPTTFQVFEFBQMJDBSVOBNPEJàDBDJÓOEFMBSSFHMPEFDPMVNOBTRVFNVFTUSBMBàHVSB PFM BSSFHMPNVZQBSFDJEPFOFMRVFFOUSBMBBMJNFOUBDJÓOBMBDPMVNOB BNBZPSQSFTJÓO TJFNQSFZ DVBOEPMBDPODFOUSBDJÓOEFMB[FÓUSPQPWBSÎFFOGPSNBDPOTJEFSBCMFDVBOEPDBNCJFMBQSFTJÓO%FCF VTUFEEFTBSSPMMBSVOTJTUFNBRVFBMJNFOUF%Z'FOFUBQBTTFQBSBEBT 4FEFTFBTFQBSBSVOBBMJNFOUBDJÓORVFDPOUJFOFNPMEFBHVBZNPMEFNFUJMFUJMDFUP OB-BBMJNFOUBDJÓOFTMÎRVJEPTBUVSBEP ZFOUSBBMBDPMVNOBDPNPMÎRVJEPTBUVSBEPBBUN -BUBTBEFBMJNFOUBDJÓOGSFTDBBMBDPMVNOBFTLHNPMI-BDPMVNOBUSBCBKBBBUN $PNJFODFDPO/ BNCBTBMJNFOUBDJPOFTFO/BMJNZ-%FOMBDPMVNOB&MEFTUJMBEP FTVOMÎRVJEPTBUVSBEP6TFVODPOEFOTBEPSUPUBMZVOWBQPSJ[BEPSUJQPSFUPSUB"KVTUFMBDPOWFS HFODJBBJUFSBDJPOFT4FEFTFBRVFMPTQSPEVDUPTUFOHBOEFQVSF[B -BDPMVNOBGVODJPOBBQTJBZUJFOFVODPOEFOTBEPSUPUBM EFTUJMBEPMÎRVJEPTBUVSBEPZVO WBQPSJ[BEPSUJQPSFUPSUB$PNJFODFDPO/V/BMJN DPO-%"KVTUFMBDPOWFSHFODJB BJUFSBDJPOFT $VBOEPUSBDFFMEJBHSBNBEFáVKP QPOHBVOBCPNCB TFMFDDJPOFFOiQSFTTVSFDIBOHFSTu DBNCJB EPSFTEFQSFTJÓO FOMBUVCFSÎBEFEFTUJMBEPRVFWBEFMBDPMVNOBZRVFFTMBBMJNFOUBDJÓOBMB DPMVNOB&MEJBHSBNBEFáVKPSFTVMUBOUFEFCFTFSQBSFDJEPBMEFMBàHVSB"&àDJFODJBEF MBCPNCBZQSFTJÓOEFTBMJEBQTJB 1BSBJOJDJBS IBHBCBMBODFTFYUFSOPTEFNBTBZDBMDVMFWBMPSFTFYBDUPTQBSBMPTEPTáVKPTEFGPO EPTTVQPOJFOEPRVFFMBHVBZMBNFUJMFUJMDFUPOBQSPEVDUPTTPOQVSPT&TQFDJàRVFRVFMBUBTBEF áVKPEFMBDPMVNOBTFB QFSP/0FTQFDJàRVFMPTGPOEPTFOMBDPMVNOB1BSBFTBDPMVNOB DPNJFODFDPO%ZBVNFOUF%FOFTDBMPOFTEF   ZTJOJOJDJBMJ[BS4JOPIBDF BKVTUFT "TQFO1MVTUFOESÃFSSPSFT0CTFSWFRVF#FOMBDPMVNOB TJFNQSF BVORVFOPMP IBZBFTQFDJàDBEP y1PSRVÊ

"VORVFOPEBVOBKVTUFQFSGFDUP MBFDVBDJÓOEF8JMTPOQSPEVDFEBUPTSB[POBCMFTEFFRVJMJCSJP WBQPSMÎRVJEP"OBMJDFMBTHSÃàDBT5Z YZZY4JÊOUBTFMJCSFQBSBCVTDBSNFKPSFTQSPHSBNBTEF FRVJMJCSJPWBQPSMÎRVJEP %FUFSNJOFMBTDPOEJDJPOFTEFPQFSBDJÓOSB[POBCMFTQBSBRVFFMBHVBUFOHBVOBGSBDDJÓONPMBS FOUSFZFOMPTGPOEPTEFMBDPMVNOBZMBNFUJMFUJMDFUPOB FOGSBDDJPOFTNPMBSFT EF BFOMPTGPOEPTEFMBDPMVNOB$VBOEPFTUÊTBUJTGFDIPDPOFMEJTFÒP DPSSBMBTJNVMB

www.FreeLibros.me

"QÊOEJDFBMDBQÎUVMP 4JNVMBDJÓOEFTJTUFNBTDPNQMFKPTEFEFTUJMBDJÓO



'*(63"" 1"/5"--"%&"41&/1-641"3"4*45&."4%&%&45*-"$*¶/"%0413&4*0/&4 DJÓOVOBWF[NÃTQBSBEJNFOTJPOBSMPTQMBUPTEFBNCBTDPMVNOBT6TFQMBUPTQFSGPSBEPTZMPT WBMPSFTQSFEFUFSNJOBEPTQBSBMBTEFNÃTWBSJBCMFT $VBOEPUFSNJOF FYBNJOFMPTáVKPTEFEFTUJMBEPy1PSRVÊTPOUBOHSBOEFT /PUFRVFIBDFORVF MPTEJÃNFUSPTEFDPMVNOBZMBTDBSHBTUÊSNJDBTTFBOHSBOEFTQBSBFTUBBMJNFOUBDJÓOUBOSFEVDJEB &TUBTHSBOEFTUBTBTEFSFDJSDVMBDJÓOZFODPOTFDVFODJBMPTEJÃNFUSPTZMBTDBSHBTUÊSNJDBT IBDFO RVFFTUFEJTFÒPTÓMPTFBFDPOÓNJDPDVBOEPFMDBNCJPEFMB[FÓUSPQPDPOMBQSFTJÓOTFBCBTUBOUF HSBOEF&MEFMBNFUJMFUJMDFUPOBZFMBHVBFTVOFKFNQMPRVFTFIBDFJOEVTUSJBMNFOUF 1BSUF#%FTUJMBDJÓOCJOBSJBEFTJTUFNBTDPOB[FÓUSPQPTIFUFSPHÊOFPT&MPCKFUJWPEFFTUBQBSUFFT EJTFÒBSVOTJTUFNBQBSFDJEPBMBàHVSB"QBSBTFQBSBSOCVUBOPMZBHVB"CSBVOBSDIJWPOVFWP &O4FUVQ BKVTUFT WFB.FUZWBMJEFMBTGBTFTWBQPSMÎRVJEPMÎRVJEP*OEJRVFRVFMPTDPNQPOFOUFT TPOOCVUBOPMZBHVB#VTDBSVONPEFMPBEFDVBEPEFFRVJMJCSJPWBQPSMÎRVJEPQBSBB[FÓUSPQPT IFUFSPHÊOFPTFTUPEPVOEFTBGÎP&MQSPHSBNB/35-3,GVFFMNFKPSNPEFMPEFMBNFEJBEPDFOB DPORVFIJDFMBQSVFCB 4JÊOUBTFMJCSFQBSBQSPCBSPUSPTNPEFMPT $PO/35-3,TFBKVTUBVOP CBTUBOUFCJFOBMBDPNQPTJDJÓOEFMWBQPSEFMB[FÓUSPQP ZBMBDPNQPTJDJÓOEFMBGBTFBDVPTB WFBMB 5UBCMBFOFMQSPCMFNB%

QFSPUJFOFCBTUBOUFFSSPSFOMBDPNQPTJDJÓOEFMBGBTFEFCVUBOPM %FTQVÊTEFBKVTUBSFMEFDBOUBEPS VTF"OBMZTJT BOÃMJTJT QBSBWFSMBTHSÃàDBT5Z YZZY$PNQÃ SFMBTDPOMPTEBUPT3FDVFSEFEFQFSNJUJSWBQPSMÎRVJEPMÎRVJEPDPNPGBTFTFO"OBMZTJT &MQSPCMFNBRVFTFRVJFSFSFTPMWFSFTTFQBSBSLHNPMIEFVOBBMJNFOUBDJÓOMÎRVJEBTBUVSBEB BBUN-BBMJNFOUBDJÓODPOUJFOFNPMEFCVUBOPMZNPMEFBHVB4FEFTFBRVFMBQVSF [BEFBNCPTQSPEVDUPTTFBPNBZPS4FEFCFVTBSVOTJTUFNBQBSFDJEPBMEFMBàHVSB" -BTDPMVNOBTGVODJPOBSÃOBBUN6TFCBMBODFTFYUFSOPTEFNBTBQBSBEFUFSNJOBSMBTUBTBT EFáVKPEFMPTEPTQSPEVDUPTEFGPOEPTTVQPOJFOEPRVFFOFTFODJBTPOCVUBOPMQVSPZBHVBQVSB GSBDDJÓONPMBSEFMPUSPDPNQPOFOUF& 

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBNÊUPEPTDPNQMFKPTEFEFTUJMBDJÓO

5SBDFFMEJBHSBNBEFáVKP6TFDPOEFOTBEPSFTUPUBMFTQBSBBNCBTDPMVNOBT-PTEPTEFTUJMBEPT QSPEVDUPEFCFOSFUJSBSTFDPNPMÎRVJEPTQBSBEFTQVÊTDPOFDUBSTFQBSBMMFHBSBMEFDBOUBEPS-B DBQBEFIJESPDBSCVSPEFMEFDBOUBEPSTFEFCFDPOFDUBSBMBBMJNFOUBDJÓOEFMBDPMVNOBEFEFTUJ MBDJÓORVFQSPEVDFCVUBOPMQVSP&MEFDBOUBEPS PBTFOUBEPSMÎRVJEPMÎRVJEP FOFMEJBHSBNBEF áVKPBQBSFDFFOTFQBSBUPST TFQBSBEPSFT &TDPKBVOBQSFTJÓOFOFMEFDBOUBEPSEFBUN VOB DBSHBUÊSNJDBEF&MDPNQPOFOUFDMBWFQBSBMBTFHVOEBGBTFFTBHVBZQPOHBFMVNCSBMB  MPTEBUPTEFFRVJMJCSJPNVFTUSBORVFFMNÃYJNPDPOUFOJEPEFBHVBFOMBGBTFPSHÃOJDBFT  1POHBMBDPOWFSHFODJBFOJUFSBDJPOFT-BDBQBEFBHVBEFMEFDBOUBEPSEFCFDPOFDUBSTFBMB BMJNFOUBDJÓOEFMBDPMVNOBEFEFTUJMBDJÓORVFQSPEVDFBHVBQVSB0CTFSWFRVFMBTDPMVNOBTEF "TQFO1MVTFOMBàHVSB"OPTFWFSÃOFYBDUBNFOUFDPNPFMBSSFHMPEFMBàHVSB"&TUBNPT VTBOEPMPTDPOEFOTBEPSFTFOMBTDPMVNOBTQBSBDPOEFOTBSMPTMÎRVJEPT6TBSFNPTMBTIPKBTEF FTQFDJàDBDJÓOQBSBRVFFMTJTUFNBTFDPNQPSUFDPNPFMEFMBàHVSB" &OMBTIPKBTEFFTQFDJàDBDJÓOQBSBMBTEPTDPMVNOBTEFEFTUJMBDJÓO MBTUVCFSÎBTRVFWJFOFOEFM EFDBOUBEPSEFCFOFOUSBSDPNPBMJNFOUBDJÓOFOMBFUBQB QSJNFSBFUBQBSFBMFOMBDPMVNOB  6TFWBQPSJ[BEPSFTUJQPNBSNJUB1POHBFMáVKPEFGPOEPTEFMBDPMVNOBEFCVUBOPMFOMPTWBMPSFT DBMDVMBEPTDPOMPTCBMBODFTEFNBTBFYUFSOPT"MQSJODJQJP MBDPMVNOBRVFSFDJCFMBBMJNFOUB DJÓOUSBCBKBDPO/ZMBBMJNFOUBDJÓOFO5BNCJÊOBMJOJDJP QPOHBFUBQBTFOMBDPMVNOB EFBHPUBNJFOUP1POHBMBUBTBEFWBQPSBMGPOEPFOLHNPMIFOMBDPMVNOBEFBHPUBNJFOUP "KVTUFMBDPOWFSHFODJBBJUFSBDJPOFTQBSBBNCBTDPMVNOBT 1POHBMBTSFMBDJPOFTEFSFáVKPFOFOBNCBTDPMVNOBT&OSFBMJEBE OPTFRVJFSFSFáVKBSEFTEF MPTDPOEFOTBEPSFT QFSPTFEFTFBUPNBSFMSFáVKPEFMEFDBOUBEPSTJOFNCBSHP TJVTUFEUSBUBEF QPOFSMBSFMBDJÓOEFSFáVKPFO "TQFO1MVTOPUSBCBKB3FEV[DBBNCBTSFMBDJPOFTEFSFáVKP

'*(63"" 4*45&."%&%&45*-"$*¶/1"3"4&1"3"3";&¶530104)&5&30(­/&04

www.FreeLibros.me

"QÊOEJDFBMDBQÎUVMP 4JNVMBDJÓOEFTJTUFNBTDPNQMFKPTEFEFTUJMBDJÓO



FO EFDSFNFOUPT IBTUB  BQSPYJNBEBNFOUF &TBT SFMBDJPOFT TPO TVàDJFOUFNFOUF QFRVFÒBT QBSBRVFMPTSFTVMUBEPTTFBDFSRVFOBMVTPEFTÓMPSFáVKPEFTEFMBTGBTFTEFMEFDBOUBEPS4JOPMP IBDFFOEFDSFNFOUPT FMDPOEFOTBEPSTFTFDBSÃZMBDPSSJEBUFOESÃFSSPSFT`%ÊMFTVTQBMNBEJUBT B"TQFO1MVTQBSBUFOFSMPDPOUFOUP "MUFSNJOBSFMMBCPSBUPSJP QPESÎBUSBUBSEFJOJDJBMJ[BSMPZWFSRVÊTVDFEFTJBKVTUBMBSFMBDJÓOEF SFáVKPFO-PTSFTVMUBEPTDVBOEPMBDPMVNOBTFTFDBOPTPOÙUJMFT %FTQVÊT EF IBCFS DPSSJEP CJFO MB TJNVMBDJÓO  PCTFSWF RVF FT QSPCBCMF RVF BNCBT DPMVNOBT OPPCUFOHBOMPTQSPEVDUPTDPOMBQVSF[BRVFTFSFRVJFSF"VNFOUFVOQPDPMBUBTBEFWBQPSBM GPOEP IBTUBLHNPMI"IPSBMPTEPTQSPEVDUPTEFCFODVNQMJSDPOMBTFTQFDJàDBDJPOFTEF QVSF[B QFSPFMCVUBOPMQSPEVDUPFTNÃTQVSPRVFMPOFDFTBSJP3FEV[DBMBTFUBQBTZEFUFSNJOFFM MVHBSÓQUJNPEFBMJNFOUBDJÓOFOMBDPMVNOBEFCVUBOPM&TPJNQMJDBRVFTFQVFEFOVTBSNFOPT FUBQBTZNFOPSSFMBDJÓOEFWBQPSBMGPOEP5SBUFEFSFEVDJS/5BNCJÊO CVTRVFMBVCJDBDJÓO ÓQUJNBEFMBBMJNFOUBDJÓOFOMBQSJNFSBDPMVNOB -BCPSBUPSJP %FTUJMBDJÓOFYUSBDUJWB&TUBUBSFBFTNÃTEFUFSNJOJTUBFJNQMJDBNFOPTFYQMPSB DJÓORVFMPTPUSPTMBCPSBUPSJPT ZBRVFFOMBEFTUJMBDJÓOFYUSBDUJWBMBDPOWFSHFODJBFTVOQSPCMFNB GSFDVFOUF&OFMBMHPSJUNPCÃTJDP àHVSB TFTVQPOFRVFFMDJDMPEFDPODFOUSBDJÓOUJFOFQPDP FGFDUPFOMPTEFNÃTDJDMPT-PTTJTUFNBTEFEFTUJMBDJÓOFYUSBDUJWBUJFOFOFRVJMJCSJPTWBQPSMÎRVJEP NVZOPJEFBMFTZMBIJQÓUFTJTBOUFSJPS DPOGSFDVFODJB OPFTDJFSUB$PNPTJFNQSFDPO"TQFO1MVTTF QVFEFPCUFOFSMBDPOWFSHFODJBDPNFO[BOEPDPOVODPOKVOUPEFDPOEJDJPOFTRVFDPOWFSKBZDBNCJBS MFOUBNFOUFMBWBSJBCMFEFJOUFSÊT QPSFKFNQMP-% QBSBBDFSDBSTFBMWBMPSRVFTFEFTFF$VBOEP UFOHBVTUFEVOQSPCMFNBEFDPOWFSHFODJB WVFMWBBJOJDJBMJ[BS3"%'3"$ZSFHSFTFBVOBDPOEJ DJÓODPOMBRVFBOUFTIBCÎBDPOWFSHFODJB 1SPCMFNB6TBSEFTUJMBDJÓOFYUSBDUJWBQBSBSPNQFSFMB[FÓUSPQPFUBOPMBHVB6TBSFMTJTUFNBEF EPTDPMVNOBTEFMBàHVSB&MTPMWFOUFFTFUJMFOHMJDPM"NCBTDPMVNOBTUSBCBKBOBBUNÓT GFSB-BBMJNFOUBDJÓOBMBDPMVNOBFTLHNPMI&TVOMÎRVJEPTBUVSBEPGPSNBEPQPS NPMEFFUBOPMZNPMEFBHVB6TF/35- &OMBàHVSB FMQSPEVDUP"TFSÃFMFUBOPMQSPEVDJEP ZFMQSPEVDUP# EFTUJMBEPEFMBDPMVNOB  TFSÃBHVB4FRVJFSFRVFFMQSPEVDUP"UFOHBVOBGSBDDJÓONPMBSEFFUBOPMEF SFCBTBMBT FTQFDJàDBDJPOFTEFMFUBOPMRVFTFVTBFOMBHBTPMJOB 6TFVOBSFMBDJÓOEFSFáVKPFYUFSOP-%  &OFMDBTPOPSNBM MPBOUFSJPSTFPQUJNJ[BSÎB QFSPQBSBBIPSSBSUJFNQP EÊKFMPTDPOTUBOUFT  &MSFáVKPSFHSFTBDPNPMÎRVJEPTBUVSBEP&TUFDPOKVOUPEFDPOEJDJPOFTEFCFFMJNJOBSTVàDJFOUF FUJMFOHMJDPMEFMEFTUJMBEPQBSBQSPEVDJSVOFUBOPMEFMBQVSF[BBEFDVBEB DPNQSVFCF QBSBBTFHV SBSTF RVFBTÎTVDFEB &MQSPEVDUPEFGPOEPTEFMBDPMVNOBEFCFUFOFSVOBGSBDDJÓONPMBSEF FUBOPMNFOPSRVF&TUFWBMPSFTCBKPQBSBBVNFOUBSMBSFDVQFSBDJÓOEFMFUBOPM &MEFTUJMBEPEFMBDPMVNOBEFCFDPOUFOFSVOBGSBDDJÓONPMBSNFOPSRVFEFFUJMFOHMJDPM &MQSPEVDUPEFGPOEPTEFMBDPMVNOBEFCFDPOUFOFSVOBGSBDDJÓONPMBSNFOPSRVFEF BHVB QPSRVFFTQSPCBCMFRVFUPEBFMBHVBFOFTUBDPSSJFOUFUFSNJOFFOFMFUBOPMQSPEVDUPBM SFDJSDVMBSFMTPMWFOUF 1BTPTZ1SJNFSP EJTFÒFMBTEPTDPMVNOBTFO3"%'3"$DPNPDPMVNOBTFOTFSJF TJOSF DJSDVMBDJÓOEFTPMWFOUF&OUPODFT UPEPFMTPMWFOUFRVFTFVTFEFCFBHSFHBSTFDPNPSFMMFOPEF TPMWFOUF1BSBFTUBQBSUFVTFVOSFMMFOPEFTPMWFOUFRVFTFBDFSRVFBMBDPODFOUSBDJÓOFTQFSBEB EFMTPMWFOUFSFDJSDVMBEP&TUPFT MBDPSSJFOUFEFTPMWFOUFEFCFUFOFSEFFUJMFOHMJDPMZ EFBHVB FOGSBDDJPOFTNPMBSFT6TFVOBUFNQFSBUVSBEFž$QBSBFMTPMWFOUFQBSBJHVBMBSBQSPYJ NBEBNFOUFMBUFNQFSBUVSBFOMBFUBQBEFBMJNFOUBDJÓOEFMTPMWFOUF /4FOMBDPMVNOB-B QSFTJÓOEFMTPMWFOUFFTBUN6TFDPOEFOTBEPSFTUPUBMFTZWBQPSJ[BEPSFTEFNBSNJUB

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBNÊUPEPTDPNQMFKPTEFEFTUJMBDJÓO

&OMBTFDDJÓOEFDPOWFSHFODJBEFMCMPRVFEFFOUSBEBT QPOHBFOMBDBOUJEBEEFJUFSBDJPOFT QBSBBNCBTDPMVNOBT 7BZBB%BUB EBUPT FOMBCBSSBEFNFOÙ ZIBHBDMJDFO#MPDLT CMPRVFT  &OFMMBEPJ[RVJFSEPEFMBQBOUBMMBIBHBDMJDFOFMTJHOP KVOUPBMCMPRVFEFMBDPMVNOBEFEFTUJ MBDJÓOQBSBMBRVFEFTFFBVNFOUBSMBDBOUJEBEEFFUBQBT%FTQVÊTCVTRVF$POWFSHFODF DPOWFS HFODJB ZIBHBDMJDFOMBDBTJMMBEFWFSJàDBDJÓOB[VMEFDPOWFSHFODJB%FFTUFNPEPTFQSFTFOUB VOBUBCMB"VNFOUFBMBDBOUJEBENÃYJNBEFJUFSBDJPOFT$PONBZPSFTWBMPSFTOPNFKPSBSà  1BTP  %JTFÒP EF MB DPMVNOB  &M TPMWFOUF TF DPOTJEFSB DPNP TFHVOEB BMJNFOUBDJÓO &O FM EJBHSBNBEFáVKP VTFMBDPOFYJÓOEFBMJNFOUBDJÓOQBSBBHSFHBSBMBTDPMVNOBTVOBBMJNFOUBDJÓO EFTPMWFOUF&OUPODFT FTQFDJàRVFTVVCJDBDJÓOFOMBUBCMBEFDPOEJDJPOFTEFFOUSBEB*OUSPEV[DB FMTPMWFOUFFOMBFUBQB/46TFVOáVKPEFTPMWFOUF4LHNPMI$PNJFODFDPO/ FOMBDPMVNOBZVCJDBDJÓOEFBMJNFOUBDJÓOFO/'&TQFDJàRVFMBUBTBEFGMVKPEFEFTUJMBEP RVFQSPEV[DBMBQVSF[BRVFRVJFSFQBSBFMFUBOPMQSPEVDUPZMBGSBDDJÓONPMBSEFTFBEBFOFMQSP EVDUPEFGPOEPT IBHBCBMBODFTFYUFSOPT %FUFSNJOFMBVCJDBDJÓOÓQUJNBEFMBBMJNFOUBDJÓOZMB DBOUJEBENÎOJNBUPUBMEFFUBQBTDPOMBTRVFTFQVFEBIBDFSMBTFQBSBDJÓORVFTFRVJFSF$PNJFODF NBOUFOJFOEPàKP/'NJFOUSBTSFEVDF/ DBOUJEBEUPUBMEFFUBQBTFOMBDPMVNOB IBTUBRVF BQFOBTPCUFOHBMBTDPODFOUSBDJPOFTEFTFBEBTFOGPOEPTZEFTUJMBEP&OUPODFTEFUFSNJOFMBFUBQB ÓQUJNBEFBMJNFOUBDJÓOZUSBUFEFSFEVDJSNÃT/&TQSPCBCMFRVFDPOWBMPSFTQFRVFÒPTEFFUBQB EFBMJNFOUBDJÓO QPSFKFNQMP /' OPDPOWFSKB1PSUBOUP DPNJFODFDPOVOOÙNFSPBMUP QBSBFMMVHBSEFMBFUBQBEFBMJNFOUBDJÓO ZSFEV[DBMFOUBNFOUF/' 1BTP%JTFÒPEFMBDPMVNOB-BBMJNFOUBDJÓOBMBDPMVNOBFTMPTGPOEPTEFMBDPMVNOB &TVOMÎRVJEPTBUVSBEPBBUN&TQFDJàRVFMBUBTBEFGMVKPEFGPOEPTRVFMFQFSNJUBPCUFOFSFM EFTUJMBEPZMPTGPOEPTDPOMBQVSF[BEFTFBEB IBHBVOCBMBODFFYUFSOPNVZFYBDUP %FUFSNJOF VOB -% NÎONVZFYBDUB /Z/'TPOTVàDJFOUFTDPNJFODFDPO-%ZBWBODF IBDJBBCBKP 5SBCBKFDPO-% -% NÎO&OUPODFTDBMDVMFFMWBMPSÓQUJNPEFMBFUBQBEF BMJNFOUBDJÓO DPNJFODFDPO/Z/' /PUFRVFMBDPMVNOBFTCBTUBOUFTFODJMMBZ USBCBKBDPOVOWBMPSCBKPEF-% 1BTP"MàOBMIBCSÃRVFDPOFDUBSFMDJSDVJUPEFSFDJSDVMBDJÓOEFTPMWFOUFEFMBDPMVNOBBMB DPMVNOB1FSPQSJNFSP JOUFSDBMFVODBNCJBEPSEFDBMPSQBSBFOGSJBSFMTPMWFOUF4JOPMPIBDF  MBDPMVNOBOPUSBCBKBSÃBMIBDFSMBDPOFYJÓOEFMDJSDVJUPEFSFDJSDVMBDJÓOEFTPMWFOUF yQPSRVÊ OP  1BSBJOUFSDBMBSFMDBNCJBEPSEFDBMPSFOMBUVCFSÎBEFMTPMWFOUF WBZBB)FBU&YDIBOHFST DBNCJBEPSFTEFDBMPS ZQPOHBVO)&"5&3 DBMFOUBEPS RVFBRVÎTFVTBDPNPFOGSJBEPS FO TVEJBHSBNBEFáVKP&OUPODFTIBHBDMJDDPOFMCPUÓOJ[RVJFSEPFOMBDPSSJFOUFEFTPMWFOUFZDMJD DPOCPUÓOEFSFDIPFO3FDPOOFDU%FTUJOBUJPO SFDPOFDUBSEFTUJOP &OUPODFTDPOFDUFMBDPSSJFOUF EFMTPMWFOUFDPOMBáFDIBFOFMDBNCJBEPSEFDBMPS0QSJNBFMCPUÓO/FYU TJHVJFOUF "QBSFDFSÃ VOBWFOUBOBQBSBFMJOUFSDBNCJBEPSEFDBMPS6TFž$-BQSFTJÓOFTBUN &O7BMJE1IBTFT GBTFTWÃMJEBT VTFiMJRVJEPOMZu TÓMPMÎRVJEB 1BSBDPNQSPCBSRVFFMDBNCJBEPSRVFEFCJFO DPOFDUBEPIBHBVOBDPSSJEBTJODBNCJBSMBUBTBEFáVKPEFMTPMWFOUF $POFDUFMBUVCFSÎBRVFTBMFEFMJOUFSDBNCJBEPSBMBDPMVNOB VTFSFDPOOFDUEFTUJOBUJPO SF DPOFDUBSEFTUJOP ZDPOÊDUFMBBMBBMJNFOUBDJÓOQBSBMBDPMVNOB &OMBUBCMBEFDPOEJDJPOFT EFFOUSBEBJOEJRVFMBDPSSJFOUFEFSFMMFOPEFTPMWFOUFZMBUVCFSÎBEFSFDJSDVMBDJÓOFOMBNJTNB FUBQB FUBQBOÙNFSP  1BSBDBMDVMBSFMáVKPEFSFMMFOPEFTPMWFOUF RVFUFSNJOBSÃQPSVTBS IBHBVOCBMBODFFYUFSOPEF NBTBBMSFEFEPSEFMTJTUFNBDPNQMFUP 5BTBEFáVKPEFSFMMFOPEFTPMWFOUF4BMJEBEFTPMWFOUFFOFMQSPEVDUP" TBMJEBEFTPMWFOUF FOFMQSPEVDUP#

www.FreeLibros.me

"QÊOEJDFBMDBQÎUVMP 4JNVMBDJÓOEFTJTUFNBTDPNQMFKPTEFEFTUJMBDJÓO



'*(63"" 1"/5"--"%&"41&/1-64%&6/4*45&."%&%&45*-"$*¶/&953"$5*7"5&3.*/"%0 -BUBTBEFáVKPSFTVMUBOUFTFSÃFYUSFNBEBNFOUFQFRVFÒB QPSRVFTPOQFRVFÒBTMBTQÊSEJEBTEF TPMWFOUF EFTQVÊTEFUPEP OBEJFEFTFBUPNBSFUJMFOHMJDPMFOTVBMDPIPMPFOTVBHVB 4JEFJONF EJBUPVTBFTUFWBMPSEFSFMMFOPEFTPMWFOUFDPNPBMJNFOUBDJÓOBMTJTUFNB "TQFO1MVTOPDPOWFS HFSÃ$PNJFODFDPOFMWBMPSRVFVTBCBBOUFTZEJTNJOÙZBMPSÃQJEBNFOUF QPSFKFNQMP FOGBDUPSFT EFP )BTUBRVFMBDPSSJFOUFEFSFMMFOPEFTPMWFOUFUFOHBFMWBMPSOFDFTBSJPQBSBFMCBMBODF FYUFSOPEFNBTB FMFUJMFOHMJDPMiTPCSBOUFuTBMESÃDPOFMEFTUJMBEP BHVBQSPEVDUP EFMBDPMVNOB &TPTFEFCFBRVFMBUBTBEFáVKPEFGPOEPTFOMBDPMVNOBFTUÃFTQFDJàDBEBZFMÙOJDPMVHBS IBDJBEPOEFQVFEFJSFMFUJMFOHMJDPTPCSBOUFFTDPOFMEFTUJMBEPEFMBDPMVNOB &TUBFTMBSB[ÓO QPSMBRVFEFCFJOEJDBSMBUBTBEFáVKPEFGPOEPTFOMBDPMVNOB 4JQPOFMBUBTBEFEFTUJMBEPFO MBDPMVNOB OPIBZMVHBSEPOEFQVFEBJSFMFUJMFOHMJDPMTPCSBOUF ZFMTJTUFNBOPDPOWFSHFSÃ  /PUFOHBFODVFOUBMPTWBMPSFTEFUBTBEFáVKPEFEFTUJMBEPZMBTDPNQPTJDJPOFTEFMEFTUJMBEPEF MBDPMVNOBTJOPIBTUBRVFVTFFMáVKPEFSFMMFOPEFTPMWFOUFRVFTBUJTGBHBFMCBMBODFHFOFSBM 6OBWF[DFSDBEFMáVKPDPSSFDUPEFMSFMMFOP DÃNCJFMPBFUJMFOHMJDPMQVSP-BBQBSJFODJBàOBMEFM TJTUFNBTFEFCFQBSFDFSBMBEFMBàHVSB" 4JQPSBMHVOBSB[ÓO OPTFSFDPNJFOEB EFCJFSBEFTBDPQMBSFMDJSDVJUPEFSFDJSDVMBDJÓO SFDVFSEF BKVTUBSMBUBTBEFáVKPEFSFMMFOPFOFMWBMPSEFTFBEP 1BTP4JFTOFDFTBSJP IBHBBKVTUFTNFOPSFTFOFUBQBT áVKPTPSFMBDJPOFTEFSFáVKPQBSBPCUF OFSMBTQSPQJFEBEFTEFTFBEBT &TPQPESÃOPOFDFTJUBSTF

$PNPNÎOJNP BOPUFMPTJHVJFOUFGSBDDJPOFTNPMBSFTEFMPTEPTQSPEVDUPTZMBTEPTDPSSJFOUFTEF GPOEPTMBTDBQBDJEBEFTUÊSNJDBTEFMPTEPTDPOEFOTBEPSFT MPTEPTWBQPSJ[BEPSFTZFMJOUFSDBNCJB EPSEFDBMPSMBTUBTBTEFáVKPEFUPEBTMBTDPSSJFOUFTFOFMQSPDFTP-%FODBEBDPMVNOB /ZVCJ DBDJPOFTEFBMJNFOUBDJÓOFODBEBDPMVNOB ZMBTUFNQFSBUVSBTEFWBQPSJ[BEPSFTZDPOEFOTBEPSFT

www.FreeLibros.me

$"1±56-0 

%FTUJMBDJÓOJOUFSNJUFOUF

-BEFTUJMBDJÓODPOUJOVBFTVONÊUPEPUFSNPEJOÃNJDBNFOUFFàDJFOUFQBSBQSPEVDJSHSBOEFTDBOUJ EBEFTEFNBUFSJBMEFDPNQPTJDJÓODPOTUBOUF$VBOEPTFSFRVJFSFOQFRVFÒBTDBOUJEBEFTEFNBUFSJBM PDPNQPTJDJPOFTWBSJBCMFTEFQSPEVDUP MBEFTUJMBDJÓOJOUFSNJUFOUFUJFOFWBSJBTWFOUBKBT&OFMMB  VOBDBSHBEFBMJNFOUBDJÓOTFBMJNFOUBFOFMWBQPSJ[BEPS TFBCSFFMWBQPSEFBHVBZEFTQVÊTEFVO QFRVFÒPQFSJPEPEFBSSBORVF TFQVFEFTBDBSQSPEVDUPEFMBQBSUFTVQFSJPSEFMBDPMVNOB$VBOEP UFSNJOBMBEFTUJMBDJÓO TFEFTDPOFDUBFMDBMPSZTFTBDBFMNBUFSJBMRVFRVFEÓFOFMWBQPSJ[BEPS%FT QVÊTTFQVFEFJOJDJBSVOOVFWPMPUF&OHFOFSBM FMEFTUJMBEPFTFMQSPEVDUPRVFTFEFTFB -BEFTUJMBDJÓOJOUFSNJUFOUFFTVOQSPDFTPNVDIPNÃTBOUJHVPRVFMBEFTUJMBDJÓODPOUJOVB-PT BMRVJNJTUBTÃSBCFT BMSFEFEPSEF%$ MBEFTBSSPMMBSPOQPSQSJNFSBWF[QBSBDPODFOUSBSBMDPIPM 7BMMFF  'VFBEPQUBEBFO&VSPQB0DDJEFOUBMZFMQSJNFSMJCSPDPOPDJEPTPCSFFMUFNBGVF -JCFSEFBSUFEJTUJMMBOEJEF)JFSPOZNVT#SVOTDIXJH QVCMJDBEPFOMBUÎOBQSJODJQJPTEFMBEÊDBEBEF &TUFMJCSPRVFEÓDPNPUFYUPGBSNBDÊVUJDPZNÊEJDPEVSBOUFNÃTEFVOTJHMP&MQSJNFSMJCSP TPCSFEFTUJMBDJÓOFTDSJUPQBSBMBDPNVOJEBEFTQFDJBMJ[BEB QFSPOPBDBEÊNJDB GVF%BT/FXHSPTT %JTUJMMJFS#VDI EF8BMUFS3ZGG QVCMJDBEPFOBMFNÃOFO 4UBOXPPE  &TUFMJCSPDPOUFOÎB VOBiMJTUBEFBQBSBUPTZUÊDOJDBTEFEFTUJMBDJÓO ZMBTQMBOUBT BOJNBMFTZNJOFSBMFTQPTJCMFTQBSBTFS EFTUJMBEPTQBSBVTPGBSNBDÊVUJDPIVNBOPu-PTBWBODFTFOMBEFTUJMBDJÓOJOUFSNJUFOUFTFIBOSFMB DJPOBEPDPOTVBQMJDBDJÓOFOMBEFTUJMBDJÓOEFBMDPIPM QSPEVDUPTGBSNBDÊVUJDPT BMRVJUSÃOEFIVMMB  QFUSÓMFPZRVÎNJDPTàOPT -BEFTUJMBDJÓOJOUFSNJUFOUFFTWFSTÃUJM6OBDPSSJEBQVFEFEVSBSEFTEFBMHVOBTIPSBTIBTUBWB SJPTEÎBT&TMBNFKPSBMUFSOBUJWBDVBOEPMBGÃCSJDBOPUSBCBKBFOGPSNBDPOUJOVBZEFCFUFSNJOBSTF FMMPUFFOVOPPEPTUVSOPT BIPSBT 4FVTBDPOGSFDVFODJBDVBOEPDPOFMNJTNPFRVJQPTF EFTUJMBOWBSJPTQSPEVDUPTEJGFSFOUFTFOEJTUJOUBTWFDFT4JTÓMPTFSFRVJFSFEFTUJMBDJÓOFOGPSNBPDB TJPOBM MBPQDJÓOTFSÎBMBEFTUJMBDJÓOJOUFSNJUFOUF -PTFRVJQPTTFQVFEFOBSSFHMBSFOEJWFSTBTDPOàHVSBDJPOFT&OMBEFTUJMBDJÓOJOUFSNJUFOUFTJN QMF àHVSB FMWBQPSTFSFUJSBFOGPSNBDPOUJOVBEFMWBQPSJ[BEPS&MTJTUFNBEJàFSFEFMBEFTUJMB DJÓOJOTUBOUÃOFBQPSRVFOPIBZFOUSBEBDPOUJOVBEFBMJNFOUBDJÓOZFMMÎRVJEPTFESFOBTÓMPBMàOBM EFMMPUF6OBBMUFSOBUJWBBMBEFTUJMBDJÓOJOUFSNJUFOUFTJNQMFFTMBEFTUJMBDJÓOJOUFSNJUFOUFBOJWFM DPOTUBOUF EPOEFTFBMJNFOUBTPMWFOUFFOGPSNBDPOUJOVBBMSFDJQJFOUFQBSBNBOUFOFSDPOTUBOUFFM OJWFMEFMMÎRVJEP (FOUJMDPSF   

www.FreeLibros.me

$BQÎUVMP  %FTUJMBDJÓOJOUFSNJUFOUF

Recipiente



'*(63" %&45*-"$*¶/*/5&3.*5&/5&4*.1-&

&O MB EFTUJMBDJÓO JOUFSNJUFOUF DPO WBSJBT FUBQBT  TPCSF FM WBQPSJ[BEPS TF DPMPDB VOB DPMVNOB EF QMBUPTPFNQBDBEB DPNPFOMBàHVSB&MSFáVKPTFSFHSFTBBMBDPMVNOB%VSBOUFFMGVODJPOB NJFOUPVTVBM FMEFTUJMBEPTFSFUJSBDPOUJOVBNFOUF #BSUPOZ3PDIF 3PCJOTPOZ(JMMJMBOE  1SBUU -VZCFO %JXFLBS  IBTUBRVFMBDPMVNOBTFEFUJFOFZTFWBDÎB&OVO NÊUPEPBMUFSOBUJWP 5SFZCBM 

OPTFSFUJSBEFTUJMBEP TJOPRVFTFIBDFDBNCJBSMBDPNQPTJDJÓO EFMMÎRVJEPFOFMBDVNVMBEPS$VBOEPFMEFTUJMBEPFOFMBDVNVMBEPSUJFOFMBDPNQPTJDJÓOZMBDBO UJEBERVFTFEFTFB TFWBDÎBOUBOUPFMBDVNVMBEPSDPNPFMWBQPSJ[BEPS-VZCFO  JOEJDÓRVF

B '*(63" %&45*-"$*¶/*/5&3.*5&/5&$0/7"3*"4&5"1"4" &426&." # '050(3"'±"%&6/ 4*45&."*/5&(3"%0%&%&45*-"$*¶/*/5&3.*5&/5&3&$61&3"$*¶/%&40-7&/5&$0/$"1"$*%"%1"3" "1309*."%".&/5&("-0/&4$035&4±"%&"17&26*1.&/5 */$ 50/08"/%" /6&7":03,

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOJOUFSNJUFOUF

FM NÊUPEP OPSNBM EFCFSÎB TFS NFKPS TJO FNCBSHP  QVFEF TFS RVF FM NÊUPEP BMUFSOBUJWP TFB NÃT TFODJMMPEFPQFSBS 0USB BMUFSOBUJWB FT MB RVF TF MMBNB EFTUJMBDJÓO JOUFSNJUFOUF JOWFSUJEB %JXFLBS   1SBUU  3PCJOTPOZ(JMMJMBOE  QPSRVFTFSFUJSBOMPTGPOEPTFOGPSNBDPOUJOVB NJFOUSBTRVFFM EFTUJMBEPTFSFUJSBTÓMPBMàOBMEFMBEFTUJMBDJÓO WFBMBàHVSBZFMQSPCMFNB$ &OFTUFDBTP  MBDBSHBTFDPMPDBFOFMBDVNVMBEPSZTFVTBVOWBQPSJ[BEPSDPOVOQFRVFÒPWPMVNFOEFSFUFODJÓO $BTJ OVODB TF VTB MB EFTUJMBDJÓO JOUFSNJUFOUF JOWFSUJEB  QFSP FT BEFDVBEB DVBOEP TF SFRVJFSF VO QSPEVDUPEFGPOEPTQVSP  %&45*-"$*¶/*/5&3.*5&/5&#*/"3*"&$6"$*¶/%&3":-&*()

-PT CBMBODFT EF NBTB QBSB MB EFTUJMBDJÓO JOUFSNJUFOUF TPO BMHP EJGFSFOUFT B MPT EF MB EFTUJMBDJÓO DPOUJOVB&OMBEFTUJMBDJÓOJOUFSNJUFOUFJOUFSFTBONÃTMBTDBOUJEBEFTUPUBMFTSFDPMFDUBEBTEFGPOEPT ZEFTUJMBEPRVFMBTUBTBT1BSBVOBEFTUJMBDJÓOJOUFSNJUFOUFCJOBSJB MPTCBMBODFTEFNBTBBMSFEFEPS EFUPEPFMTJTUFNBEVSBOUFFMUJFNQPUPUBMEFPQFSBDJÓOTPO 

;2L[^cVa 9idiVa 





;m; 2mL![^cVaL[^cVa 9idiVam9!egdb 



-BBMJNFOUBDJÓOBMBDPMVNOBFT'LHNPMDPOGSBDDJÓONPMBSY'EFMDPNQPOFOUFNÃTWPMÃUJM-BTNP MFTàOBMFTFOFMWBQPSJ[BEPSBMUÊSNJOPEFMMPUFTPO8àOBMDPOGSBDDJÓONPMBSY8 àOBM4FVTBFMTÎNCPMP 8 EFXBTUF EFTQFSEJDJP

QPSRVFFMNBUFSJBMRVFRVFEBFOFMWBQPSJ[BEPSTVFMFTFSVOEFTFDIP %UPUBMTPOMPTLHNPMUPUBMFTEFEFTUJMBEPDPOVOBDPODFOUSBDJÓOQSPNFEJPY% QSPN-BTFDVBDJPOFT  Z  TPOBQMJDBCMFTBEFTUJMBDJÓOJOUFSNJUFOUFTJNQMFZBMBEFTUJMBDJÓOJOUFSNJUFOUFOPSNBM DPOWBSJBTFUBQBT4FSFRVJFSFOBMHVOPTDBNCJPTQFRVFÒPTFOMBTEFàOJDJPOFTEFMBTWBSJBCMFTFOFM DBTPEFMBEFTUJMBDJÓOJOUFSNJUFOUFJOWFSUJEB &OHFOFSBM TFFTQFDJàDBO' Y'ZFMWBMPSEFTFBEPEFY8 àOBMPY% QSPN4FSFRVJFSFVOBFDVBDJÓO NÃTQBSBEFTQFKBSMBTUSFTJODÓHOJUBT%UPUBM 8àOBMZY8 àOBM PY% QSPN &TUBFDVBDJÓOBEJDJPOBM MMBNBEB FDVBDJÓOEF3BZMFJHI 3BZMFJHI 

TFEFEVDFDPOVOCBMBODFEJGFSFODJBMEFNBTB4VQPOHBNPT RVFMBSFUFODJÓOFOMBDPMVNOBZFOFMBDVNVMBEPSTFQVFEFEFTQSFDJBS&OUPODFT TJTFTBDBEFM TJTUFNBVOBDBOUJEBEEJGFSFODJBMEFNBUFSJBM ¢E8 DPODPODFOUSBDJÓOY% FMCBMBODFEJGFSFODJBMEF NBTBFT 

¢4BMJEBBDVNVMBDJÓOFOFMWBQPSJ[BEPS



− m9 YL2− YLmL 



PTFB 

-BFDVBDJÓO  TFEFTBSSPMMBDPNPTJHVF 

− m9 YL2− LYmL − mLYL 



&OUPODFT BMPSEFOBSFJOUFHSBSRVFEB L [^cVa

 L2;

m

YL 2 L

L![^cVa

m

Ym L  m9 − mL

;

www.FreeLibros.me



  %FTUJMBDJÓOJOUFSNJUFOUFCJOBSJBTJNQMF



RVFFT m



L acP [^cVa R2− ;

;

m

Ym L  m9 − mL



L![^cVa

&MTJHOPNFOPTQSPWJFOFEFJOUFSDBNCJBSMPTMÎNJUFTEFJOUFHSBDJÓO-BFDVBDJÓO  FTVOBGPSNB EFMBFDVBDJÓOEF3BZMFJHI WÃMJEBQBSBEFTUJMBDJÓOJOUFSNJUFOUFUBOUPTJNQMFDPNPEFWBSJBTFUBQBT /BUVSBMNFOUF QBSBVTBSFTUBFDVBDJÓOTFEFCFSFMBDJPOBSY%DPOY8ZIBDFSMBJOUFHSBDJÓOSFTQFDUJ WB&TUPMPWFSFNPTFOMBTTFDDJPOFTZ &OMBEFEVDDJÓOEFMBFDVBDJÓO  OPBQBSFDFFMUJFNQPFOGPSNBFYQMÎDJUB QFSPJNQMÎDJUB NFOUFFTUÃQSFTFOUFQPSRVF8 Y8ZFOHFOFSBMY% UPEBT EFQFOEFOEFMUJFNQP  %&45*-"$*¶/*/5&3.*5&/5&#*/"3*"4*.1-&

&OFMTJTUFNBEFEFTUJMBDJÓOJOUFSNJUFOUFCJOBSJBTJNQMFRVFNVFTUSBMBàHVSB FMWBQPSQSPEVDUP FTUÃFOFRVJMJCSJPDPOFMMÎRVJEPFOFMWBQPSJ[BEPSFOUPEPNPNFOUP$PNPTFVTBVODPOEFOTBEPS UPUBM ZY%"MTVTUJUVJSFTUPFOMBFDVBDJÓO  RVFEB m



L ac [^cVa 2− ;

m

;

m

Ym 2− n− m

L![^cVa

;

m

Ym  [m− m



L![^cVa

EPOEFBIPSBZZYFTUÃOFOFRVJMJCSJPZMBFDVBDJÓOEFFRVJMJCSJPFTZG Y Q 1BSBDVBMRVJFSFDVB DJÓO EBEB EF FRVJMJCSJP  TF QVFEF JOUFHSBS BOBMÎUJDBNFOUF MB FDVBDJÓO 

 HSÃàDBNFOUF P CJFO OVNÊSJDBNFOUF &MQSPDFEJNJFOUPHFOFSBMEFJOUFHSBDJÓOQBSBMBFDVBDJÓO  FT  (SBàDBSMBDVSWBEFFRVJMJCSJPZYPBKVTUBSMB  $BMDVMBSZ¢YQBSBVOBTFSJFEFWBMPSFTEFY  (SBàDBS Z¢Y FOGVODJÓOEFYPBKVTUBS BY VOBFDVBDJÓO  *OUFHSBS HSÃàDBPOVNÊSJDBNFOUFEFTEFY'IBTUBY8 àOBM&OMBàHVSBTFNVFTUSBMBJOUFHSBDJÓO HSÃàDB  $POMBFDVBDJÓO  DBMDVMBSMBDBSHBàOBMEFNBUFSJBMFOFMWBQPSJ[BEPS m

;



L[^cVa 2;Zme− m

Ym 2;Z"ÌgZV  n− m

B C

L![^cVa

FMÃSFBTFNVFTUSBFOMBàHVSB  -BDPODFOUSBDJÓOQSPNFEJPEFMEFTUJMBEP Y% QSPN TFQVFEFDBMDVMBSDPOMPTCBMBODFTEFNBTB"M SFTPMWFSMBTFDVBDJPOFT  Z 

 

m 9!egdb 2

;m ; − L[^cVam L![^cVa  ; − L[^cVa

9idiVa 2;− L[^cVa 





5BNCJÊOTFQVFEFJOUFHSBSOVNÊSJDBNFOUFMBFDVBDJÓOEF3BZMFJHI6ONÊUPEPBEFDVBEPQBSB IBDFSMPFTBQMJDBSMBSFHMBEF4JNQTPO QPSFKFNQMP WFB.JDLMFZFUBM  QÃHT 4JBMB PSEFOBEBEFMBàHVSBTFMFMMBNBG Y

VOBGPSNBEFMBSFHMBEF4JNQTPOFT

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOJOUFSNJUFOUF

Área

'*(63" */5&(3"$*¶/(3¦'*$"1"3" %&45*-"$*¶/*/5&3.*5&/5&4*.1-& &+&.1-0 m ;

[mYm2

 m

m ; − m L![^cVa m ; m P[m L![^cVa  )[ L![^cVa  [m ;R  + '



L![^cVa

FOMBRVFMPTUÊSNJOPTTFNVFTUSBOFOMBàHVSB-BSFHMBEF4JNQTPOFTFYBDUBTJG Y FTDÙCJDBPEF PSEFONFOPS1BSBDVSWBTVOJGPSNFT DPNPMBEFMBàHVSB MBSFHMBEF4JNQTPOFTCBTUBOUFFYBDUB WFBFMFKFNQMP 1BSBGPSNBTDPNQMFKBT MBSFHMBEF4JNQTPOFTNÃTFYBDUBTJTFQVFEFIBDFSMB JOUFHSBDJÓOFOEPTPNÃTQBSUFT WFBFMFKFNQMP -BSFHMBEF4JNQTPOFTFMDPNBOEPRVBE EF iRVBESBUVSFu DVBESBUVSB FO."5-"# 1SBUBQ  &TQPTJCMFVTBSPUSBTGÓSNVMBTEFJOUFHSBDJÓO NÃTFYBDUBT 4JTFFTQFDJàDBMBDPODFOUSBDJÓOQSPNFEJPEFMEFTUJMBEP TFSFRVJFSFVOQSPDFEJNJFOUPEFQSVFCB ZFSSPS$POTJTUFFOQSPQPOFSMBDPODFOUSBDJÓOàOBMEFMSFDJQJFOUF Y8 àOBMZDBMDVMBSFMÃSFBEFMBàHVSB  ZBTFBHSÃàDBNFOUFPDPOMBSFHMBEF4JNQTPO&OUPODFT DPOMBFDVBDJÓO  TFDBMDVMB8àOBMZ TFVTBMBFDVBDJÓO  QBSBDPNQSPCBSFMWBMPSEFY% QSPN1BSBVOBTPMVDJÓOHSÃàDBTFQVFEFIBDFS FMQSPDFEJNJFOUPEFQSVFCBZFSSPSQBSUJFOEPEFVOWBMPSQSPQVFTUPEFY8 àOBMRVFTFBNVZBMUP&OUPO DFT DBEBWF[RVFEJTNJOVZBFMWBMPSEFY8 àOBM TFTVNBFMÃSFBBEJDJPOBMBMÃSFBRVFZBTFDBMDVMÓ 4JMBFDVBDJÓOEFFRVJMJCSJPTFEBFOGPSNBEFWPMBUJMJEBESFMBUJWBDPOTUBOUF TFQVFEFJOUFHSBS BOBMÎUJDBNFOUFMBFDVBDJÓOEF3BZMFJHI&OFTUFDBTP MBFYQSFTJÓOEFFRVJMJCSJPFTMBFDVBDJÓO 

 RVFSFQFUJSFNPTBRVÎ n2

αm & α − &m

­TUBTFTVTUJUVZFFOMBFDVBDJÓO  ZTFJOUFHSB QBSBPCUFOFS 

& L m & m ; & m ; ac [^cVa 2 ac L![^cVa  ac  & ; & m L![^cVa m ;& m L![^cVa

www.FreeLibros.me



  %FTUJMBDJÓOJOUFSNJUFOUFCJOBSJBTJNQMF



$VBOEPTFQVFEF FTPCWJPRVFMBBQMJDBDJÓOEFMBFDVBDJÓO  FTNÃTGÃDJMRVFMBJOUFHSBDJÓO HSÃàDBPOVNÊSJDB &+&.1-0 %FTUJMBDJÓOTJNQMFEF3BZMFJHI 4FEFTFBVTBSVOEFTUJMBEPSJOUFSNJUFOUFTJNQMF DPOVOBFUBQBEFFRVJMJCSJP QBSBTFQBSBS NFUBOPMEFBHVB-BDBSHBEFBMJNFOUBDJÓOBMBSFUPSUBFTEFNPMFTEFVOBNF[DMBDPO NPMEFNFUBOPM4FEFTFBRVFMBDPODFOUSBDJÓOQSPNFEJPEFMEFTUJMBEPTFBNPM EFNFUBOPM$BMDVMBSMBDBOUJEBEEFEFTUJMBEPSFDPMFDUBEP MBDBOUJEBEZMBDPODFOUSBDJÓO EF NBUFSJBM RVF RVFEB FO FM WBQPSJ[BEPS -B QSFTJÓO FT  BUN -PT EBUPT EFM FRVJMJCSJP NFUBOPMBHVBBBUN FTUÃOFOMBUBCMBEFMQSPCMFNB% 4PMVDJÓO " %FGJOB&MTJTUFNBFTFMEFMBàHVSB-BTDPOEJDJPOFTTPOQBUN ' Y' ZY% QSPN4FEFTFBEFUFSNJOBSY8 àOBM %UPUZ8àOBM # &YQMPSF$PNPFMSFDJQJFOUFGVODJPOBDPNPVODPOUBDUPEFFRVJMJCSJP MBFDVBDJÓOEF 3BZMFJHIUPNBMBGPSNBEFMBTFDVBDJPOFT  Z  1BSBVTBSFTBTFDVBDJPOFTTF SFRVJFSFVOBHSÃàDBEF Z¢Y FRVJMFOGVODJÓOEFY QBSBQPEFSVTBSJOUFHSBDJÓOHSÃàDB PMBSFHMBEF4JNQTPO"RVÎJMVTUSBSFNPTBNCPTNÊUPEPT$PNPY8 àOBMTFEFTDPOPDF  TFOFDFTJUBSÃVOQSPDFEJNJFOUPEFUBOUFPTQBSBDVBMRVJFSSVUJOBEFJOUFHSBDJÓO $ 1MBOFF1SJNFSPUSBDFMBHSÃàDBEF Z¢Y DPOUSBYDPOMPTEBUPTEFFRVJMJCSJP&M QSPDFEJNJFOUPEFQSVFCBZFSSPSFTFMTJHVJFOUF  4FQSPQPOFY8 àOBM  *OUFHSFQBSBEFUFSNJOBS m

;

Ym n− m

ÌgZV2 m

L![^cVa

 $BMDVMF8àOBMDPOMBFDVBDJÓOEF3BZMFJHIZY% DBMDDPOFMCBMBODFEFNBTB  $PNQSPCBDJÓOyY% DBMDY% QSPN 4JOPMPFT DPOUJOÙFDPOMPTUBOUFPT % )ÃHBMP$POMPTEBUPTEFFRVJMJCSJPFTGÃDJMHFOFSBSMBTJHVJFOUFUBCMB

  

m

n

n− m

& n− m

##,* #,% #+* #+% #*%

#.&* #-.* #-,& #-)* #-'* #,-%

#&&* #&)* #&,& #&.* #''* #'-%

-#+. +#-. *#-* *#&( )#)) (#*,

&TUPTEBUPTTFHSBàDBOFOMBàHVSB1BSBMBTPMVDJÓOOVNÊSJDBTFFMBCPSÓVOBHSÃ àDBHSBOEF FOQBQFMNJMJNÊUSJDP 1SJNFSWBMPSQSPQVFTUPY8 àOBM %FMBàHVSB m

;

ÍgZV2 m

Ym 2%#,%)) n− m

L![^cVa

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOJOUFSNJUFOUF



&OUPODFT 8àOBM'FYQ ¢¦SFB F¢ 9XVaX 2;− L[^cVa 2'*#'m 9!XVaX 2



&MQSPDFEJNJFOUPBMUFSOBUJWPEFJOUFHSBDJÓORVFVTBMBSFHMBEF4JNQTPOEBDPNPSF TVMUBEP ÍgZV 2 



;m ; − L[^cVam L![^cVa 2%#-.9XVaX

& n−m



& m ; − m L![^cVa    + n−m m

m

L![^cVa

)

&  n−m

m

L![^cVa

m $' ;



&  n−m

m ;

L![^cVa

FTFMWBMPSEF Z¢Y DBMDVMBEPFOY8 àOBM ÌgZV2 %#& P*#-* )+#-. -#+.R2%#,%&++ +



&OUPODFT QBSBMBSFHMBEF4JNQTPO 8àOBM %DBMDZY% DBMD1BSFDF RVFMBSFHMBEF4JNQTPOFTCBTUBOUFFYBDUB8àOBMUJFOFVOBEJGFSFODJBEFZY% DBMD FTJHVBMRVFFMDÃMDVMPNÃTFYBDUP1BSFDFRVFFTUPTWBMPSFTTFBDFSDBOBMWBMPSEFTFB EP QFSPUPEBWÎBOPDPOPDFNPTMBTFOTJCJMJEBEEFMDÃMDVMP  4FHVOEBUFOUBUJWBY8 àOBM$PODÃMDVMPTTJNJMBSFTBMPTEFMBQSJNFSBUFOUBUJWBTF PCUJFOFO  ¦SFB 8àOBM %DBMD Y% DBMD$POMBàHVSBZY% DBMD DBMDVMBEBDPOMBSFHMBEF4JNQTPO&TUPTWBMPSFTUBNCJÊOTPODFSDBOPT QFSPTPOCBKPT 1BSBFTUFQSPCMFNB FMWBMPSEFY%FTJOTFOTJCMFBY8 àOBM  5FSDFSBUFOUBUJWBY8 àOBM-PTSFTVMUBEPTEFMPTDÃMDVMPTTPO  ¦SFB 8àOBM %DBMD Y% DBMDEFMBàHVSBZY% DBMD DPOFMDÃMDVMPEFMÃSFBDPOMBSFHMBEF4JNQTPO BNCPTDFSDBOPTBMWBMPSFTQFDJàDBEP EF  1PSMPBOUFSJPS VTFY8 àOBMDPNPSFTVMUBEP & $PNQSVFCF&MCBMBODFHFOFSBMEFNBTBEFCFDVBESBS3FTVMUB8àOBMY8 àOBM %DBMDY% DBMD  RVFTFDPNQBSBDPO'Y'&MFSSPSFT ¢ ¤  BDFQUBCMF ' (FOFSBMJDF-BJOUFHSBDJÓOUBNCJÊOTFQVFEFIBDFSOVNÊSJDBNFOUFFOVOBDPNQVUBEPSB RVFJODMVZBMBSFHMBEF4JNQTPOPVONÊUPEPBMUFSOBUJWPEFJOUFHSBDJÓO&TVOBWFOUB KB QPSRVFFOUPODFTTFQVFEFQSPHSBNBSUPEPFMQSPDFEJNJFOUPEFQSVFCBZFSSPS0C TFSWFRVFHSBOEFTEJGFSFODJBTFOY8 àOBM ZQPSDPOTJHVJFOUFFO8àOBM DBVTBOEJGFSFODJBT CBTUBOUFQFRVFÒBTFOY% QSPN&OUPODFT QBSBFTUFQSPCMFNBQPESÃOPTFSDSÎUJDPUFOFS VODPOUSPMFYBDUPEFMTJTUFNBJOUFSNJUFOUF&TUFQSPCMFNBJMVTUSBVOBEJàDVMUBEDPNÙO FOMBEFTUJMBDJÓOJOUFSNJUFOUFTJNQMFOPTFQVFEFOPCUFOFSVOEFTUJMBEPQVSPZVOPT GPOEPTQSPEVDUPQVSPT BNFOPTRVFMBWPMBUJMJEBESFMBUJWBTFBNVZHSBOEF0CTFSWF RVFBVORVFMBFDVBDJÓO  OPFTBQMJDBCMFFOTFOUJEPFTUSJDUP QPSRVFFMFRVJMJCSJP EFNFUBOPMBHVBOPUJFOFVOBWPMBUJMJEBESFMBUJWBDPOTUBOUF TFQVEPVTBSEFOUSPEFMPT NÃSHFOFTFTUSFDIPTEFFTUBEFTUJMBDJÓOJOUFSNJUFOUF

www.FreeLibros.me

  %FTUJMBDJÓOJOUFSNJUFOUFBOJWFMDPOTUBOUF



6OQSPDFTPRVFTFSFMBDJPOBNVDIPDPOMBEFTUJMBDJÓOJOUFSNJUFOUFTJNQMFFTMBDPOEFOTBDJÓOEJGF SFODJBM 5SFZCBM  &OFTUFQSPDFTP FMWBQPSTFDPOEFOTBMFOUBNFOUFZFMMÎRVJEPDPOEFOTBEP TFSFUJSBSÃQJEBNFOUF$POVOBEFEVDDJÓOTJNJMBSBMBEFMBFDVBDJÓOEF3BZMFJHIQBSBVOTJTUFNB CJOBSJPTFMMFHBB 

ac

; 9[^cVa

n

9![^cVa

2n

;

Yn  n− m



EPOEF'FTMBTNPMFTEFWBQPSBMJNFOUBEP EFGSBDDJÓONPMZ' Z%àOBMFTFMWBQPSEFTUJMBEPRVFRVF EB EFGSBDDJÓONPMBSZ% àOBM  %&45*-"$*¶/*/5&3.*5&/5&"/*7&-$0/45"/5&

6OBBQMJDBDJÓOGSFDVFOUFEFMBEFTUJMBDJÓO PFWBQPSBDJÓO JOUFSNJUFOUFFTFMDBNCJPEFTPMWFOUFT FOVOQSPDFTPEFQSPEVDDJÓO1PSFKFNQMP QPESÃTFSOFDFTBSJPJOUFSDBNCJBSTPMWFOUFTBOUFTEFVO QBTPEFDSJTUBMJ[BDJÓOPVOBSFBDDJÓO&MDBNCJPEFTPMWFOUFTFQVFEFIBDFSFOVOTJTUFNBJOUFSNJ UFOUFTFODJMMP DBSHBOEPFMSFDJQJFOUFDPOBMJNFOUBDJÓO DPODFOUSBOEP TJFTOFDFTBSJP MBTPMVDJÓO  FWBQPSBOEPMBNBZPSQBSUFEFMTPMWFOUFPSJHJOBM EFCFRVFEBSBMHPEFTPMWFOUFQBSBNBOUFOFSMB BHJUBDJÓO NBOUFOFSBMTPMVUPFOTPMVDJÓOZNBOUFOFSDVCJFSUBFMÃSFBEFUSBOTGFSFODJBEFDBMPS  BHSFHBSFMOVFWPTPMWFOUFZIBDFSVOBTFHVOEBEFTUJMBDJÓOJOUFSNJUFOUFQBSBFMJNJOBSFMSFTUPEFM TPMWFOUFPSJHJOBM4JTFEFTFB TFQVFEFEJMVJSMBTPMVDJÓOBHSFHBOEPNÃTEFMTPMWFOUFEFTFBEP"VO RVFFTUFQSPDFTPFTTJNJMBSBMRVFVTBOMPTRVÎNJDPTFOFMMBCPSBUPSJP FOMBTFHVOEBEFTUJMBDJÓO JOUFSNJUFOUFTFFWBQPSBVOBDBOUJEBEDPOTJEFSBCMFEFMTFHVOEPTPMWFOUF$PNPBMUFSOBUJWBTFQVF EFIBDFSMBTFHVOEBEFTUJMBDJÓOJOUFSNJUFOUFBOJWFMDPOTUBOUF EPOEFTFBHSFHBDPOUJOVBNFOUFFM TFHVOEPTPMWFOUFQVSPEVSBOUFFMMB DPOVOáVKPRVFNBOUFOHBDPOTUBOUFTMBTNPMFTFOMBSFUPSUB (FOUJMDPSF  /PTFOGPDBSFNPTBMQBTPEFEFTUJMBDJÓOJOUFSNJUFOUFBOJWFMDPOTUBOUF 1BSBVOBEFTUJMBDJÓOJOUFSNJUFOUFBOJWFMDPOTUBOUF FMCBMBODFNPMBSHFOFSBMFT 

&OUSBEB¢4BMJEB"DVNVMBDJÓOFOFMWBQPSJ[BEPS

B

1BSBFMCBMBODFNPMBSUPUBMFTUPFT&OUSBEB¢4BMJEB QPSRVFMBTNPMFTTPODPOTUBOUFTFOFMWB QPSJ[BEPS&OUPODFT TJTFBHSFHBOE4NPMFTEFMTFHVOEPTPMWFOUF FMCBMBODFNPMBSHFOFSBM QBSBMB EFTUJMBDJÓOJOUFSNJUFOUFBOJWFMDPOTUBOUF FT 

E7E4

C

EPOEFE7TPOMBTNPMFTEFWBQPSRVFTBMFO 4JTFIBDFVOCBMBODFNPMBSEFDPNQPOFOUFTFOFMTPMWFOUFPSJHJOBM TFTVQPOFRVFFMTPMVUPFT OPWPMÃUJMZOPTFUPNBFODVFOUB

PCUFOESFNPT QBSBVOTJTUFNBBOJWFMDPOTUBOUF MPTJHVJFOUF 

% − nYK 2LYml 

B

EPOEFZZYXTPOMBGSBDDJÓONPMBSEFMQSJNFSTPMWFOUFFOFMWBQPSZFOFMMÎRVJEP SFTQFDUJWBNFOUF &TUPTFTVTUJUVZFFOMBFDVBDJÓO C ZSFTVMUB 

−nYH 2LYml

C

0CTFSWFRVF DPNPMBDBOUJEBEEFMÎRVJEP8FTDPOTUBOUF OPIBZUÊSNJOPFRVJWBMFOUFBMÙMUJNPFO MBFDVBDJÓO  1PSJOUFHSBDJÓOEFMBFDVBDJÓO C

ZDPOVOMJHFSPSFBDPNPEP MMFHBNPTB

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOJOUFSNJUFOUF

$



m

H L2

m

l!^c^X^Va

l![^cVa

Ym L  n



:BRVFTFTVQPOFRVFWBQPSZMÎRVJEPFTUÃOFOFRVJMJCSJPZTFSFMBDJPOBDPOYXDPOMBSFMBDJÓOEF FRVJMJCSJP-BFDVBDJÓO  TFQVFEFJOUFHSBSFOGPSNBHSÃàDBPOVNÊSJDB DPOVOQSPDFEJNJFOUP CBTUBOUFQBSFDJEPBMRVFTFVTBQBSBMBEFTUJMBDJÓOJOUFSNJUFOUFTJNQMF&MQSPCMFNB%MPHVJBSÃ QPSFTUPTDÃMDVMPTEFEFTUJMBDJÓOJOUFSNJUFOUFBOJWFMDPOTUBOUF&OFMQSPCMFNB&TFFYBNJOBFM QBTPEFEJMVDJÓOTFHVJEPQPSVOBEFTUJMBDJÓOJOUFSNJUFOUFTJNQMF 4J TF QVFEF TVQPOFS RVF MB WPMBUJMJEBE SFMBUJWB FOUSF MPT EPT TPMWFOUFT FT DPOTUBOUF  TF QVF EFTVTUJUVJSMBFDVBDJÓO  FOMB 

QBSBJOUFHSBSFMSFTVMUBEPBOBMÎUJDBNFOUF (FOUJMDPSF    

H $L 2

& m l!^c^X^Va ac α m l![^cVa

α−& m − m l![^cVa  α  l!^c^X^Va



(FOUJMDPSF  QSFTFOUBVOBNVFTUSBEFDÃMDVMP DPOWPMBUJMJEBESFMBUJWBDPOTUBOUF RVFJMVTUSBMB WFOUBKBEFMBEFTUJMBDJÓOJOUFSNJUFOUFBOJWFMDPOTUBOUFDVBOEPTFVTBQBSBJOUFSDBNCJBSTPMWFOUFT  %&45*-"$*¶/*/5&3.*5&/5&103"33"453&$0/7"103%&"(6"

&O MB EFTUJMBDJÓO JOUFSNJUFOUF QPS BSSBTUSF DPO WBQPS EF BHVB  FM WBQPS TF FTQBSDF EJSFDUBNFOUF FOFMWBQPSJ[BEPS DPNPTFWFFOMBàHVSB&TUPTFIBDFFOGPSNBOPSNBMDPOTJTUFNBTRVFTPO JONJTDJCMFTDPOBHVB-BTSB[POFTQBSBBHSFHBSFMWBQPSFOGPSNBEJSFDUBBMSFDJQJFOUFTPORVFNBO UJFOFMBUFNQFSBUVSBBNFOPTEFMQVOUPEFFCVMMJDJÓOEFMBHVB FMJNJOBMBOFDFTJEBEEFTVQFSàDJF EFUSBOTGFSFODJBEFDBMPSZBZVEBBNBOUFOFSCJFONF[DMBEPTMPTMPEPTZDJFOPTQBSBRVFTFQVFEBO CPNCFBS &M VTP QSJODJQBM FT FO FM USBUBNJFOUP EF EFTFDIPT RVF DPOUJFOFO TVTUBODJBT PSHÃOJDBT WPMÃUJMFTWBMJPTBT&TUBTDPSSJFOUFTEFEFTFDIP RVFTFEFTUJMBOQPSBSSBTUSFDPOWBQPSEFBHVB TPO HMJDFSJOB BDFJUFTMVCSJDBOUFT ÃDJEPTHSBTPTFIJESPDBSCVSPTIBMPHFOBEPT 8PPEMBOE  1BSB FTUBTFDDJÓO MBTFDDJÓOFTQSFSSFRVJTJUP -BEFTUJMBDJÓOJOUFSNJUFOUFQPSBSSBTUSFDPOWBQPSEFBHVBTFTVFMFUSBCBKBSFOQSFTFODJBEF BHVBMÎRVJEBFOFMWBQPSJ[BEPS&OUPODFT UBOUPFMBHVBMÎRVJEBDPNPMBTGBTFTPSHÃOJDBTMÎRVJEBT FKFSDFOTVQSPQJBQSFTJÓOEFWBQPS&MFRVJMJCSJPTFEFàOFDPOMBTFDVBDJPOFT  B 

DVBOEP IBZQSFTFOUFTVOBTVTUBODJBPSHÃOJDBWPMÃUJMZBMHVOBTTVTUBODJBTPSHÃOJDBTOPWPMÃUJMFT4JFNQSF RVFIBZBVOBSSBTUSFNÎOJNP OPTFHBOBOJOHVOBWFOUBKBBMUFOFSNÃTEFVOBFUBQB1BSBMPTDPN QVFTUPTPSHÃOJDPTEFCBKPQFTPNPMFDVMBS MBTFàDJFODJBTEFWBQPSJ[BDJÓO EFàOJEBTDPNPMBQSFTJÓO QBSDJBMSFBMEJWJEJEBFOUSFMBQSFTJÓOQBSDJBMFOFMFRVJMJCSJP Q 

(Sustancias orgánicas)

Agua de desecho Sin agua

'*(63" %&45*-"$*¶/ */5&3.*5&/5&103"33"453& $0/7"103%&"(6"

Vapor

www.FreeLibros.me

  %FTUJMBDJÓOJOUFSNJUFOUFFOWBSJBTFUBQBT





ekda{i^a

:2



e kda{i^a

2

ekda{i^a





EK kda{i^a m kda{i^a

DBFODPOGSFDVFODJBEFOUSPEFMPTMÎNJUFTEFB $BSFZ  &TUBFàDJFODJBTFBDFSDBMP TVàDJFOUFBMFRVJMJCSJP QBSBRVFMPTDÃMDVMPTEFMFRVJMJCSJPTFBOBEFDVBEPT &MTJTUFNBEFMBàHVSBTFQVFEFBOBMJ[BSDPOCBMBODFTEFNBTBTJOBHVB-PTCBMBODFTEF NBTBTPOMBTFDVBDJPOFT  Z 

EFMBTRVFTFQVFEFEFTQFKBS8àOBMTJTFQSPQPSDJPOBY8 àOBM 

L[^cVa 2;

m9 − m; m9 − m l![^cVa





$POVOBTPMBTVTUBODJBPSHÃOJDBWPMÃUJM Y%TJFMBSSBTUSFFTEFTQSFDJBCMF&OUPODFT 

L[^cVa 2;

&− m ; &− m l![^cVa





ZMBUBTBEFáVKPEFMQSPEVDUPEFTUJMBEPFT 92;− L[^cVa 





5BNCJÊOTFQVFEFVTBSMBFDVBDJÓOEF3BZMFJHI ZTFPCUJFOFOMPTNJTNPTSFTVMUBEPT &ODVBMRVJFSNPNFOUP TFQVFEFODBMDVMBSMBTNPMFTJOTUBOUÃOFBTEFBHVB EOX BSSBTUSBEBFO FMWBQPS DPOMBFDVBDJÓO  &TBFDVBDJÓOTFUSBOTGPSNBFO 

Yc l 2Yc dg\

eidi − EKkda{i^a m kda{i^aZcdg\  EKkda{i^a m kda{i^aZcdg\



-BTNPMFTUPUBMFTEFBHVBBSSBTUSBEBFOFMWBQPSTFDBMDVMBOJOUFHSBOEPMBTJHVJFOUFFDVBDJÓO 9 idiVa



cl 2 %

eidi − EKkda{i^a m kda{i^aZcdg\ EKkda{i^a m kda{i^aZcdg\

Yc dg\ 



%VSBOUFMBEFTUJMBDJÓOJOUFSNJUFOUFQPSBSSBTUSFDPOWBQPS WBSÎBMBGSBDDJÓONPMBSEFMBTTVTUBODJBT PSHÃOJDBTWPMÃUJMFTFOFMWBQPSJ[BEPS QPSMPRVFWBSÎBMBUFNQFSBUVSBEFMSFDJQJFOUF EFUFSNJOBEB QPSMBFDVBDJÓO  4FQVFEFJOUFHSBSMBFDVBDJÓO  OVNÊSJDBNFOUFFOJODSFNFOUPT-BT NPMFTUPUBMFTEFBHVBSFRVFSJEBTPOOX NÃTMBTNPMFTEFBHVBDPOEFOTBEBQBSBDBMFOUBSMBBMJNFO UBDJÓOZFWBQPSBSMPTDPNQVFTUPTPSHÃOJDPTWPMÃUJMFT  %&45*-"$*¶/*/5&3.*5&/5&&/7"3*"4&5"1"4

$PO GSFDVFODJB  MB TFQBSBDJÓO BMDBO[BEB FO VOB TPMB FUBQB EF FRVJMJCSJP OP FT MP CBTUBOUF HSBO EF QBSB PCUFOFS VOB DPODFOUSBDJÓO EFTFBEB EFM EFTUJMBEP Z BM NJTNP UJFNQP VOB DPODFOUSBDJÓO TVàDJFOUFNFOUFCBKBFOMPTGPOEPT&OFTUFDBTP TFDPMPDBVOBDPMVNOBEFEFTUJMBDJÓOBSSJCBEFM WBQPSJ[BEPS DPNPTFWFFOMBàHVSB"DPOUJOVBDJÓOTFEFUBMMBSÃFMQSPDFEJNJFOUPEFDÃMDVMP QBSBVOBDPMVNOBEFFUBQBT QFSPTFQVFEFOEJTFÒBSGÃDJMNFOUFDPMVNOBTFNQBDBEBTRVFVTFOMPT QSPDFEJNJFOUPTRVFTFEFTDSJCJSÃOFOFMDBQÎUVMP 1BSBTJTUFNBTEFWBSJBTFUBQBT Y%ZY8ZBOPFTUÃOFOFRVJMJCSJP QPSMPRVFOPTFQVFEFJO UFHSBSMBFDVBDJÓOEF3BZMFJHI FDVBDJÓO 

TJOPIBTUBIBCFSFODPOUSBEPVOBSFMBDJÓOFOUSFY% ZY8&TUBSFMBDJÓOTFQVFEFPCUFOFSDPODÃMDVMPTEFFUBQBQPSFUBQB4VQPOESFNPTRVFIBZVOB SFUFODJÓOEFTQSFDJBCMFFODBEBQMBUP FOFMDPOEFOTBEPSZFOFMBDVNVMBEPS&OUPODFT FODVBMRVJFS

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOJOUFSNJUFOUF

NPNFOUPFTQFDÎàDP QPESFNPTFTDSJCJSCBMBODFTEFNBTBZFOFSHÎBFOUPSOPBMBFUBQBKZMBQBSUF TVQFSJPSEFMBDPMVNOB DPNPTFWFFOMBàHVSB"-PTCBMBODFTTFTJNQMJàDBOB &OUSBEB4BMJEB QPSRVF TF TVQVTP RVF MB BDVNVMBDJÓO FT EFTQSFDJBCMF  FYDFQUP FO FM WBQPSJ[BEPS &OUPODFT  FO DVBMRVJFSNPNFOUPU 

K_ & 2A_ 9 

B



K_ &n_ & 2A_m_ 9m9 

C



FX K_ &=_ & 2A_]_ 9]9 

D

&OFTUBTFDVBDJPOFT 7 -Z%TPOBIPSBUBTBTEFáVKPNPMBM&TUPTCBMBODFTTPO FOFTFODJB MBT NJTNBTFDVBDJPOFTRVFPCUVWJNPTQBSBMBTFDDJÓOEFSFDUJàDBDJÓOEFVOBDPMVNOBDPOUJOVB FYDFQ UPRVFMBTFDVBDJPOFT  TPOEFQFOEJFOUFTEFMUJFNQP4JQPEFNPTTVQPOFSRVFIBZEFSSBNF NPMBMDPOTUBOUF MBTUBTBTEFáVKPEFWBQPSZEFMÎRVJEPTFSÃOJHVBMFTFODBEBFUBQBZOPTFOFDFTJUB FMCBMBODFEFFOFSHÎB"MDPNCJOBSMBTFDVBDJPOFT B Z C ZEFTQFKBSBZK  PCUFOFNPTMB FDVBDJÓOEFPQFSBDJÓOQBSBEFSSBNFNPMBMDPOTUBOUF 

n_ & 2

A A m &− m  K _ K 9



&ODVBMRVJFSNPNFOUP MBFDVBDJÓO  SFQSFTFOUBVOBSFDUBFOVOEJBHSBNBZY-BQFOEJFOUF TFSÃ-7ZFMDSVDFDPOMBMÎOFBZYTFSÃY%$PNPY%P-7UFOESÃORVFWBSJBSEVSBOUFMBEFTUJMB DJÓOJOUFSNJUFOUF MBMÎOFBEFPQFSBDJÓODBNCJBSÃDPOUJOVBNFOUF 9.5.1

Relación de reflujo constante

&MNÊUPEPEFPQFSBDJÓONÃTDPNÙOFTVTBSVOBSFMBDJÓOEFSFáVKPDPOTUBOUFZEFKBSWBSJBSBY%&TUF QSPDFEJNJFOUPDPSSFTQPOEFBVOBPQFSBDJÓOJOUFSNJUFOUFTJNQMFFOMBRVFY%UBNCJÊOWBSÎB-BSF MBDJÓOFOUSFY%ZY8TFQVFEFEFUFSNJOBSFOUPODFTDPOVODÃMDVMPEFFUBQBQPSFUBQBDPOVOBOÃMJTJT EF.D$BCF5IJFMF-BFDVBDJÓOEFPQFSBDJÓO MB 

TFHSBàDBFOVOEJBHSBNBEF.D$BCF5IJFMF QBSBVOBTFSJFEFWBMPSFTEFY%&OUPODFTTFFTDBMPOBMBDBOUJEBEFTQFDJàDBEBEFDPOUBDUPTEFFRVJ MJCSJPFODBEBMÎOFBEFPQFSBDJÓO QBSUJFOEPEFY%QBSBEFUFSNJOBSFMWBMPSEFY8RVFDPSSFTQPOEBB FTBY%&TUFQSPDFEJNJFOUPTFNVFTUSBFOMBàHVSBZFOFMFKFNQMP &MBOÃMJTJTEF.D$BCF5IJFMFQSPEVDFWBMPSFTEFY8QBSBVOBTFSJFEFWBMPSFTEFY%"IPSB QPEFNPT DBMDVMBS  Y% ¢ Y8  -B JOUFHSBM EF MB FDVBDJÓO   TF QVFEF EFUFSNJOBS QPS JOUFHSB DJÓOOVNÊSJDB DPNPMBSFHMBEF4JNQTPOEFMBFDVBDJÓO 

PQPSJOUFHSBDJÓOHSÃàDB6OBWF[ FODPOUSBEPTWBMPSFTEFY8QBSBWBSJPTWBMPSFTEFY% TFQVFEFVTBSFMNJTNPQSPDFEJNJFOUPRVFTF VTÓQBSBMBEFTUJMBDJÓOJOUFSNJUFOUFTJNQMF"TÎ 8àOBMTFEFUFSNJOBDPOMBFDVBDJÓO 

Y% QSPNDPO MBFDVBDJÓO  Z%UPUBMDPOMBFDVBDJÓO  4JTFFTQFDJàDBY% QSPN TFOFDFTJUBSÃEFOVFWPVO QSPDFEJNJFOUPEFQSVFCBZFSSPS &+&.1-0 %FTUJMBDJÓOJOUFSNJUFOUFFOWBSJBTFUBQBT 4FEFTFBEFTUJMBSJOUFSNJUFOUFNFOUFLHNPMEFVOBBMJNFOUBDJÓORVFDPOUJFOFNPM EFFUBOPMZNPMEFBHVB&MTJTUFNBUJFOFVOWBQPSJ[BEPSZEPTFUBQBTEFFRVJMJCSJPZVO DPOEFOTBEPSUPUBM&MSFáVKPSFHSFTBDPNPMÎRVJEPTBUVSBEP6TBSFNPT-%4FEFTFB RVFMBDPNQPTJDJÓOàOBMFOFMWBQPSJ[BEPSTFBNPMEFFUBOPM$BMDVMBSMBDPNQPTJDJÓO

www.FreeLibros.me

  %FTUJMBDJÓOJOUFSNJUFOUFFOWBSJBTFUBQBT



'*(63" %*"(3"." .$$"#&5)*&-&1"3" %&45*-"$*¶/*/5&3.*5&/5& $0/7"3*"4&5"1"4$0/-% $0/45"/5& &+&.1-0 QSPNFEJPEFMEFTUJMBEP MBDBSHBàOBMFOFMWBQPSJ[BEPSZMBDBOUJEBEEFEFTUJMBEPSFVOJEP -BQSFTJÓOFTBUN 4PMVDJÓO " %FGJOB&MTJTUFNBTFNVFTUSBFOMBàHVSBTJHVJFOUF Líquido saturado

Vaporizador

$BMDVMF8àOBM %UPUBMZY% QSPN

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOJOUFSNJUFOUF

#Z$&YQMPSFZQMBOFF$PNPTFQVFEFTVQPOFSEFSSBNFNPMBMDPOTUBOUF TFQVFEFVTBS VOEJBHSBNBEF.D$BCF5IJFMF àHVSB "RVÎSFMBDJPOBSFNPTY%DPOY8FODVBM RVJFSNPNFOUP$PNPY'ZY8 àOBMTFDPOPDFO TFQVFEFVTBSMBFDVBDJÓOEF3BZMFJHI  FDVBDJÓO 

PMBFDVBDJÓO  QBSBEFUFSNJOBS8àOBM&OUPODFTTFQVFEFOEFUFSNJ OBSY% QSPNZ%UPUBMDPOMBTFDVBDJPOFT  Z 

SFTQFDUJWBNFOUF&OFTUFQSPCMFNB OPTFOFDFTJUBVOQSPDFEJNJFOUPEFQSVFCBZFSSPS % )ÃHBMP&OMBàHVSBTFNVFTUSBFMEJBHSBNBEF.D$BCF5IJFMFQBSBBMHVOPTWBMP SFTBSCJUSBSJPTEFY%-BMÎOFBTVQFSJPSEFPQFSBDJÓOFT n2 A m K



 & − A m 9 K

FOEPOEF A 2 A $9 2 '$( 2 ' K & A $9 *$( *



4FVTBOMPTWBMPSFTDPSSFTQPOEJFOUFTEFY8ZY%QBSBDBMDVMBSY%¢Y8 ZEFTQVÊT  Y%¢Y8 QBSBDBEBWBMPSEFY8&TUPTWBMPSFTTFHSBàDBSPOFOMBàHVSB BMHVOPT OPBQBSFDFOFOMBàHVSB QFSPTÎTFWFOFOMB &MÃSFBCBKPMBDVSWB CBKBOEP IBTUBFMWBMPSDFSPEFMBTPSEFOBEBT

EFY'IBTUBY8 àOBM FT QPSJOUFHSB DJÓOHSÃàDB  &OUPODFT EFMBFDVBDJÓO   8àOBM'F¢¦SFB  FYQ ¢ 



%FMBFDVBDJÓO  %UPUBM'¢8àOBM

'*(63" */5&(3"$*¶/(3¦'*$" &+&.1-0

www.FreeLibros.me

  %FTUJMBDJÓOJOUFSNJUFOUFFOWBSJBTFUBQBT





ZEFBDVFSEPDPOMBFDVBDJÓO   m 9!egdb 2

;m ; − L[^cVa m L![^cVa ;− L[^cVa

2%#+)-

5BNCJÊOTFQVFEFDBMDVMBSFMÃSFBDPOMBSFHMBEF4JNQTPO4JOFNCBSHP QPSMB GPSNBEFMBDVSWBRVFNVFTUSBMBàHVSB FTQSPCBCMFRVFTFBNFOPTFYBDUBRVFFO FMFKFNQMP$POMBSFHMBEF4JNQTPOTFPCUJFOF ÌgZV 2



m ; − m L![^cVa +



& &   m L![ ) m9 − m L m9 − m L

 



m  ;

L![ '



&  m9 − m L

m ;

EPOEF Y8 àOBM Y'  Z Y%¢Y8 FOFTUFQVOUPNFEJP ÌgZV2



m

%#',* P'#*& )'#&) '#-'R2%#+(++ +

&TUPTFQVFEFDPNQSPCBSEFTDPNQPOJFOEPFMÃSFBFOEPTQBSUFTZBQMJDBOEPBDBEB VOBMBSFHMBEF4JNQTPO6OBQBSUFTFIBDFQBSBY8 àOBMBY8 ZMBPUSB EFTEFIBTUBY'$BEBVOBEFMBTEPTQBSUFTEFCFTFSSFMBUJWBNFOUFGÃDJMEF BKVTUBSDPOVOBFDVBDJÓODÙCJDB&OUPODFT ÌgZVeVgiZ&2

%#&%− %#%)* P'#*& )'#%( '#%%R2%#&&*+

ÌgZVeVgiZ'2

%#('− %#&% P'#%% )'#'( '#-'R2%#*%(+

¦SFBUPUBM /PUFRVFMBàHVSBFTNVZÙUJMQBSBEFUFSNJOBSMPTWBMPSFTEF Y%¢Y8 FOMPT QVOUPTJOUFSNFEJPTY8 WBMPS ZY8 WBMPS &MÃSFBUPUBM DBMDVMBEB TF BDFSDB NÃT BM SFTVMUBEP PCUFOJEP HSÃàDBNFOUF EJGFSFODJB EF  FO DPNQBSBDJÓODPOMBEJGFSFODJBEFQBSBMBQSJNFSBFTUJNBDJÓO  &OUPODFT  DPO MPT NJTNPT DÃMDVMPT RVF BOUFT  DPO ¦SFB 8àOBM   %UPUBM  Z  Y% QSPN

& $PNQSVFCF-PTCBMBODFTEFNBTBQBSBUPEPVODJDMP FDVBDJPOFT  Z 

EFCFO TFS TBUJTGFDIPT Z  EF IFDIP  TF TBUJTGBDFO $PNP MB JOUFHSBDJÓO HSÃàDB Z MB SFHMB EF 4JNQTPO IFDIBFOEPTQBSUFT QSPEVDFOSFTVMUBEPTTJNJMBSFT FTUPTJSWFQBSBBTFHV SBSTF ' (FOFSBMJDF/PUFRVFOPOFDFTJUBNPTDBMDVMBSFMWBMPSFYBDUPEFY%PEFY' OJEFX8 àOBM TÓMPOPTBTFHVSBNPTEFRVFOVFTUSPTWBMPSFTDBMDVMBEPTSFCBTBSBOFTPTWBMPSFT&TP TVDFEFDPOBNCPTNÊUPEPTEFJOUFHSBDJÓO/VFTUSPTFKFT FOMBàHVSB TFTFMFDDJP OBSPOQBSBPCUFOFSMBNÃYJNBFYBDUJUVEFOUPODFT OPHSBàDBNPTQBSUFTEFMEJBHSBNB RVFOPVTÃSBNPT-BNJTNBJEFBHFOFSBMTFBQMJDBDVBOEPTFBKVTUBOEBUPTTFBKVTUBO EBUPTTÓMPFOMBSFHJÓOOFDFTBSJB1BSBUFOFSNÃTFYBDUJUVE FTNVZÙUJMMBàHVSB QBSBJOUFSQPMBSZEFUFSNJOBSWBMPSFTQBSBMBSFHMBEF4JNQTPO4JTFWBBVTBSMBSFHMB EF4JNQTPOQBSBDVSWBTDPODBNCJPTNVZSÃQJEPT MBFYBDUJUVENFKPSBSÃTJMBDVSWB TFEJWJEFFOEPTPNÃTQBSUFT"MDPNQBSBSMPTSFTVMUBEPTPCUFOJEPTDPOJOUFHSBDJÓO

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOJOUFSNJUFOUF

HSÃàDBDPOMPTPCUFOJEPTDPOMBJOUFHSBDJÓOFOEPTQBSUFTDPOMBSFHMBEF4JNQTPO TF WFVOBEJGFSFODJBFOY% QSPNJHVBMB&TUPRVFEBEFOUSPEFMBFYBDUJUVEEFMPTEBUPT EFFRVJMJCSJP 6OBWF[EFUFSNJOBEBTYX àOBM %Z8àOBM TFQVFEFODBMDVMBSMPTWBMPSFTEF2D 23ZFMUJFNQPEF PQFSBDJÓO WFBMBTFDDJÓO  9.5.2

Relación de reflujo variable

-BDPMVNOBEFEFTUJMBDJÓOJOUFSNJUFOUFUBNCJÊOQVFEFGVODJPOBSDPOSFMBDJÓOEFSFáVKPWBSJBCMF QBSB NBOUFOFS DPOTUBOUF B Y% -B FDVBDJÓO EF PQFSBDJÓO   TJHVF TJFOEP WÃMJEB "IPSB WB B WBSJBSMBQFOEJFOUF QFSPRVFEBSÃDPOTUBOUFMBJOUFSTFDDJÓODPOMBMÎOFBZY FOY%1BSBFTUFDBTP  FMEJBHSBNBEF.D$BCF5IJFMFTFWFFOMBàHVSB&OFTUFEJBHSBNBTFSFMBDJPOBY8DPOY%ZTF QVFEFJOUFHSBSMBFDVBDJÓOEF3BZMFJHIDPNPFOMBàHVSB:BRVFY%TFNBOUJFOFDPOTUBOUF FM QSPDFEJNJFOUPEFDÃMDVMPFTBMHPEJGFSFOUF $VBOEPTFFTQFDJàDBOY%ZMBDBOUJEBEEFFUBQBT FMWBMPSJOJDJBMEF-7TFEFUFSNJOBQPSQSVF CBZFSSPSQBSBMMFHBSBMBDPODFOUSBDJÓOEFMBBMJNFOUBDJÓOY'-BQFOEJFOUFEFMBMÎOFBEFPQFSB DJÓO -7 TFBVNFOUBIBTUBRVFDPOMBDBOUJEBEFTQFDJàDBEBEFDPOUBDUPTEFFRVJMJCSJPTFPCUFOHB Y8Y8 àOBM6OBWF[EFUFSNJOBEBY8 àOBM TFDBMDVMB8àOBMDPOFMCBMBODFEFNBTB FDVBDJPOFT  Z  -PTWBMPSFTNÃYJNPTSFRVFSJEPTEF2DZ23 ZFMUJFNQPEFPQFSBDJÓO TFQPESÃOEFUFSNJOBS BDPOUJOVBDJÓO WFBMBTFDDJÓO  4JOPFTWÃMJEBMBIJQÓUFTJTEFVOBSFUFODJÓOEFTQSFDJBCMF MBSFUFODJÓOFODBEBFUBQBZFOFM BDVNVMBEPSGVODJPOBDPNPVOWPMBOUFZSFUBSEBMPTDBNCJPT&OFTUFDBTPTFSFRVJFSFVOQSPDFEJ NJFOUPEFDÃMDVMPEJGFSFOUF BTÎDPNPQBSBMPTTJTUFNBTEFWBSJPTDPNQPOFOUFT #BSUPOZ3PDIF  %JXFLBS  

'*(63" %*"(3".".$$"#& 5)*&-&1"3"%&45*-"$*¶/*/5&3.*5&/5& $0/7"3*"4&5"1"4 9%$0/45"/5&: 3&-"$*¶/%&3&'-6+07"3*"#-&

www.FreeLibros.me

  5JFNQPEFPQFSBDJÓO



 5*&.10%&01&3"$*¶/

&MUJFNQPEFGVODJPOBNJFOUPZFMUBNBÒPEFMMPUFQVFEFOFTUBSDPOUSPMBEPTQPSMBFDPOPNÎBZQPS PUSPTGBDUPSFT1PSFKFNQMP OPFTSBSPRVFUPEPFMMPUF JODMVZFOEPFMBSSBORVFZFMQBSP TFIBHBFO VOUVSOPEFPDIPIPSBT4JTFVTBFMNJTNPBQBSBUPQBSBWBSJBTTVTUBODJBTEJGFSFOUFT QPESÃOWBSJBS MPTUBNBÒPTEFMPUF"EFNÃT FMUJFNQPQBSBDBNCJBSEFVOBTVTUBODJBBPUSBQVFEFTFSCBTUBOUF MBSHP QPSRVFRVJ[ÃTFSFRVJFSFVOSJHVSPTPQSPDFEJNJFOUPEFMJNQJF[B &MUJFNQPUPUBMEFMMPUF UMPUF FT 

UMPUFUQBSP UPQ



&MUJFNQPEFQBSP UJFNQPNVFSUP

UQBSP JODMVZFWBDJBSMPTGPOEPT MJNQJBS DBSHBSFMTJHVJFOUFMPUF ZDBMFOUBSMPIBTUBRVFDPNJFODFBBQBSFDFSSFáVKP&TFUJFNQPTFQVFEFFTUJNBSBQBSUJSEFMBFYQF SJFODJB&MUJFNQPEFPQFSBDJÓO UPQ FTFMQFSJPEPSFBMEVSBOUFFMRVFTFFGFDUÙBMBEFTUJMBDJÓO QPSMP RVFEFCFTFSJHVBMBMBDBOUJEBEUPUBMEFEFTUJMBEPSFVOJEP EJWJEJEBFOUSFFMáVKPEFEFTUJMBEP 

ide 2

9idiVa  9



%UPUBMTFDBMDVMBDPOFMQSPDFEJNJFOUPDPOMBFDVBDJÓOEF3BZMFJHI FTUBOEPàKB'ZBTFBQPSFMUB NBÒPEFMSFDJQJFOUFPQPSFMUBNBÒPEFMBDBSHB1BSBVOBQBSBUPFYJTUFOUF MBUBTBEFáVKP%EFM EFTUJMBEP FOLHNPMI OPTFQVFEFFTUBCMFDFSFOGPSNBBSCJUSBSJB-BDPMVNOBGVFEJTFÒBEBQBSB EFUFSNJOBEBWFMPDJEBENÃYJNBEFWBQPS VJOVOE RVFDPSSFTQPOEFBMBUBTBNÃYJNBEFáVKPNPMBM  7NÃY WFBFMDBQÎUVMP &OUPODFT EFMCBMBODFEFNBTBFOUPSOPBMDPOEFOTBEPS 

9b{m 2

Kb{m  A & 9



4FTVFMFPQFSBSBDJFSUBGSBDDJÓOEFFTUFáVKP DPNPQPSFKFNQMP%%NÃY&OUPODFT DPOMBT FDVBDJPOFT  Z  TFQVFEFFTUJNBSUPQ4JFMUMPUFRVFSFTVMUBOPFTBEFDVBEP FTOFDFTBSJP IBDFSBKVTUFT -BTOFDFTJEBEFTEFFOFSHÎBFOFMWBQPSJ[BEPSPSFUPSUB 23 ZFOFMDPOEFOTBEPSUPUBM 2D TF QVFEFOFTUJNBSDPOCBMBODFTEFFOFSHÎBFOFMDPOEFOTBEPSZFOUPSOPBUPEPFMTJTUFNB1BSBVO DPOEFOTBEPS UPUBM  FT WÃMJEB MB FDVBDJÓO 

 QFSP 7  I% Z ) QPESÃO TFS UPEBT GVODJPOFT EFM UJFNQP TJWBSÎBY% MBTFOUBMQÎBTWBOBWBSJBS 4JFMSFáVKPFTVOMÎRVJEPTBUVSBEP FOUPODFT)¢I%  4JVTBNPT QSPN MBFDVBDJÓO  TFTJNQMJàDBB 

FX 2−K&λegdb 



%VSBOUFMBPQFSBDJÓO ZBDBSHBEPZDBMFOUBEPFMWBQPSJ[BEPS ZWBQPSáVZFOEPQPSUPEBMBDPMVN OB

FMCBMBODFEFFOFSHÎBFOUPSOPBUPEPFMTJTUFNBFT 

FG 2−FX 9]9 



&TUBFDVBDJÓOFTEJTUJOUBBMB B

QPSRVFEVSBOUFMBPQFSBDJÓOOPIBZBMJNFOUBDJÓOOJQSPEVDUP EFGPOEPT1BSBVOBQBSBUPFYJTUFOUFEFEFTUJMBDJÓOJOUFSNJUFOUF EFCFNPTDPNQSPCBSRVFFMDPO EFOTBEPSZFMWBQPSJ[BEPSUFOHBOFMUBNBÒPTVàDJFOUFQBSBNBOFKBSMPTWBMPSFTDBMDVMBEPTEF]2D]Z 234J]2D]P23TPONVZHSBOEFT IBCSÃRVFSFEVDJSMBSBQJEF[EFFWBQPSBDJÓO)BCSÃRVFBVNFOUBS FMUJFNQPEFPQFSBDJÓO UPQ PCJFOSFEVDJSMBDBSHBBMWBQPSJ[BEPS

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOJOUFSNJUFOUF

-BEFTUJMBDJÓOJOUFSNJUFOUFUJFOFOFDFTJEBEFTBMHPEJGFSFOUFTEFEJTFÒPZEFDPOUSPMEFMQSPDFTPDPO SFTQFDUPBMBEFTUJMBDJÓODPOUJOVB"EFNÃT FMBSSBORVFZMBMPDBMJ[BDJÓOEFGBMMBTTPOBMHPEJGFSFO UFT&MMFSCF  EFTDSJCFFTUPTBTQFDUPT  3&46.&/m0#+&5*704

&OFTUFDBQÎUVMPIFNPTFYQMPSBEPMPTDÃMDVMPTQBSBEFTUJMBDJÓOCJOBSJBJOUFSNJUFOUF&OFTUFNP NFOUP VTUFEEFCFTFSDBQB[EFDVNQMJSMPTPCKFUJWPTTJHVJFOUFT  &YQMJDBSMBPQFSBDJÓOEFMPTTJTUFNBTEFEFTUJMBDJÓOJOUFSNJUFOUFTJNQMFTZEFWBSJBTFUBQBT  %FTDSJCJSMBTEJGFSFODJBTFOUSFMBPQFSBDJÓOJOUFSNJUFOUFZDPOUJOVB  %FEVDJSZVTBSMBFDVBDJÓOEF3BZMFJHIQBSBEFTUJMBDJÓOJOUFSNJUFOUFTJNQMF  3FTPMWFSQSPCMFNBTEFEFTUJMBDJÓOJOUFSNJUFOUFDPOOJWFMDPOTUBOUF  3FTPMWFSQSPCMFNBTEFEFTUJMBDJÓOJOUFSNJUFOUFQPSBSSBTUSFDPOWBQPSEFBHVB  6TBS FM NÊUPEP EF .D$BCF5IJFMF QBSB BOBMJ[BS MB EFTUJMBDJÓO JOUFSNJUFOUF FO WBSJBT FUBQBT  QBSB B %FTUJMBDJÓOJOUFSNJUFOUFDPOSFMBDJÓOEFSFáVKPDPOTUBOUF C %FTUJMBDJÓOJOUFSNJUFOUFDPODPNQPTJDJÓODPOTUBOUFEFEFTUJMBEP D %FTUJMBDJÓOJOUFSNJUFOUFJOWFSUJEB  %FUFSNJOBSFMUJFNQPEFPQFSBDJÓOZMBTOFDFTJEBEFTEFFOFSHÎBQBSBVOBEFTUJMBDJÓOJOUFSNJ UFOUF 3&'&3&/$*"4

#BSUPO 1Z&$3PDIF +S i#BUDI%JTUJMMBUJPOu 4FDDJÓOFO4DIXFJU[FS 1" &E )BOECPPL PG4FQBSBUJPO5FDIOJRVFTGPS$IFNJDBM&OHJOFFST ‰&E .D(SBX)JMM /FX:PSL  $BSFZ +4 i%JTUJMMBUJPOuFO+)1FSSZ &E

$IFNJDBM&OHJOFFST)BOECPPL ‰&E .D(SBX )JMM /FX:PSL  QÃHT %JXFLBS 68 #BUDI%JTUJMMBUJPO4JNVMBUJPO 0QUJNBM%FTJHOBOE$POUSPM 5BZMPSBOE'SBODJT  8BTIJOHUPO %$  &MMFSCF 38 i#BUDI%JTUJMMBUJPOu FO1"4DIXFJU[FS &E

)BOECPPLPG4FQBSBUJPO5FDIOJRVFT GPS$IFNJDBM&OHJOFFST .D(SBX)JMM /FX:PSL  1ÃH (FOUJMDPSF .+ i3FEVDFTPMWFOU6TBHFJO#BUDI%JTUJMMBUJPOu $IFN&OH1SPHS  

 &OF   -VZCFO 8- i4PNF1SBDUJDBM"TQFDUTPG0QUJNBM#BUDI%JTUJMMBUJPOu *OE&OH$IFN1SPD%FT %FWFMPQ     .JDLMFZ  ) 4  4IFSXPPE  5 , Z 3FFE  $ &  "QQMJFE .BUIFNBUJDT JO $IFNJDBM &OHJOFFSJOH  .D(SBX)JMM /FX:PSL  1ÃHT 1SBUBQ 3 (FUUJOH4UBSUFEXJUI."5-"# 0YGPSE6OJW1SFTT 0YGPSE  1SBUU )3$ $PVOUFSDVSSFOU4FQBSBUJPO1SPDFTTFT &MTFWJFS /FX:PSL  3BZMFJHI -PSE 1IJM.BH  

   3PCJOTPO  $ 4 Z & 3 (JMMJMBOE  &MFNFOUT PG 'SBDUJPOBM %JTUJMMBUJPO  ‰ &E  .D(SBX)JMM  /FX :PSL  DBQÎUVMPTZ 4UBOXPPE $ i'PVOEJOUIF0UINFS-JCSBSZu $IFNJDBM)FSJUBHF  

 PUPÒPEF  5SFZCBM 3& .BTT5SBOTGFS0QFSBUJPOT ‰FEJDJÓO .D(SBX)JMM /FX:PSL  5SFZCBM 3& i"TJNQMF.FUIPEGPS#BUDI%JTUJMMBUJPOu $IFN&OH  

 EFPDUVCSFEF  

www.FreeLibros.me

5BSFB



7BMMFF #- i"MDPIPMJOUIF8FTUFSO8PSMEu 4DJFOUJGJD"NFSJDBO  KVOJPEF  8PPEMBOE -3 i4UFBN%JTUJMMBUJPOu FO%+%F3FO[P &E

6OJU0QFSBUJPOTGPS5SFBUNFOUPG )B[BSEPVT*OEVTUSJBM8BTUFT /PZFT%BUB$PSQ 1BSL3JEHF /+  QÃHT 5"3&"

" 1SPCMFNBTQBSBEJTDVTJÓO " y1PSRVÊFMWBQPSJ[BEPSEFMBàHVSB#FTNVDIPNBZPSRVFMBDPMVNOB " &OMBEFEVDDJÓOEFMBFDVBDJÓOEF3BZMFJHI B &OMBFDVBDJÓO  yQPSRVÊTFUJFOF¢Y%E8ZOP¢Y%E% C &OMBFDVBDJÓO  yQPSRVÊFMMBEPJ[RVJFSEPFT¢Y%E8ZOP¢E Y%8

" &YQMJRVFDÓNPTFQPESÎBMMFWBSBDBCPMBJOUFHSBDJÓOHSÃàDBEFMBTàHVSBTZOVNÊSJDB NFOUFFOVOBDPNQVUBEPSB " %FTDSJCBMBTWFOUBKBTZEFTWFOUBKBTEFMBEFTUJMBDJÓOJOUFSNJUFOUFDPOSFTQFDUPBMBEFTUJMBDJÓO DPOUJOVBy&TQFSBVTUFERVFIBZBEFTUJMBDJÓOJOUFSNJUFOUFPDPOUJOVBFOMBTTJHVJFOUFTJOEVT USJBT y1PSRVÊ B 6OBHSBOQMBOUBEFTVTUBODJBTRVÎNJDBTCÃTJDBT C 6OBQMBOUBRVFQSPEV[DBSFBDUJWPTRVÎNJDPTàOPT D 6OBSFàOFSÎBEFQFUSÓMFP E 6OBQMBOUBQFUSPRVÎNJDB F 6OBQMBOUBGBSNBDÊVUJDB G 6OBQMBOUBDSJPHÊOJDBQBSBSFDVQFSBSPYÎHFOPEFMBJSF H 6OSFDJQJFOUFQBSBSFDVQFSBSTPMWFOUFFOVOBPQFSBDJÓOEFQJOUVSB I *OTUBMBDJPOFTEFQSPEVDDJÓOEFFUBOPMEFVOBHSJDVMUPS 5FOHBFODVFOUBRVFMBEFTUJMBDJÓODPOUJOVBTFVTBDPOGSFDVFODJBFODBNQBÒBT&TUPFT MB QMBOUBQSPEVDFVOBTVTUBODJBFOGPSNBDPOUJOVB QFSPEVSBOUFVOUJFNQPSFMBUJWBNFOUFDPSUP y$ÓNPIBDFFTUPRVFDBNCJFOTVTSFTQVFTUBT " 4VQPOJFOEPRVFTFQVEJFSBVTBSEFTUJMBDJÓOJOUFSNJUFOUFPDPOUJOVB yDVÃMDPOTVNJSÎBNFOPT FOFSHÎB &YQMJRVFQPSRVÊ " -PUF EF /PDIF  4" IB EFTBSSPMMBEP VO TJTUFNB OVFWP Z TJNQMF  JOUFSNJUFOUF Z DPO SFáVKP àHVSB DPOBMHPEFMBDPSSJFOUF%SFáVKBEBIBTUBFMWBQPSJ[BEPS RVF BTFHVSBO GVODJPOB NFKPSRVFFMTJTUFNBOPSNBMJOUFSNJUFOUFTJNQMF àHVSB 4VQPOHBRVFEFTFBVTUFEEFTUJ MBSFOGPSNBJOUFSNJUFOUFVOBNF[DMBTJNJMBSBMBEFNFUBOPMZBHVB EPOEFOPIBZB[FÓUSPQP  ZOPTFGPSNBOEPTGBTFTMÎRVJEBT"NCPTTJTUFNBTTFDBSHBODPOMBNJTNBDBSHBEF'NPMFT  DPOMBNJTNBGSBDDJÓONPMBSY' ZTFEFTUJMBIBTUBUFOFSFMNJTNPWBMPSEFY8 àOBMy&MWBMPSEF YE QSPNEFMTJTUFNBJOUFSNJUFOUFTJNQMFDPOSFáVKPTFSÃ B .BZPSRVF C *HVBMB D .FOPSRVF FMWBMPSYE QSPNEFMBEFTUJMBDJÓOJOUFSNJUFOUFTJNQMFOPSNBM &YQMJRVFTVSFTQVFTUB " $VBOEP IBZ WBSJBT FUBQBT FO MB EFTUJMBDJÓO JOUFSNJUFOUF  MPT DÃMDVMPT TF QBSFDFO B MPT EFM EJBHSBNBEF.D$BCF5IJFMFQBSBWBSJBT B $PMVNOBTEFBHPUBNJFOUP C $PMVNOBTEFFOSJRVFDJNJFOUP D $PMVNOBTDPOVOBBMJNFOUBDJÓOFOFMMVHBSÓQUJNP " -BEFTUJMBDJÓOJOUFSNJUFOUFDPOWBSJBTFUBQBTFTNÃTGÃDJMEFPQFSBS

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOJOUFSNJUFOUF

B "GSBDDJÓONPMBSDPOTUBOUFFOEFTUJMBEP C "SFMBDJÓOEFSFáVKPDPOTUBOUF D "GSBDDJÓONPMBSDPOTUBOUFFOMPTGPOEPT " 'PSNFTVUBCMBEFSFMBDJPOFTDMBWFQBSBFTUFDBQÎUVMP # (FOFSBDJÓOEFBMUFSOBUJWBT # )BHBVOBMJTUBEFMBTEJGFSFOUFTGPSNBTFORVFTFQVFEFOFTQFDJàDBSVOQSPCMFNBEFEFTUJMBDJÓO CJOBSJBPEFEFTUJMBDJÓOCJOBSJBJOWFSUJEBy$VÃMFTEFFMMBTEFCFSÃOTFSEFQSVFCBZFSSPS # y2VÊTFQVFEFIBDFSTJVOTJTUFNBFYJTUFOUFEFEFTUJMBDJÓOJOUFSNJUFOUFOPQVFEFQSPEVDJS MPTWBMPSFTEFY%ZY8RVFTFEFTFBO BVOCBKPDPOEJDJPOFTEFSFáVKPUPUBM (FOFSFJEFBTQBSB PQFSBSZNPEJàDBSFMFRVJQP $ %FEVDDJPOFT $ %FEV[DBMBFDVBDJÓO   $ 4VQPOHBRVFMBSFUFODJÓOFOMBDPMVNOBZFOFMWBQPSJ[BEPSUPUBMFTEFTQSFDJBCMFFOVOBEFT UJMBDJÓOJOUFSNJUFOUFJOWFSUJEB àHVSB  B  %FEV[DBMBGPSNBBEFDVBEBEFMBFDVBDJÓOEF3BZMFJHI C %FEV[DBMBTFDVBDJPOFTEFPQFSBDJÓOOFDFTBSJBTQBSBEFSSBNFNPMBMDPOTUBOUF5SBDFFT RVFNBTEFEJBHSBNBTEF.D$BCF5IJFMF $ %FEV[DBFMFDVBDJÓO   % 1SPCMFNBT  -BTSFTQVFTUBTEFQSPCMFNBTDPOVOBTUFSJTDPFTUÃOFOMBQBSUFGJOBMEFMMJCSP % 4FVTBVOEFTUJMBEPSJOUFSNJUFOUFTJNQMF VOBFUBQBEFFRVJMJCSJP QBSBTFQBSBSFUBOPMEFBHVB -BBMJNFOUBDJÓOBMWBQPSJ[BEPSFTLNPMEFVOBNF[DMBEFNPMEFFUBOPM-BDPODFOUSB DJÓOàOBMFOFMWBQPSJ[BEPSEFCFTFSNPMEFFUBOPM-PTEBUPTEFMFRVJMJCSJPFUBOPMBHVB FTUÃOFOMBUBCMB$BMDVMF B -BDBSHBàOBMEFNBUFSJBM 8àOBM FOFMWBQPSJ[BEPS C -BDBOUJEBEEFEFTUJMBEPSFDPMFDUBEP %UPUBM D -BGSBDDJÓONPMBSQSPNFEJPEFMEFTUJMBEP Y% QSPN 4VHFSFODJB"QMJRVFMBSFHMBEF4JNQTPO

'*(63" %&45*-"$*¶/*/5&3.*5&/5& */7&35*%"

www.FreeLibros.me

5BSFB



%  4FEFTFBVTBSVOEFTUJMBEPSJOUFSNJUFOUFTJNQMF VOBFUBQBEFFRVJMJCSJP QBSBTFQBSBSNF UBOPMZBHVB-BDBSHBBMJNFOUBEBBMWBQPSJ[BEPSFTNPMEFVOBNF[DMBDPONPMEF NFUBOPM4FEFTFBRVFMBDPODFOUSBDJÓOàOBMEFMPTGPOEPTDPOUFOHBNPMEFNFUBOPM $BMDVMFMBDBOUJEBEEFEFTUJMBEPSFDPMFDUBEP MBDBOUJEBEEFNBUFSJBMRVFRVFEBZFMWBQPSJ [BEPSZMBDPODFOUSBDJÓOQSPNFEJPEFMEFTUJMBEP-BQSFTJÓOFTBUN-PTEBUPTEFFRVJMJCSJP FTUÃOFOMBUBCMB %  4FEFTFBVTBSVOTJTUFNBEFEFTUJMBDJÓODPOVOWBQPSJ[BEPSNÃTVOBDPMVNOBRVFUJFOFVOB FUBQBEFFRVJMJCSJPFOVOBEFTUJMBDJÓOJOUFSNJUFOUFEFNFUBOPMZBHVB4FVTBVODPOEFOTBEPS UPUBM-BBMJNFOUBDJÓODPOUJFOFNPMEFNFUBOPM4FRVJFSFRVFMBDPODFOUSBDJÓOEFMPT GPOEPTàOBMFTTFBNPMEFNFUBOPM-BQSFTJÓOFTL1B&MSFáVKPFTMÎRVJEPTBUVSBEP  Z-%FTDPOTUBOUF$BMDVMF8àOBM %UPUBMZY% QSPN-PTEBUPTEFFRVJMJCSJPNFUBOPMBHVB FTUÃOFOMBUBCMB6TFVOBCBTFEFDÃMDVMPEFLHNPMEFBMJNFOUBDJÓO % 4FEFTFBFGFDUVBSVOBEFTUJMBDJÓOJOUFSNJUFOUFTJNQMF DPOUBDUPEFFRVJMJCSJP EFVOBNF[DMB EFBDFUPOBZFUBOPM-BDBSHBEFBMJNFOUBDJÓODPOUJFOFNPMEFBDFUPOB-BDPODFOUSBDJÓO àOBMFOFMSFDJQJFOUFTFSÃNPMEFBDFUPOB-BDBOUJEBEàOBMEFNBUFSJBMFOFMSFDJQJFOUFFT LHNPMFT-PTEBUPTEFFRVJMJCSJPWBQPSMÎRVJEPFTUÃOFOFMQSPCMFNB%$BMDVMFMBUBTBEF BMJNFOUBDJÓO' MBGSBDDJÓONPMBSQSPNFEJPEFMEFTUJMBEPZMPTLHNPMEFEFTUJMBEPSFDPMFDUBEP % 4FVTBVOTJTUFNBEFEFTUJMBDJÓOJOUFSNJUFOUFTJNQMFDPOVOWBQPSJ[BEPSQBSBEFTUJMBS LHNPMEFVOBNF[DMBEFOCVUBOPMZBHVB&MTJTUFNBUJFOFVODPOEFOTBEPSUPUBMZFMEFTUJMBEP TFSFUJSB-BBMJNFOUBDJÓODPOUJFOFNPMEFBHVBZNPMEFOCVUBOPM6TFMBSFHMB EF4JNQTPOQBSBDBMDVMBSMBTNPMFTàOBMFTFOFMWBQPSJ[BEPS6TFVOCBMBODFEFNBTBQBSB EFUFSNJOBSMBGSBDDJÓONPMQSPNFEJPFOFMEFTUJMBEP % 4FUJFOFVOEFTUJMBEPSTJNQMFQBSBTFQBSBS EJDMPSPFUBOPZ  USJDMPSPFUBOP-BQSFTJÓO FTBUN-BWPMBUJMJEBESFMBUJWBEFFTUFTJTUFNBFTDBTJDPOTUBOUF DPOVOWBMPSEF4FSFDP NJFOEBVTBSMBFDVBDJÓO   B -BDBSHB ' FTLHNPM&TUBBMJNFOUBDJÓODPOUJFOFNPMEFEJDMPSPFUBOP4FEFTFB RVFMBDPODFOUSBDJÓOàOBMFOFMWBQPSJ[BEPSTFBNPMEFEJDMPSPFUBOP$BMDVMFMBTNP MFTàOBMFTFOFMWBQPSJ[BEPSZMBGSBDDJÓONPMQSPNFEJPFOFMQSPEVDUPEFTUJMBEP C 3FQJUBMBQBSUFB TJMBDBSHBEFBMJNFOUBDJÓOFTLHNPM D 4JMBDBSHBEFBMJNFOUBDJÓOFTLHNPM MBBMJNFOUBDJÓODPOUJFOFNPMEFEJDMPSPFUBOP ZTJTFEFTFBRVFFMEFTUJMBEPDPOUFOHBVOBDPODFOUSBDJÓOQSPNFEJPEFNPMEFEJDMP SPFUBOP DBMDVMFMBTNPMFTàOBMFTFOFMWBQPSJ[BEPSZMBGSBDDJÓONPMBSàOBMEFEJDMPSPFUBOP FOFMWBQPSJ[BEPS % 4FEFTFBVTBSVOTJTUFNBEFEFTUJMBDJÓOJOUFSNJUFOUFDPOVOWBQPSJ[BEPSZVOBFUBQBEFFRVJMJ CSJP FOUPUBM DPOUBDUPTEFFRVJMJCSJP QBSBEFTUJMBSVOBBMJNFOUBDJÓODPONPMEFBHVB ZNPMEFOCVUBOPM WFBMPTEBUPTEFFRVJMJCSJPWBQPSMÎRVJEPFOMBUBCMB -BQSFTJÓO FTBUN-BDBSHBFTLHNPM4FEFTFBRVFMBDPODFOUSBDJÓOàOBMFOFMWBQPSJ[BEPSTFB NPMEFBHVB&MTJTUFNBUJFOFVODPOEFOTBEPSUPUBMZFMSFáVKPSFHSFTBDPNPMÎRVJEPTBUVSBEP -BSFMBDJÓOEFSFáVKPFT-%$BMDVMFMBDBOUJEBEàOBMEFNPMFTFOFMWBQPSJ[BEPSZMB DPODFOUSBDJÓOQSPNFEJPEFMEFTUJMBEP % 4FFTUÃEFTUJMBOEPFOGPSNBJOUFSNJUFOUFVOBNF[DMBEFBDFUPOBZFUBOPMFOVOTJTUFNBRVF UJFOFVOWBQPSJ[BEPSNÃTVOBFUBQBEFFRVJMJCSJP EPTDPOUBDUPTEFFRVJMJCSJP FOUPUBM -B BMJNFOUBDJÓODPOUJFOFGSBDDJÓONPMBSEFBDFUPOB-BSFMBDJÓOEFSFáVKPFYUFSOPFTDPOT UBOUFZTVWBMPSFT-%-BQSFTJÓOFTBUN4FEFTFBRVFMBDBOUJEBEàOBMZMBGSBDDJÓO NPMàOBMFOFMWBQPSJ[BEPSTFBOLHNPMZEFBDFUPOB SFTQFDUJWBNFOUF4VQPOHBEF SSBNFNPMBMDPOTUBOUF-PTEBUPTEFFRVJMJCSJPFTUÃOFOFMQSPCMFNB%$BMDVMF

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOJOUFSNJUFOUF

B -BDBOUJEBEEFBMJNFOUBDJÓO' FOLHNPM RVFEFCFBHSFHBSTF C -BDBOUJEBEEFEFTUJMBEPZMBGSBDDJÓONPMBMQSPNFEJPEFBDFUPOBFOFMEFTUJMBEP %  4FEFTFBEFTUJMBSFOGPSNBJOUFSNJUFOUFVOBNF[DMBEFCVUBOPMZBHVB$PNPFTUFTJTUFNB UJFOFVOB[FÓUSPQPIFUFSPHÊOFP WFBFMDBQÎUVMP VTBSFNPTFMTJTUFNBRVFNVFTUSBMBàHVSB TJHVJFOUF-BDBQBMÎRVJEBJOGFSJPSRVFDPOUJFOFNPMEFBHVBTFSFUJSBDPNPQSPEVDUP ZMBDBQBMÎRVJEBTVQFSJPS DPONPMEFBHVB TFSFHSFTBBMWBQPSJ[BEPS-BQSFTJÓOFT BUN-BBMJNFOUBDJÓOFTLHNPMZDPOUJFOFNPMEFBHVB-PTEBUPTEFFRVJMJCSJPFTUÃO FOFMQSPCMFNB%

%

%

%

%

B 4JMBDPODFOUSBDJÓOàOBMFOMBSFUPSUBEFCFTFSY8 àOBM yDVÃMFTMBDBOUJEBEàOBMEF EFTUJMBEP %UPUBM SFDPMFDUBEP FOLHNPM C 4JMBEFTUJMBDJÓOJOUFSNJUFOUFFTDPOUJOVB yDVÃMFTFMWBMPSNÃTCBKPEFY8 àOBMRVFQVFEF PCUFOFSTFNJFOUSBTDPOUJOÙBQSPEVDJÊOEPTFVOEFTUJMBEPEFY% 4FRVJFSFIBDFSVOBEFTUJMBDJÓOJOUFSNJUFOUFEFVOBNF[DMBEFFUBOPMZBHVB-BBMJNFOUB DJÓODPOUJFOF GSBDDJÓONPMEFFUBOPM ZEFTFBNPTDPOUJOVBSMBEFTUJMBDJÓOIBTUBMMFHBSB Y8 àOBM GSBDDJÓONPMBSEFFUBOPM-BDBSHBJOJDJBMFT'LHNPM&MTJTUFNBJOUFSNJ UFOUFUJFOFVOWBQPSJ[BEPS RVFGVODJPOBDPNPVODPOUBDUPEFFRVJMJCSJPZVOBDPMVNOBDPO VOBFUBQBEFFRVJMJCSJP FOUPUBM DPOUBDUPTEFFRVJMJCSJP &MWBQPSEFTUJMBEPTFDPOEFOTB FOVODPOEFOTBEPSUPUBM6TBSFNPTVOBSFMBDJÓOEFSFáVKPFYUFSOP-% -PTEBUPTEF FRVJMJCSJPWBQPSMÎRVJEPFTUÃOFOMBUBCMB$BMDVMF8àOBM %UPUBMZY% QSPN 4FQBSBSFNPTLHNPMEFVOBNF[DMBEFOCVUBOPZOIFYBOPFOVOEFTUJMBEPSJOUFSNJUFOUF TJNQMF-BBMJNFOUBDJÓODPOUJFOFNPMEFOCVUBOPZNPMEFOIFYBOP-BQSFTJÓO FTL1B&MDPOUFOJEPàOBMEFMWBQPSJ[BEPSEFCFUFOFSNPMEFOCVUBOP)BHBVO DÃMDVMPEFQVOUPEFCVSCVKBFOMBTDPOEJDJPOFTEFMBBMJNFOUBDJÓOZPUSPFOMBTDPOEJDJPOFT àOBMFT-PTWBMPSFT,TFQVFEFOPCUFOFSFOMBTHSÃàDBTEF%F1SJFTUFS$BMDVMFMBTWPMBUJMJEB EFTSFMBUJWBTBFTUBTEPTDPOEJDJPOFTZEFTQVÊTMBWPMBUJMJEBESFMBUJWBNFEJBHFPNÊUSJDBQBSB VTBSMBFOMBFDVBDJÓO  %FUFSNJOFMBDBOUJEBEàOBMFOFMWBQPSJ[BEPS MBDBOUJEBEEF EFTUJMBEPSFDPMFDUBEP MBGSBDDJÓONPMQSPNFEJPEFMEFTUJMBEPZMBUFNQFSBUVSBEFMWBQPSJ[B EPSDVBOEPUFSNJOBFMMPUF -PT EBUPT EF FRVJMJCSJP WBQPSMÎRVJEP QBSB BDFUPOBFUBOPM FTUÃO FO FM QSPCMFNB % 4F UJFOFOLHNPMEFVOBNF[DMBEFBDFUPOBZFUBOPMRVFRVFSFNPTTFQBSBSFOVOEFTUJMBEPS JOUFSNJUFOUFTJNQMF-BBMJNFOUBDJÓODPOUJFOFNPMEFBDFUPOB&MSFTJEVPàOBMFOFM WBQPSJ[BEPSEFCFDPOUFOFSNPMEFBDFUPOB$BMDVMFMBDBOUJEBEàOBMFOFMWBQPSJ[BEPS  MBDBOUJEBEEFEFTUJMBEPSFDPMFDUBEPZMBGSBDDJÓONPMBSQSPNFEJPFOFMEFTUJMBEP 4FGPSNBVOTJTUFNBEFEFTUJMBDJÓOJOUFSNJUFOUFQBSBTFQBSBSBHVBZOCVUBOPM DPOVOWB QPSJ[BEPS VOBDPMVNOBDPOFUBQBT VODPOEFOTBEPSUPUBMZVOTFQBSBEPSMÎRVJEPMÎRVJEP

www.FreeLibros.me

5BSFB



-BDBQBEFBHVBEFMTFQBSBEPSMÎRVJEPMÎRVJEP  GSBDDJÓONPMBSEFBHVB TFUPNBDPNP QSPEVDUPEFTUJMBEP-BDBQBPSHÃOJDBEFFTFTFQBSBEPSMÎRVJEPMÎRVJEP EFBHVB GSBD DJÓONPMBS TFSFHSFTBBMBDPMVNOBDPNPSFáVKP-PTEBUPTEFFRVJMJCSJPWBQPSMÎRVJEPFTUÃO FO MB UBCMB  -B BMJNFOUBDJÓO BM TJTUFNB JOUFSNJUFOUF FT  LHNPM  DPO  EF BHVB  GSBDDJÓONPMBS-BPQFSBDJÓOFTBBUNZFTWÃMJEPFMEFSSBNFNPMBMDPOTUBOUF B 4J EFTFBNPT RVF FM SFTJEVP àOBM DPOUFOHB  EF BHVB  GSBDDJÓO NPMBM  DBMDVMF %UPUBM Z 8àOBM C y$VÃMFTMBSFMBDJÓOEFSFáVKPJOUFSOP -7 BMJOJDJPEFMBEFTUJMBDJÓOJOUFSNJUFOUF D y$VÃMFTFMWBMPSNÎOJNPEFY8 àOBMRVFQVFEFPCUFOFSTFDPOFTUFTJTUFNBEFEFTUJMBDJÓO JOUFSNJUFOUF %  4F MMFWB B DBCP VOB EFTUJMBDJÓO TJNQMF QPS BSSBTUSF DPO WBQPS EF BHVB FO FM BQBSBUP RVF NVFTUSBMBàHVSB-BBMJNFOUBDJÓOPSHÃOJDBDPOUJFOFNPMEFOEFDBOPZNPM EFTVTUBODJBTPSHÃOJDBTOPWPMÃUJMFT&MTJTUFNBTFPQFSBDPOBHVBMÎRVJEBFOFMWBQPSJ[BEPS -BEFTUJMBDJÓOTFDPOUJOÙBIBTUBRVFMBDBQBPSHÃOJDBFOFMEFTUJMBEPSDPOUFOHBNPMEF OEFDBOP'LHNPM-BQSFTJÓOFTNN)H B "MUÊSNJOPEFMBPQFSBDJÓOyDVÃMFTMBUFNQFSBUVSBFOFMWBQPSJ[BEPS C y$VÃMFT8àOBM y$VÃMFT%UPUBM D &TUJNFMBTNPMFTEFBHVBRVFQBTBOFOFMWBQPSQPSNPMEFOEFDBOPBMàOBMEFMBEFTUJ MBDJÓO %BUPT4VQPOHBRVFFMBHVBZFMOEFDBOPTPOUPUBMNFOUFJONJTDJCMFT-PTEBUPTEFQSFTJÓO EFWBQPSEFO$TFFODVFOUSBOFOFMFKFNQMP-PTEBUPTEFQSFTJÓOEFWBQPSEFBHVB FTUÃOFOFMQSPCMFNB% % 4FEFTFBIBDFSVOBEFTUJMBDJÓOJOUFSNJUFOUFEFLHNPMEFVOBNF[DMBEFOCVUBOPMZBHVB &MTJTUFNBDPOTJTUFFOVOWBQPSJ[BEPSJOUFSNJUFOUFNÃTVOBFUBQBEFFRVJMJCSJP&MTJTUFNB FTUÃ BBUN-B BMJNFOUBDJÓODPOUJFOFNPMEFBHVBZNPMEFCVUBOPM&MWBQPS EFTUJMBEPTFDPOEFOTBZTFNBOEBBVOTFEJNFOUBEPSMÎRVJEPMÎRVJEP&MQSPEVDUPSJDPFOBHVB GSBDDJÓONPMBSEFBHVB TFTBDBDPNPQSPEVDUPEFTUJMBEPZMBDBQBSJDBFOCVUBOPM   GSBDDJÓONPMBSEFBHVB TFSFáVKBBMBDPMVNOB4FEFTFBRVFMBGSBDDJÓONPMBSFOFMQSPEVDUP àOBMFOFMWBQPSJ[BEPSDPOUFOHBEFBHVB GSBDDJÓONPMBS"MWBQPSJ[BEPSFOUSBFOFSHÎBB UBTBDPOTUBOUF QPSMPRVF7DPOTUBOUF0CTFSWFRVFFMQSPEVDUPEFTUJMBEPDPOUJFOFGSBDDJÓO NPMBSDPOTUBOUF-BSFMBDJÓOEFSFáVKPBVNFOUBBNFEJEBRVFEFDSFDFMBGSBDDJÓONPMBSFO FMWBQPSEFTUJMBEP EVSBOUFFMDVSTPEFMBEFTUJMBDJÓOJOUFSNJUFOUF-PTEBUPTEFFRVJMJCSJPTF FODVFOUSBOFOMBUBCMB B $BMDVMFMBDBOUJEBEàOBMEFNBUFSJBMFOFMWBQPSJ[BEPSZMBDBOUJEBEEFEFTUJMBEPSFDPMFD UBEP C $BMDVMFMBTSFMBDJPOFTJOJDJBMZàOBMEFSFáVKPJOUFSOP WBMPSFTEF-7  %  4FEFTFBIBDFSVOBEFTUJMBDJÓOJOUFSNJUFOUFOPSNBMDPONFUBOPMZBHVB&MTJTUFNBUJFOF VOWBQPSJ[BEPSRVFBDUÙBDPNPVOBFUBQBEFFRVJMJCSJPZVOBDPMVNOBDPOEPTFUBQBTEF FRVJMJCSJP VOUPUBMEFUSFTDPOUBDUPTEFFRVJMJCSJP -BDPMVNOBUJFOFVODPOEFOTBEPSUPUBM ZTFSFHSFTBSFáVKPDPNPMÎRVJEPTBUVSBEP-BDPMVNOBTFUSBCBKBDPOVOBSFMBDJÓOWBSJBCMF EFSFáVKP EFUBMNPEPRVFTFNBOUFOHBY%DPOTUBOUF-BDBSHBJOJDJBMFT'LHNPMZ DPOUJFOFNPMEFNFUBOPM%FTFBNPTRVFMBDPODFOUSBDJÓOàOBMFOFMWBQPSJ[BEPSTFB NPMEFNFUBOPMZMBEFMEFTUJMBEPEFCFTFSNPMEFNFUBOPM-BQSFTJÓOFTBUN&T WÃMJEPFMEFSSBNFNPMBMDPOTUBOUF-PTEBUPTEFFRVJMJCSJPFTUÃOFOMBUBCMB B y2VÊSFMBDJÓOJOJDJBMEFSFáVKPFYUFSOP -% EFCFVTBSTF C y2VÊSFMBDJÓOàOBMEFSFáVKPFYUFSOPEFCFVTBSTF

www.FreeLibros.me



%



%

%

%



%

$BQÎUVMP  %FTUJMBDJÓOJOUFSNJUFOUF

D y$VÃOUP QSPEVDUP EFTUJMBEP TF SFUJSB Z DVÃM FT MB DBOUJEBE àOBM  8àOBM  RVF RVFEB FO FM WBQPSJ[BEPS 6OTPMVUPOPWPMÃUJMTFEJTVFMWFFOLHNPMEFNFUBOPM%FTFBNPTJOUFSDBNCJBSFMTPMWFOUF QPSBHVB$PNPMBTPMVDJÓOZBFTUÃDPODFOUSBEB OPTFSFRVJFSFVOBQSJNFSBEFTUJMBDJÓOJOUFS NJUFOUFQBSBDPODFOUSBSMB%FTFBNPTRVFFMTPMVUPFTUÊDPOUFOJEPFOLHNPMEFTPMVDJÓO ZRVFDPOUFOHBEFBHVBZNPMEFNFUBOPM&TUPTFQVFEFIBDFSDPOVOBEFTUJMB DJÓOJOUFSNJUFOUFBOJWFMDPOTUBOUF PEFTUJMBOEPMBNF[DMBDPOBHVBZIBDJFOEPEFTQVÊTVOB EFTUJMBDJÓOJOUFSNJUFOUFTJNQMF-PTEBUPTEFFRVJMJCSJPWBQPSMÎRVJEP TJOUFOFSFODVFOUB FMFGFDUPEFMTPMVUP FTUÃOFOMBUBCMB-MFWFBDBCPVOBEFTUJMBDJÓOJOUFSNJUFOUFBOJWFM DPOTUBOUFEFTEFY. JOJDJBM NFUBOPMQVSP IBTUBY. àOBM$BMDVMFMBTNPMFTEFBHVB BHSFHBEBEVSBOUFMBEFTUJMBDJÓOJOUFSNJUFOUFBOJWFMDPOTUBOUFZMBTNPMFTEFBHVBFWBQPSBEB DPOFMNFUBOPMFOFMEFTUJMBEP-PTSFTVMUBEPTTFQVFEFODPNQBSBSDPOMBEJMVDJÓOTFHVJEB QPSEFTUJMBDJÓOJOUFSNJUFOUFTJNQMFFOFMQSPCMFNB& /PUB$PNPY. àOBMFTNVZQFRVFÒB ZFTNVZHSBOEFFOFTUFMÎNJUF6OBBQMJDBDJÓO EJSFDUBEFMBSFHMBEF4JNQTPO EFTEFYN JOJDJBMIBTUBY. àOBMOPTFSÃFYBDUB%FCF EJWJEJSTFMBJOUFHSBMFOBMNFOPTEPTTFDDJPOFT 4FVTBSÃVOEFTUJMBEPSJOUFSNJUFOUFTJNQMF VODPOUBDUPEFFRVJMJCSJP FMWBQPSJ[BEPS QBSB TFQBSBSLHNPMEFVOBNF[DMBEFOQFOUBOPZOPDUBOPBL1BEFQSFTJÓO-BBMJNFO UBDJÓODPOUJFOFNPMEFOQFOUBOP4FEFTFBRVFMBDPODFOUSBDJÓOàOBMFOFMWBQPSJ[BEPS TFBNPMEFOQFOUBOP$BMDVMFMBDBOUJEBEàOBMFOFMWBQPSJ[BEPS MBDBOUJEBEEFEFTUJMBEP SFDPMFDUBEPZMBGSBDDJÓONPMQSPNFEJPFOFMEFTUJMBEP 4FVTBVOEFTUJMBEPSJOUFSNJUFOUFTJNQMFQBSBQSPDFTBSLHNPMEFVOBNF[DMBRVFDPOUJFOF NPMEFBHVBZNPMEFOCVUBOPM4FEFTFBRVFMBDPODFOUSBDJÓOàOBMFOFMWBQPSJ[B EPSTFBNPMEFBHVB-BQSFTJÓOFTBUN-PTEBUPTEFFRVJMJCSJPFTUÃOFOMBUBCMB $BMDVMFMBDBOUJEBEàOBMFOFMWBQPSJ[BEPS MBDBOUJEBEEFEFTUJMBEPSFDPMFDUBEPZMBGSBDDJÓO NPMQSPNFEJPFOFMEFTUJMBEP4JUPEPFMMÎRVJEPEFTUJMBEPTFSFDJCFFOVOUBORVFBHJUBEPZTF EFKBTFEJNFOUBS yRVFEBSÃVOBPRVFEBSÃOEPTGBTFT 1BSBBQSPWFDIBSFMB[FÓUSPQPIFUFSPHÊOFPTFVTBFMTJTUFNBEFEFTUJMBDJÓOJOUFSNJUFOUFEFM QSPCMFNB%QBSBLHNPMEFBMJNFOUBDJÓODPONPMEFBHVBZNPMEFOCVUB OPM-BPQFSBDJÓOFTBBUN4FEFTFBVOBDPODFOUSBDJÓOàOBMFOFMWBQPSJ[BEPSEF NPMEFBHVB&MEFTUJMBEPTJFNQSFDPOUJFOFNPMEFBHVB-PTEBUPTEFFRVJMJCSJPFTUÃO FOMBUBCMB B y$VÃMFTTPO8àOBMZ%UPUBM C y$VÃMFTMBSFMBDJÓOJOJDJBMEFSFáVKPFYUFSOP -% D y$VÃMFTMBSFMBDJÓOàOBMEFSFáVKPFYUFSOP -% 2VFSFNPTIBDFSVOBEFTUJMBDJÓOJOUFSNJUFOUFEFLHNPMEFVOBNF[DMBEFBDFUPOBZFUBOPM -BBMJNFOUBDJÓODPOUJFOFNPMEFBDFUPOB4FRVJFSFRVFMBDPODFOUSBDJÓOàOBMFOFMWB QPSJ[BEPSTFBNPMEFBDFUPOB&MTJTUFNBEFEFTUJMBDJÓOJOUFSNJUFOUFFTUÃGPSNBEPQPS FMWBQPSJ[BEPSZVOBDPMVNOBDPOVOBFUBQBEFFRVJMJCSJP&MSFáVKPTFSFHSFTBDPNPMÎRVJEP TBUVSBEP ZMBSFMBDJÓOEFSFáVKPFYUFSOPTFNBOUJFOFDPOTUBOUFFO-%-BQSFTJÓOFT BUN-PTEBUPTEFFRVJMJCSJPWBQPSMÎRVJEPFTUÃOFOFMQSPCMFNB%$BMDVMFMBDBOUJEBEàOBM FOFMWBQPSJ[BEPS MBDBOUJEBEEFEFTUJMBEPSFDPMFDUBEPZMBGSBDDJÓONPMBSQSPNFEJPFOFMEFT UJMBEP$PNQBSFTVTSFTVMUBEPTDPOMPTEFMTJTUFNBJOUFSNJUFOUFTJNQMFEFMQSPCMFNB% 4FIBDFVOBEFTUJMBDJÓOJOUFSNJUFOUFEFVOBNF[DMBDPONPMEFNFUBOPMZNPMEF BHVBFOVOTJTUFNBDPOVOWBQPSJ[BEPSZVOBDPMVNOBDPOFUBQBEFFRVJMJCSJP FOUPUBM  DPOUBDUPTEFFRVJMJCSJP 'LHNPM&MTJTUFNBUSBCBKBBVOBDPODFOUSBDJÓODPOTUBOUFEFM EFTUJMBEPEFNPMEFNFUBOPM%FTFBNPTRVFMBDPODFOUSBDJÓOàOBMFOFMWBQPSJ[BEPSTFB

www.FreeLibros.me

5BSFB



NPMEFNFUBOPM&MSFáVKPFTVOMÎRVJEPTBUVSBEPZWBSÎBMBSFMBDJÓOEFSFáVKPFYUFSOP  -% 4VQPOHB EFSSBNF NPMBM DPOTUBOUF -PT EBUPT EF FRVJMJCSJP WBQPSMÎRVJEP FTUÃO FO MB UBCMB B $BMDVMF%UPUBMZ8àOBM LHNPM  C $BMDVMFFMWBMPSàOBMEFMBSFMBDJÓOEFSFáVKPFYUFSOP -% % %FTFBNPTIBDFSVOBEFTUJMBDJÓOJOUFSNJUFOUFBVOBNF[DMBEFFUBOPMZBHVB-BBMJNFOUBDJÓO DPOUJFOFNPMEFFUBOPM-BPQFSBDJÓOFTBBUN&MTJTUFNBEFEFTUJMBDJÓOJOUFSNJUFOUF DPOTJTUFFOVOWBQPSJ[BEPSNÃTVOBDPMVNOB DPOFMFRVJWBMFOUFEFDPOUBDUPTEFFRVJMJCSJP ZVODPOEFOTBEPSUPUBM5SBCBKBSFNPTBVOBSFMBDJÓOEFSFáVKPFYUFSOPDPOTUBOUFFJHVBMB -BDBSHBJOJDJBMBMWBQPSJ[BEPSFTLH%FTFBNPTRVFMBDPODFOUSBDJÓOàOBMFOFM WBQPSJ[BEPS DPOUFOHB  EF FUBOPM  GSBDDJÓO NPMBS -PT EBUPT EF FRVJMJCSJP FTUÃO FO MB UBCMB$POWJFSUBMBDBOUJEBEEFBMJNFOUBDJÓOFOLHNPMVTBOEPVOQFTPNPMFDVMBSQSPNF EJP$BMDVMF8àOBMZ%UPUBM FOLHNPM ZY% QSPN  /PUB&TDBMPOBSFUBQBTQBSBWBSJBTMÎOFBTEFPQFSBDJÓOQBSFDFEFNBTJBEPUSBCBKP4JOFN CBSHP EFTQVÊTEFIBCFSMPIFDIPVOBWF[OPUBSÃRVFIBZVODBNJOPDPSUPQBSBEFUFSNJOBSMB SFMBDJÓOFOUSFY%ZY8 % "WFDFTTVQMBOUBEFCFEFTUJMBSJOUFSNJUFOUFNFOUFVOBNF[DMBEFBDFUPOBZFUBOPM-BDBSHB JOJDJBMFTLHNPMEFVOBNF[DMBDPONPMEFBDFUPOB-BEFTUJMBDJÓOJOUFSNJUFOUFTF IBDFFOVOTJTUFNBDPOVOWBQPSJ[BEPSZFUBQBTEFFRVJMJCSJP4VKFGFEFTFBRVFMBDPODFO USBDJÓOEFMEFTUJMBEPTFBDPOTUBOUF JHVBMBY% GSBDDJÓONPMBSEFBDFUPOB-PTEBUPT FTUÃOFOFMQSPCMFNB% B 4JIVCJFSBEJTQPOJCMFVOBDBOUJEBEJOàOJUBEFFUBQBT yDVÃMTFSÎB -% NÎO  C $POMPTDPOUBDUPTEFFRVJMJCSJPEJTQPOJCMFT yDVÃMFTMBGSBDDJÓONPMBSNÎOJNBFOFMWB QPSJ[BEPSRVFUBMWF[TFQVFEBPCUFOFS SFáVKPUPUBM

D "QSPYJNBEBNFOUF yRVÊSFMBDJÓOEFSFáVKP -7 JOJDJBMEFCFVTBSTF E 4JMBNÃYJNBSFMBDJÓOEFSFáVKPRVFQVFEFVTBSTFFOMBQSÃDUJDBFT-7yDVÃMFTY8 àOBM F y$VÃMFTTPO8àOBMZ%UPUBM FOLHNPM  -BGPSNBGÃDJMFTVTBSCBMBODFTEFNBTBHFOFSBMZEF BDFUPOB

& &



1SPCMFNBTNÃTDPNQMFKPT 4FIBDFVOBEFTUJMBDJÓOJOUFSNJUFOUFEFPDUBOPM FOVOBFUBQBZQPSBSSBTUSFDPOWBQPSEFBHVB -BVOJEBEUSBCBKBBNN)H-BEFTUJMBDJÓOJOUFSNJUFOUFQPSBSSBTUSFDPOWBQPSEFBHVBTF USBCBKBFOQSFTFODJBEFBHVBMÎRVJEB&MWBQPSEFTUJMBEPTFDPOEFOTBZTFGPSNBOEPTDBQBTMÎRVJ EBTJONJTDJCMFT-BBMJNFOUBDJÓODPOUJFOFEFPDUBOPMZFMSFTUPTPODPNQVFTUPTPSHÃOJDPT OPWPMÃUJMFT-BBMJNFOUBDJÓOFTLHNPM%FTFBNPTSFDVQFSBSEFMPDUBOPM -PTEBUPTEFQSFTJÓOEFWBQPSQBSBFMBHVBFTUÃOFOFMQSPCMFNB%1BSBJOUFSWBMPTQF RVFÒPTEFUFNQFSBUVSBFTUPTEBUPTTFQVFEFOBKVTUBSBMBGPSNBEFMBFDVBDJÓOEF"OUPJOF  DPO$-BFDVBDJÓOEFQSFTJÓOEFWBQPSEFMPDUBOPMFTUÃFOFMQSPCMFNB% B $BMDVMFMBUFNQFSBUVSBEFPQFSBDJÓOEFMWBQPSJ[BEPSBMJOJDJBSZBMUFSNJOBSMBDPSSJEB C $BMDVMFMBDBOUJEBEEFNBUFSJBPSHÃOJDBRVFRVFEBFOFMWBQPSJ[BEPSBMàOBMEFMMPUF D $BMDVMFMBTNPMFTEFPDUBOPMSFDVQFSBEPFOFMEFTUJMBEP E $BMDVMFMBTNPMFTEFBHVBDPOEFOTBEBFOFMQSPEVDUPEFTUJMBEP1BSBFMMP VTFMBUFNQF SBUVSBQSPNFEJPEFMWBQPSJ[BEPSQBSBFTUJNBSMBQSFTJÓOEFWBQPSQSPNFEJPEFMPDUBOPM  RVFQVFEFTVQPOFSDPOTUBOUF1BSBJOUFHSBSOVNÊSJDBNFOUFMBFDVBDJÓO 

SFMBDJPOF YPSHDPOOPSH DPOVOCBMBODFEFNBTBFOUPSOPBMWBQPSJ[BEPSJOUFSNJUFOUF F $PNQBSFDPOTVSFTQVFTUBFOFMQSPCMFNB%y$VÃMTJTUFNBQSPEVDFNÃTBHVBFOFM EFTUJMBEP y1PSRVÊ

www.FreeLibros.me



$BQÎUVMP  %FTUJMBDJÓOJOUFSNJUFOUF

& 4FIBDFVOBEFTUJMBDJÓOQPSBSSBTUSFDPOWBQPSEFBHVB FOVOBFUBQB DPOLHNPMEFVOB BMJNFOUBDJÓORVFDPOUJFOFNPMEFPDJNFOP $) ZNPMEFDPNQVFTUPTOPWP MÃUJMFT-BEFTUJMBDJÓOTFIBDFFOQSFTFODJBEFBHVBMÎRVJEB&MWBQPSEFTUJMBEPTFDPOEFOTBZ TFGPSNBOEPTDBQBTMÎRVJEBTJONJTDJCMFT PDJNFOPZBHVB -BQSFTJÓOUPUBMFTNN)H %FTFBNPTSFDVQFSBSEFMPDJNFOP  -PTEBUPTEFQSFTJÓOEFWBQPSQBSBFMBHVBFTUÃOFOFMQSPCMFNB%1BSBJOUFSWBMPTQF RVFÒPTEFUFNQFSBUVSBMPTEBUPTTFQVFEFOBKVTUBSBVOBGPSNBEFFDVBDJÓOEF"OUPJOF DPO $-BQSFTJÓOEFWBQPSEFMPDJNFOPTFQVFEFDBMDVMBSDPOMBFDVBDJÓOEF"OUPJOF  MPH 17 "¢# 5 $

 $PO" # $ 5FOHSBEPTDFOUÎHSBEPTZ17FTMBQSFTJÓOEFWBQPS  FONN)H'VFOUF-BOHFT)BOECPPLPG$IFNJTUSZ ‰FEJDJÓO 1ÃH  B $BMDVMFMBDBOUJEBEEFTVTUBODJBPSHÃOJDBFOFMWBQPSJ[BEPSBMàOBMEFMBEFTUJMBDJÓO C $BMDVMFMBTNPMFTEFPDJNFOPSFDVQFSBEBTFOFMEFTUJMBEP D $BMDVMFMBTUFNQFSBUVSBTEFPQFSBDJÓOEFMWBQPSJ[BEPSBMJOJDJPZBMàOBMEFMBEFTUJMBDJÓO E $BMDVMFMBTNPMFTEFBHVBDPOEFOTBEBFOFMQSPEVDUPEFTUJMBEP6TFMBUFNQFSBUVSBQSP NFEJPEFMWBQPSJ[BEPSQBSBFTUJNBSVOBQSFTJÓOEFWBQPSQSPNFEJPEFPDJNFOP RVFTF TVQPOFDPOTUBOUF*OUFHSFOVNÊSJDBNFOUFMBFDVBDJÓO 

SFMBDJPOBOEPYPSHDPOOPSHDPO VOCBMBODFEFNBTBFOUPSOPBMWBQPSJ[BEPS & &OMBEFTUJMBDJÓOJOUFSNJUFOUFJOWFSUJEB MBDBSHBEFBMJNFOUBDJÓOTFDPMPDBFOFMBDVNVMBEPSEF MBQBSUFTVQFSJPSEFMBDPMVNOB àHVSB 4FBMJNFOUBMÎRVJEPBMBQBSUFTVQFSJPSEFMBDP MVNOB"MGPOEPEFMBDPMVNOBTFSFUJSBOMPTGPOEPTFOGPSNBDPOUJOVBZQBSUFEFMBDPSSJFOUF TFNBOEBBVOWBQPSJ[BEPSUPUBMTFFWBQPSBZTFSFHSFTBBMBDPMVNOB%VSBOUFFMDVSTPEFMB EFTUJMBDJÓOJOUFSNJUFOUF FMDPNQPOFOUFNFOPTWPMÃUJMTFFMJNJOBMFOUBNFOUFEFMMÎRVJEPFOFM BDVNVMBEPS ZBVNFOUBMBGSBDDJÓONPMBSEFMDPNQPOFOUFNÃTWPMÃUJM YE4VQPOJFOEPRVFMB SFUFODJÓOFOFMWBQPSJ[BEPSUPUBM DPOEFOTBEPSUPUBMZMPTQMBUPTFTQFRVFÒB FODPNQBSBDJÓO DPOMBSFUFODJÓOFOFMBDVNVMBEPS MBFDVBDJÓOEF3BZMFJHIQBSBMBEFTUJMBDJÓOJOUFSNJUFOUF JOWFSUJEBFT ac9[^cVa$;2−mVa^b ∫ mY![^cVa PYmY$mY ¶m7R

"MJNFOUBSFNPTFMTJTUFNBJOUFSNJUFOUFJOWFSUJEPRVFNVFTUSBMBàHVSBDPO'LHNPM EFVOBBMJNFOUBDJÓOGPSNBEBQPSNPMEFFUBOPMZNPMEFBHVB%FTFBNPTRVFMB GSBDDJÓONPMBSTFBFOFMEFTUJMBEPàOBM)BZEPTFUBQBTEFFRVJMJCSJPFOMBDPMVNOB&M WBQPSJ[BEPSUPUBM FMDPOEFOTBEPSUPUBMZFMBDVNVMBEPSOPTPODPOUBDUPTEFFRVJMJCSJP-PT EBUPTEFFRVJMJCSJPWBQPSMÎRVJEPTFFODVFOUSBOFOMBUBCMB$BMDVMF%àOBM #UPUBMZY# QSPN TJ MBSFMBDJÓOEFWBQPSBMGPOEPFT & 4FEJTVFMWFVOTPMVUPOPWPMÃUJMFOLHNPMEFNFUBOPM%FTFBNPTDBNCJBSFMTPMWFOUFQPS BHVB$PNPMBTPMVDJÓOZBFTUÃDPODFOUSBEB OPTFSFRVJFSFVOBQSJNFSBEFTUJMBDJÓOJOUFSNJ UFOUFQBSBDPODFOUSBSMB%FTFBNPTRVFFMTPMVUPUFOHBLHNPMEFTPMVDJÓODPOEF BHVBZNPMEFNFUBOPM&TUPTFQVFEFIBDFSZBTFBDPOVOBEFTUJMBDJÓOJOUFSNJUFOUFB OJWFM DPOTUBOUF  P CJFO EJMVZFOEP MB NF[DMB DPO BHVB  QBSB FOUPODFT IBDFS VOB EFTUJMBDJÓO JOUFSNJUFOUFTJNQMF-PTEBUPTEFFRVJMJCSJPWBQPSMÎRVJEP OPUFOHBFODVFOUBFMFGFDUPEFM TPMVUP FTUÃOFOMBUBCMB%JMVZBFMNFUBOPMPSJHJOBMQVSP NÃTTPMVUP DPOBHVB ZBDPO UJOVBDJÓOIBHBVOBEFTUJMBDJÓOJOUFSNJUFOUFTJNQMF QBSBUSBUBSEFPCUFOFS8àOBMZY. àOBM $BMDVMFMBTNPMFTEFBHVBBHSFHBEBTZMBTNPMFTEFBHVBFWBQPSBEBTEVSBOUFMBEFTUJ MBDJÓOJOUFSNJUFOUF$PNQBSFTVTSFTVMUBEPTDPOMBEFTUJMBDJÓOJOUFSNJUFOUFBOJWFMDPOTUBOUF EFMQSPCMFNB%

www.FreeLibros.me

$"1±56-0 

%JTFÒPEFDPMVNOBTEFQMBUPT ZFNQBDBEBT

&OMPTDBQÎUVMPTBOUFSJPSFTWJNPTDÓNPEFUFSNJOBSMBDBOUJEBEEFFUBQBTEFFRVJMJCSJPZMBTFQBSBDJÓO FOMBTDPMVNOBTEFEFTUJMBDJÓO&OMBQSJNFSBQBSUFEFFTUFDBQÎUVMPEFTDSJCJSFNPTMPTEFUBMMFTEFM EJTFÒPEFDPMVNOBTEFQMBUPTDPNPMBHFPNFUSÎBEFMPTQMBUPT MBEFUFSNJOBDJÓOEFMBFàDJFODJBEF MBDPMVNOB FMDÃMDVMPEFMEJÃNFUSPEFMBDPMVNOB FMUBNBÒPEFM PEFMB CBKBOUFZMBEJTUSJCVDJÓO EFMQMBUP$PNFO[BSFNPTDPOVOBEFTDSJQDJÓODVBMJUBUJWBEFMBTQBSUFTJOUFSOBTFOMBTDPMVNOBT QBSB FOUPODFTQSPDFEFSBVOBEFTDSJQDJÓODVBOUJUBUJWBEFMDÃMDVMPEFMBFàDJFODJB MBEFUFSNJOBDJÓOEFMEJÃ NFUSPEFMBDPMVNOB FMEJTFÒPEFQMBUPTQFSGPSBEPTZFMEJTFÒPEFQMBUPTZEFWÃMWVMBT&OMBTFHVOEB QBSUF TFDDJPOFTB EFTDSJCJSFNPTFMEJTFÒPEFDPMVNOBTFNQBDBEBT JODMVZFOEPMBTFMFDDJÓO EFMPTNBUFSJBMFTEFFNQBRVF ZMBEFUFSNJOBDJÓOEFMBMPOHJUVEZFMEJÃNFUSPEFMBDPMVNOB4FFTQFSB RVFMPTJOHFOJFSPTSFDJÊOFHSFTBEPTQVFEBOIBDFSFTUPTDÃMDVMPT-BTQBSUFTJOUFSOBTEFMBTDPMVNOBT EFEFTUJMBDJÓOTVFMFOEJTFÒBSTFCBKPMBTVQFSWJTJÓOEFFYQFSUPTDPONVDIPTBÒPTEFFYQFSJFODJB &TUFDBQÎUVMPOPFTVOBUBKPQBSBWPMWFSTFFYQFSUPTJOFNCBSHP BMUFSNJOBSMPEFCFSÎBQPEFS FKFDVUBSVOEJTFÒPQSFMJNJOBSEFMBTQBSUFTJOUFSOBTEFMBTDPMVNOBTEFQMBUPTZFNQBDBEBT ZQPEFS EJTDVUJSDPOFYQFSUPT FOGPSNBJOUFMJHJCMF MPTEJTFÒPTQBSBEFTUJMBDJÓO  %&4$3*1$*¶/%&-04&26*104&/-"4$0-6./"4%&1-"504

&OFMDBQÎUVMPTFQSFTFOUÓVOBJNBHFOCÃTJDBEFMFRVJQPFOMBTDPMVNOBTEFQMBUPTFOFTUBTFDDJÓO QSFTFOUBSFNPTVODVBESPDVBMJUBUJWPNVDIPNÃTEFUBMMBEP(SBOQBSUFEFMNBUFSJBMRVFTFJODMVZF BRVÎQSPWJFOFEFVOBTFSJFEFBSUÎDVMPTZMJCSPTEF,JTUFS    

FMMJCSPEF-VEXJH  ZFMDBQÎUVMPEF-BSTPOZ,JTUFS  1BSBDPOPDFSNÃTEFUBMMFT DPOTVMUFFTBTGVFOUFT -PTQMBUPTEFQMBDBTQFSGPSBEBTRVFTFJMVTUSBSPOFOMBàHVSBTPOGÃDJMFTEFGBCSJDBSZOPTPO DPTUPTPT-PTBHVKFSPTTFUSPRVFMBOPCBSSFOBO MPDVBMFTNÃTDBSP FOMBQMBDBNFUÃMJDB)BZCBT UBOUFJOGPSNBDJÓOEJTQPOJCMFQBSBFMEJTFÒPZ DPNPMPTEJTFÒPTOPTPOQBUFOUBEPT DVBMRVJFSBQVFEF DPOTUSVJSVOBDPMVNOBEFQMBUPTQFSGPSBEPT-BFàDJFODJBFTCVFOBFOMBTDPOEJDJPOFTEFEJTFÒP4JO FNCBSHP FOFMSFDIB[P RVFFTFMGVODJPOBNJFOUPBMPQFSBSBNFOPTEFMáVKPEFEJTFÒP FTSFMBUJWB NFOUFNBMP&TPRVJFSFEFDJSRVFMBPQFSBDJÓOBáVKPTBQSFDJBCMFNFOUFNFOPSFTRVFMBTDPOEJDJPOFT EFEJTFÒPIBSÃRVFMBFàDJFODJBTFBNFOPS1BSBMPTQMBUPTQFSGPSBEPT MBFàDJFODJBCBKBNVDIPDPO áVKPTEFHBTNFOPSFTRVFBQSPYJNBEBNFOUFEFMWBMPSEFEJTFÒP1PSMPUBOUP FTPTQMBUPTOPTPO 

www.FreeLibros.me



$BQÎUVMP  %JTFÒPEFDPMVNOBTEFQMBUPTZFNQBDBEBT

NVZáFYJCMFT-PTQMBUPTQFSGPSBEPTTPONVZCVFOPTFOBQMJDBDJPOFTTVDJBTPDVBOEPIBZTÓMJEPTQSF TFOUFT QPSRVFTPOGÃDJMFTEFMJNQJBS"DUVBMNFOUF MPTQMBUPTQFSGPSBEPTTPODPNVOFTFOMBJOEVTUSJB QFSPFTQSPCBCMFRVFMBTOVFWBTDPMVNOBTUFOHBOQMBUPTEFWÃMWVMBT ,JTUFS   -PTQMBUPTEFWÃMWVMBTTFEJTFÒBOQBSBUFOFSNFKPSFTQSPQJFEBEFTEFSFDIB[PRVFMPTQMBUPT QFSGPSBEPT QPSMPRVFTPONÃTáFYJCMFTDVBOEPWBSÎBMBUBTBEFBMJNFOUBDJÓO)BZNVDIPTEJTFÒPT QBUFOUBEPTEFQMBUPTEFWÃMWVMBTVOPEFFMMPTTFJMVTUSBFOMBàHVSB&MQMBUPEFWÃMWVMBTFQB SFDFBVOPQFSGPSBEPQPSRVFUJFOFVOQJTPDPOBHVKFSPTQBSBRVFQBTFFMHBT ZCBKBOUFTQBSBFMáVKP EFMÎRVJEP-BEJGFSFODJBFTRVFMPTBHVKFSPT RVFTPOCBTUBOUFHSBOEFT FTUÃOFRVJQBEPTDPOiWÃM WVMBTuUBQBTRVFQVFEFOTVCJSZCBKBSDVBOEPDBNCJBOMBTQSFTJPOFTFOFMWBQPSZFMMÎRVJEP$BEB WÃMWVMB UJFOF QBUBT  P VOB KBVMB  RVF SFTUSJOHFO TV NPWJNJFOUP EF TVCJEB -BT WÃMWVMBT SFEPOEBT DPOQBUBTTPODPNVOFT QFSPFMEFTHBTUFEFMBTQBUBTQVFEFTFSVOQSPCMFNB ,JTUFS  "BMUBT WFMPDJEBEFTEFWBQPS MBWÃMWVMBTFFODPOUSBSÃUPUBMNFOUFBCJFSUBZQSPQPSDJPOBSÃVOBBCFSUVSB P SFOEJKB NÃYJNBQBSBFMáVKPEFMHBT WFBMBàHVSB $VBOEPEJTNJOVZFMBWFMPDJEBEEFMHBT  MBWÃMWVMBCBKB&TPNBOUJFOFDBTJDPOTUBOUFBMBWFMPDJEBEEFMHBTRVFQBTBQPSMBSFOEJKB MPRVF

'*(63" " $0/+6/50%&6/"7¦-76-"(-*54$)"# 1-"50(-*54$) "1&26&µ0 %&#"-"453&$035&4±"%&(-*54$) */$ %"--"4 5&9"4

www.FreeLibros.me

  %FTDSJQDJÓOEFMPTFRVJQPTFOMBTDPMVNOBTEFQMBUPT



NBOUJFOFMBFàDJFODJBDBTJDPOTUBOUFZFWJUBFMHPUFP6OBWÃMWVMBJOEJWJEVBMFTFTUBCMFTÓMPFOMBQP TJDJÓOUPUBMNFOUFDFSSBEBPUPUBMNFOUFBCJFSUB"WFMPDJEBEFTJOUFSNFEJBT BMHVOBTEFMBTWÃMWVMBT FOFMQMBUPFTUBSÃOBCJFSUBTZBMHVOBTFTUBSÃODFSSBEBT&OFMDBTPOPSNBM MBTWÃMWVMBTBMUFSOBOFOUSF MBTQPTJDJPOFTBCJFSUBZDFSSBEB-BWÃMWVMBWFOUVSJUJFOFFMMBCJPEFMBHVKFSPWJFOEPIBDJBBSSJCB  QBSBQSPEVDJSVOBBCFSUVSBUJQPWFOUVSJ RVFNJOJNJ[BMBDBÎEBEFQSFTJÓO "MBUBTBEFáVKPEFEJTFÒPQBSBFMWBQPS MPTQMBUPTEFWÃMWVMBTUJFOFONÃTPNFOPTMBNJTNB FàDJFODJB RVF MPT QMBUPT QFSGPSBEPT 4JO FNCBSHP  TVT DBSBDUFSÎTUJDBT EF SFDIB[P TPO NFKPSFT FO HFOFSBMZMBFàDJFODJBQFSNBOFDFBMUBDVBOEPCBKBFMáVKPEFHBT5BNCJÊOTFQVFEFOEJTFÒBSQBSB UFOFSNFOPSDBÎEBEFQSFTJÓORVFMPTQMBUPTQFSGPSBEPT BVORVF FOFMDBTPOPSNBM MBDBÎEBEFQSF TJÓOTFSÃNBZPSRVFMBEFMPTQMBUPTQFSGPSBEPT-BTEFTWFOUBKBTEFMPTQMBUPTEFWÃMWVMBTTPORVF DVFTUBOVONÃTRVFMPTQMBUPTQFSGPSBEPT (MJUTDI  ZRVFTPONÃTQSPQFOTPTBFOTVDJBSTF PUBQBSTFTJTFEFTUJMBOTPMVDJPOFTTVDJBT &OMBàHVSBTFJMVTUSBOCBSCPUFBEPSFTQBSBQMBDBT&OFMCBSCPUFBEPS PDBQVDIBEFCVS CVKFP IBZVOBTVCJEBPWFSUFEPSFOUPSOPBDBEBBHVKFSPEFMQMBUP6OBDBQVDIBDPOSBOVSBTP BHVKFSPT TF DPMPDB TPCSF FTUB TVCJEB Z FM WBQPS CVSCVKFB QPS FTPT BHVKFSPT &TUF EJTFÒP FT NVZ áFYJCMFZUSBCBKBFOGPSNBTBUJTGBDUPSJBBUBTBTEFáVKPEFMÎRVJEPNVZBMUBTZNVZCBKBT4JOFN CBSHP FMBSSBTUSFFTBQSPYJNBEBNFOUFFMUSJQMFRVFFOVOQMBUPQFSGPSBEPZ FOHFOFSBM IBCSÃVO HSBEJFOUFBQSFDJBCMFEFMÎRVJEPBUSBWÊTEFMQMBUP&MSFTVMUBEPOFUPFTRVFMBBMUVSBFOUSFQMBUPT EFCF TFS CBTUBOUF NBZPS RVF QBSB MPT QMBUPT QFSGPSBEPT -B BMUVSB QSPNFEJP FOUSF QMBUPT FO MBT DPMVNOBTQFRVFÒBTFTEFVOBTQVMHBEBT NJFOUSBTRVFFOMBTEFTUJMBDJPOFTBMWBDÎPTFVTBOEF BQVMHBEBT-BTFàDJFODJBTTVFMFOTFSJHVBMFTPNFOPSFTRVFQBSBMPTQMBUPTQFSGPSBEPTZDPO GSFDVFODJBMBTDBSBDUFSÎTUJDBTEFSFDIB[PTPOQFPSFT-BDBQVDIBEFCVSCVKFPUJFOFQSPCMFNBTDPO DPRVJ[BDJPOFT GPSNBDJÓOEFQPMÎNFSPTPDPONF[DMBTRVFFOTVDJFONVDIP-PTQMBUPTDPODBQVDIBT EFCVSCVKFPDVFTUBOVOBTDVBUSPWFDFTNÃTRVFMPTQMBUPTEFWÃMWVMBT (MJUTDI  "DUVBMNFO UF TFFTUÃODPOTUSVZFOEPNVZQPDBTDPMVNOBTOVFWBTDPODBQVDIBTEFCVSCVKFP4JOFNCBSHP FT QSPCBCMFRVFMPTJOHFOJFSPTSFDJÊOFHSFTBEPTWFBODPMVNOBTBOUFSJPSFTDPODBQVDIBTEFCVSCVKFP RVFUPEBWÎBFTUÃOUSBCBKBOEP)BZHSBOEFTDBOUJEBEFTEFEBUPTEJTQPOJCMFTQBSBEJTFÒBSQMBUPTDPO

'*(63" %*7&3404%*4&µ04%&#"3#05&"%03&4 5"1"4%&#63#6+&0  '"#3*$"%04103(-*54$) */$ $035&4±"%&(-*54$) */$ %"--"4 5&9"4

www.FreeLibros.me



$BQÎUVMP  %JTFÒPEFDPMVNOBTEFQMBUPTZFNQBDBEBT

DBQVDIBTEFCVSCVKFP:BRVFFYJTUFOEFTDSJQDJPOFTFYDFMFOUFTTPCSFFMEJTFÒPEFMBTDPMVNOBTEF CBSCPUFBEPSFT #PMMFT -VEXJH 

OPQSFTFOUBSFNPTBRVÎTVTEFUBMMFT -BTQMBDBTQFSGPSBEBTTJOCBKBOUFTTFQBSFDFOBMBTQMBDBTQFSGPSBEBTOPSNBMFT QFSPDPOBHVKF SPTCBTUBOUFNBZPSFT-BQMBDBTFEJTFÒBQBSBRVFFMMÎRVJEPHPUFFBUSBWÊTEFMPTBHVKFSPTBMNJTNP UJFNQPRVFFMWBQPSQBTBQPSFMDFOUSPEFMBHVKFSP-BWFOUBKBEFFTUFEJTFÒPFTRVFTFFMJNJOBFM DPTUPZFMFTQBDJPSFMBDJPOBEPDPOMPT PMBT CBKBOUFT4VNBZPSEFTWFOUBKBFTRVFOPFTSPCVTUB &TUPFT TJBMHPFTUÃNBM MBDPMVNOBOPUSBCBKBSÃFOBCTPMVUPFOMVHBSEFPQFSBSBNFOPSFàDJFODJB &TBTDPMVNOBTTVFMFOFTUBSEJTFÒBEBTQPSMBFNQSFTBRVFWFOEFFMTJTUFNB-VEXJH  QSFTFOUB BMHVOPTEFUBMMFTTPCSFTVEJTFÒP 10.1.1

Platos, bajantes y vertederos

"EFNÃTEFTFMFDDJPOBSFMUJQPEFQMBUP FMEJTFÒBEPSEFCFTFMFDDJPOBSMBQBVUBEFáVKPTPCSFMPT QMBUPTZEJTFÒBSMPTWFSUFEPSFT PWFSUFEFSPT PSFCPTBEFSPT ZMPTCBKBOUFT&OFTUBTFDDJÓODPOUJ OVBSFNPTTJFOEPDVBMJUBUJWPT -BQBVUBEFáVKPNÃTDPNÙOTPCSFVOQMBUPFTMBUSBOTWFSTBM RVFTFWFFOMBàHVSBZTF SFQJUFFOMBàHVSB"&TUBQBVUBGVODJPOBCJFOQBSBUBTBTQSPNFEJPEFáVKPZQVFEFEJTFÒBSTF QBSBNBOFKBSTÓMJEPTTVTQFOEJEPTFOMBBMJNFOUBDJÓO&MVTVBSJPQVFEFEJTFÒBSMPTQMBUPTEFáVKP USBOTWFSTBMDPOCBTFFOMBJOGPSNBDJÓOFOMBTQVCMJDBDJPOFT #PMMFT 'BJS    ,JTUFS   -VEXJH 

BQBSUJSEFJOGPSNBDJÓOFOMPTNBOVBMFTEFEJTFÒPEFMBT DPNQBÒÎBT (MJUTDI ,PDI 

PDPOBMHVOPTEFMPTGBCSJDBOUFTEFDPMVNOBTEFEFTUJMBDJÓO EFQMBUPT.ÃTBEFMBOUFEFTDSJCJSFNPTMPTEFUBMMFTEFEJTFÒPQBSBMPTQMBUPTEFáVKPUSBOTWFSTBM -PTQMBUPTEFWBSJPTQBTPTTFVTBOFODPMVNOBTEFHSBOEJÃNFUSPDPOBMUPTáVKPTEFMÎRVJEP -PTQMBUPTEFEPCMFQBTP àHVSB# TPODPNVOFT 1JMMJOH  &MáVKPEFMÎRVJEPTFEJWJEF FOEPTQBSUFT PQBTPT QBSBSFEVDJSFMHSBEJFOUFEFMÎRVJEPTPCSFFMQMBUPZSFEVDJSMBDBSHBTPCSF FMCBKBOUF$PODBSHBTEFMÎRVJEPUPEBWÎBNBZPSFT TFVTBOQMBUPTEFDVBUSPQBTPT 1JMMJOH   &TUFUJQPEFQMBUPTVFMFTFSEJTFÒBEPQPSFYQFSUPT BVORVFTFQVFEFOPCUFOFSEJTFÒPTQSFMJNJOBSFT TJHVJFOEPMBTJOEJDBDJPOFTFOMPTNBOVBMFTEFEJTFÒPRVFQVCMJDBOBMHVOPTGBCSJDBOUFTEFMFRVJQP (MJUTDI ,PDI   y$VÃMEJTUSJCVDJÓOEFáVKPTFSÃBEFDVBEBQBSBVOQSPCMFNBEBEP "NFEJEBRVFBVNFOUBOMPT áVKPTEFMÎRVJEP BVNFOUBFMEJÃNFUSPEFMBUPSSF4JOFNCBSHP MBDBQBDJEBEQBSBNBOFKBSFMáVKP EFMÎRVJEPBVNFOUBDPOMBMPOHJUVEEFMWFSUFEPS NJFOUSBTRVFMBDBQBDJEBEEFáVKPEFHBTBVNFOUB DPOFMDVBESBEPEFMEJÃNFUSPEFMBUPSSF"TÎ BMàOBMTFOFDFTJUBSÃOQMBUPTEFWBSJPTQBTPT&OMB

'*(63" 1"65"4%&'-6+040#3&1-"504 " '-6+053"/47&34"-# %0#-&1"40

www.FreeLibros.me

  %FTDSJQDJÓOEFMPTFRVJQPTFOMBTDPMVNOBTEFQMBUPT



Capacidad de líquido, Gal/min

Doble paso

Flujo transversal

Flujo inverso

Diámetro de la torre, pies

'*(63" (6±"1"3"4&-&$$*0/"3 1-"5041&3'03"%043&*.13&40$0/ "6503*;"$*0/&4%&)6"/(:)0%40/  1&530-&6.3&'*/&3  

 

 $01:3*()5 (6-'16#$0

àHVSB )VBOHZ)PETPO  TFQSFTFOUBVOBHVÎBEFTFMFDDJÓO QFSPTÓMPFTBQSPYJNBEB FO FTQFDJBMDFSDBEFMBTMÎOFBTRVFTFQBSBOMPTEJTUJOUPTUJQPTEFQMBUPT -PTCBKBOUFTZMPTWFSUFEPSFTTPONVZJNQPSUBOUFTQBSBMBPQFSBDJÓODPSSFDUBEFMBTDPMVNOBT EFFUBQBTQPSRVFDPOUSPMBOMBEJTUSJCVDJÓOZFMáVKPEFMMÎRVJEP4FVTBOEJWFSTPTEJTFÒPT&OMBàHVSB TFNVFTUSBODVBUSP ,JTUFS F  &OMBTDPMVNOBTQFRVFÒBTZMBTQMBOUBTQJMPUPTFTVFMF VTBSFMUVCPDJSDVMBSEFMBàHVSB"&TFUVCPQVFEFTPCSFTBMJSEFMQMBUPQBSBTFSWJSDPNPWFSUFEPS PVTBSTFVOWFSUFEPSTFQBSBEP&OFMEJTFÒP0MEFSTIBX EFVTPDPNÙOFOQMBOUBTQJMPUP FMUVCPFTUÃ FOFMDFOUSPEFMQMBUPQFSGPSBEPZFTUÃSPEFBEPQPSBHVKFSPT&MEJTFÒPNÃTGSFDVFOUFFOMBTDPMVNOBT Vertedor Vertedor opcional Vertedor Tubo redondo Vertedor Vertedor

Bajante Vertedor

www.FreeLibros.me

'*(63"  %*4&µ04%& #"+"/5&4: 7&35&%03&4 " 56#0$*3$6-"3 # 3&$50 4&(.&/5"%0 $ #"+"/5&4$0/ 1&/%*&/5& % &/70-7&/5&



$BQÎUVMP  %JTFÒPEFDPMVNOBTEFQMBUPTZFNQBDBEBT

DPNFSDJBMFTFTFMCBKBOUFWFSUJDBMTFHNFOUBEPEFMBàHVSB#&TUFUJQPFTQPDPDPTUPTPFOTVDPOT USVDDJÓO GÃDJMEFJOTUBMBS FTDBTJJNQPTJCMFJOTUBMBSMPFOGPSNBJODPSSFDUBZTFQVFEFEJTFÒBSQBSBVOB HSBOWBSJFEBEEFáVKPTEFMÎRVJEP4JTFEJàDVMUBMBTFQBSBDJÓOMÎRVJEPWBQPS QVFEFVTBSTFVOPEFMPT EJTFÒPTTFHNFOUBEPTDPOQFOEJFOUFEFMBàHVSB$&TPTEJTFÒPTBZVEBOBNBOUFOFSFMÃSFBBDUJWB EFMQMBUPEFBCBKP%FTBGPSUVOBEBNFOUFTPONÃTDPTUPTPTZFTGÃDJMJOTUBMBSMPTBMSFWÊT1BSBUBTBTEF áVKPMÎRVJEPNVZQFRVFÒBT BWFDFTTFVTBFMEJTFÒPEFFOWPMWFOUFRVFNVFTUSBMBàHVSB% &MEJTFÒPNÃTTJNQMFEFWFSUFEPSFTFMSFDUPIPSJ[POUBM DPOBQVMHBEBTEFBMUVSB àHVSBT Z &TUFUJQPFTFMNFOPTDPTUPTP QFSPOPUJFOFMBTNFKPSFTDBSBDUFSÎTUJDBTEFSFDIB[P&M WFSUFEPSBKVTUBCMFEFMBàHVSB"FTBUSBDUJWPQPSRVFQBSFDFSFTPMWFSFMQSPCMFNBEFMSFDIB[P %FTBGPSUVOBEBNFOUF TJTFBKVTUBNBM QVFEFDBVTBSNVDIPTQSPCMFNBT DPNPVOHPUFPFYDFTJWPP CJFORVFTFTFRVFOMPTQMBUPT QPSMPRVFEFCFFWJUBSTF$VBOEPTFEFTFBUFOFSáFYJCJMJEBEFOáVKPT EFMÎRVJEP VOPEFMPTWFSUFEPSFTDPONVFTDBT PEFDFSDBEFWBMMB RVFTFWFOFOMBàHVSB# USBCBKBCJFO 1JMMJOH  ZOPTPONVDIPNÃTDPTUPTPTRVFVOWFSUFEPSSFDUP-PTWFSUFEPSFTEF NVFTDBTTPOÙUJMFTFOQBSUJDVMBSDPOCBKPTáVKPTEFMÎRVJEP -PTQMBUPT WFSUFEPSFTZCBKBOUFTOFDFTJUBOFTUBSTPQPSUBEPTNFDÃOJDBNFOUF&TPTFJMVTUSBFO MBàHVSB ;FO[  -BJEFBFTTPQPSUBSFOGPSNBBEFDVBEBFMQFTPEFMQMBUPNÃTMBNÃYJNB DBSHBQPTJCMFEFMÎRVJEPRVFQVFEBUFOFS TJOFTUPSCBSEFNBTJBEPFMÃSFBEFáVKPEFWBQPSOJFMÃSFB BDUJWBEFMQMBUP"MBVNFOUBSFMEJÃNFUSPEFMBDPMVNOBTFWVFMWFNÃTDSÎUJDPFMTPQPSUFEFMQMBUP 7FBNÃTEFUBMMFTFO-VEXJH  P,JTUFS E    10.1.2

Entradas y salidas

-BTDPOFYJPOFTEFFOUSBEBZTBMJEBEFCFOEJTFÒBSTFDPODVJEBEPQBSBFWJUBSQSPCMFNBT ,JTUFS B  C   (MJUTDI -VEXJH  4FEFCFEJTFÒBSMBTFOUSBEBTQBSBFWJUBSUBOUPEF NBTJBEPHPUFPDPNPBSSBTUSFDVBOEPFOUSBWBQPSBHSBOWFMPDJEBE&OMBàHVSBTFWFOWBSJPTEJ TFÒPTBDFQUBCMFTQBSBVOBBMJNFOUBDJÓOPVOSFáVKPBMQMBUPTVQFSJPS-BQMBDBEFTWJBEPSBPDPEPEFM UVCPFWJUBRVFFMáVJEPBBMUBWFMPDJEBETBMHBEJTQBSBEPDSV[BOEPFMQMBUP-PTEJTFÒPTEFMBTàHVSBT %Z&TFQVFEFOVTBSDVBOEPIBZBQSPCBCJMJEBEEFDPOUFOJEPEFWBQPSFOMBBMJNFOUBDJÓO&TPT EPTEJTFÒPTOPQFSNJUJSÃORVFIBZBEFNBTJBEPBSSBTUSF-BJOUSPEVDDJÓOEFMBBMJNFOUBDJÓOFOQMBUPT JOUFSNFEJPTFTQBSFDJEBZFOMBàHVSBTFNVFTUSBOWBSJPTEJTFÒPTGSFDVFOUFT-BTBMJNFOUBDJPOFT MÎRVJEBTDPOCBKBWFMPDJEBEQVFEFOFOUSBSBUSBWÊTEFMMBEPEFMBDPMVNOB DPNPNVFTUSBMBàHVSB "&OMBTàHVSBT#Z$TFWFOBMJNFOUBDJPOFTBWFMPDJEBEFTNBZPSFTRVFDPOUJFOFOWBQPSZ SFRVJFSFOQMBDBTEFTWJBEPSBT&MWBQPSTFEJSJHFIBDJBMPTMBEPTPIBDJBBCBKPQBSBFWJUBSVOBSSBTUSF FYDFTJWP$VBOEPIBZVOBHSBODBOUJEBEEFWBQPSFOMBBMJNFOUBDJÓO FMQMBUPEFBMJNFOUBDJÓOEFCF UFOFSVOFTQBDJPBEJDJPOBMQBSBTFQBSBSMÎRVJEPZWBQPS1BSBDPMVNOBTEFHSBOEJÃNFUSP TFVTBDPO GSFDVFODJBBMHÙOUJQPEFEJTUSJCVJEPSDPNPFMEFMBàHVSB% &MSFHSFTPEFMWBQPSBMGPOEPEFMBDPMVNOBEFCFTBMJSBMNFOPTQVMHBEBTTPCSFMBTVQFSàDJF EFMMÎRVJEP DPNPTFWFFOMBàHVSB"&MPCKFUPEFMBCBOEFKBEFTFMMPFTNBOUFOFSBMMÎRVJEP FOFMCBKBOUF-BFOUSBEBEFWBQPSOPEFCFDIPDBSTPCSFFMMÎRVJEP DPNPNVFTUSBMBàHVSB#

'*(63" %*4&µ04%& 7&35&%03" "+645"#-&  # $0/.6&4$"4

www.FreeLibros.me

  %FTDSJQDJÓOEFMPTFRVJQPTFOMBTDPMVNOBTEFQMBUPT



Registro de hombre Bajante y vertedor Zona de calmado

Viga principal

Anillo de soporte de plato

Viga principal, con conexiones soldadas a la pared de la torre

Viga secundaria con conexión de soporte

Viga principal

Viga secundaria con conexión de soporte Viga secundaria con conexión de soporte Anillo de soporte del plato, hecho de ángulo

Sujeciones periféricas al anillo. Viga secundaria Observe el plato ranurado, con conexión Anillo de soporte sujeto por fricción, para facilitar de soporte de ángulo acomodos térmicos

'*(63" 401035&4.&$¦/*$041"3"1-"5041&3'03"%04 %&;&/;  3&*.13&40 $0/"6503*;"$*¶/%&4$)8&*5;&3 )"/%#00,0'4&1"3"5*0/5&$)/*26&4'03$)&.*$"- &/(*/&&34 5&3$&3"&%*$*¶/ ¥ .$(3"8)*-- /6&7":03, $VBOEPTFVTBVOWBQPSJ[BEPSEFUFSNPTJGÓO VOUJQPGSFDVFOUFEFWBQPSJ[BEPS

SFTVMUBÙUJMMBTBMJ EBEJWJEJEBRVFNVFTUSBMBàHVSB$ -BTTBMJEBTMÎRVJEBTJOUFSNFEJBTOFDFTJUBOBMHÙONÊUPEPEFTFQBSBDJÓOEFMÎRVJEPZWBQPS-B GPSNBNFOPTDPTUPTBEFIBDFSMPFTDPOVOBTBMJEBEFMCBKBOUFDPNPTFWFFOMBàHVSB"6O NÊUPEPNÃTDPTUPTPQFSPNÃTTFHVSPFTVTBSVOQMBUPDPODIJNFOFB T  àHVSB# ­TUFQSPQPS DJPOBVOWPMVNFOMÎRVJEPTVàDJFOUFQBSBMMFOBSMBTUVCFSÎBTZQFSNJUJSFMBSSBORVFEFMBTCPNCBT/P IBZBHVKFSPTOJWÃMWVMBTFOMBQMBDBEFFTUFQMBUP FOUPODFT OPDVFOUBQBSBMBUSBOTGFSFODJBEFNBTBZ OPEFCFDPOUBSTFDPNPFUBQBEFFRVJMJCSJP$POGSFDVFODJB MPTQMBUPTEFDIJNFOFBTPQPSUBOCBTUBOUF

'*(63" &/53"%"41"3" 3&'-6+00"-*.&/5"$*¶/"-1-"50 461&3*03

www.FreeLibros.me



$BQÎUVMP  %JTFÒPEFDPMVNOBTEFQMBUPTZFNQBDBEBT

Canal deflector

'*(63" 4*45&."4%& "-*.&/5"$*¶/*/5&3.&%*" " &/53"%"-"5&3"-  # :$ %&'-&$503&4  % %*453*#6*%03 MÎRVJEP ZFODPOTFDVFODJBTPOJNQPSUBOUFTTVTTPQPSUFTNFDÃOJDPT ,JTUFS  6OBBMUFSOBUJWB QBSBFMQMBUPEFDIJNFOFBFTVTBSVOBTBMJEBEFMCBKBOUFDPOVOUBNCPSFYUFSOPEFSFUFODJÓO &MEJTFÒPEFMBTTBMJEBTEFWBQPSFTSFMBUJWBNFOUFTFODJMMPZFTNFOPTQSPQFOTPBDBVTBSQSPCMF NBTRVFMBTTBMJEBTEFMÎRVJEP ,JTUFS  -BDPOTJEFSBDJÓOQSJODJQBMFTRVFMBUVCFSÎBEFCFUFOFS VOEJÃNFUSPTVàDJFOUFNFOUFHSBOEFDPNPQBSBRVFMBDBÎEBEFQSFTJÓOTFBNPEFTUB&OMBQBSUF TVQFSJPSEFMBDPMVNOBTFEFCFVTBSVOTFQBSBEPSEFOJFCMBQBSBFWJUBSFMBSSBTUSFEFMÎRVJEP6OB BMUFSOBUJWBFTJOTUBMBSVOUBNCPSTFQBSBEPSFOMBUVCFSÎBBOUFTEFDVBMRVJFSDPNQSFTPS

Entrada de vapor

Retorno de vapor Charola de sello

Al vaporizador

Fondos producto

'*(63" &/53"%"%&7"103"-'0/%0 :4"-*%"4%&-±26*%0" $033&$50 &/53"%"%&7"1031"3"-&-""-"$)"30-"%&4&--0 # */$033&$50$0%0%&&/53"%"%& 7"103)"$*""#"+0 40#3&&--±26*%0 $ 4"-*%"%&7"103%&-'0/%0 $0/7"103*;"%03 %&5&3.04*'¶/

www.FreeLibros.me

  &GJDJFODJBTEFQMBUPT



Chimenea para vapor

Cárcamo

Cárcamo

Salida del bajante

'*(63" 4"-*%"*/5&3.&%*"%&-±26*%0" $¦3$".0%&#"+"/5&  # 1-"50$0/$)*.&/&"4 /0"1"3&$&&-#"+"/5&"-4*(6*&/5&1-"50   &'*$*&/$*"4%&1-"504

-BTFàDJFODJBTEFQMBUPTTFQSFTFOUBSPOFOFMDBQÎUVMPFOFTUBTFDDJÓOMBTEFTDSJCJSFNPTDPONÃT EFUBMMFZFYQMPSBSFNPTNÊUPEPTQBSBFTUJNBSFMWBMPSEFMBFàDJFODJB&MFGFDUPEFMBTUBTBTEFUSBOT GFSFODJBEFNBTBTPCSFMBFàDJFODJBEFMQMBUPTFEFTDSJCJSÃFOFMDBQÎUVMP -BFàDJFODJBHFOFSBM &0 FT 

:D 2

CZfj^a CgZVa





-BEFUFSNJOBDJÓOEFMBDBOUJEBEEFFUBQBTEFFRVJMJCSJPOFDFTBSJBTQBSBMBTFQBSBDJÓOJOEJDBEBOP EFCFJODMVJSVOWBQPSJ[BEPSQBSDJBMOJVODPOEFOTBEPSQBSDJBM-BNFEJDJÓOZFMVTPEFMBFàDJFODJB HFOFSBMFTFTFYUSFNBEBNFOUFGÃDJM QPSDPOTJHVJFOUF FMWBMPSEFFàDJFODJBFTEFVTPNÃTDPNÙOFO MBQMBOUB4JOFNCBSHP FTEJGÎDJMSFMBDJPOBSMBFàDJFODJBHFOFSBMDPOMPTQSPDFTPTGVOEBNFOUBMFTEF USBOTGFSFODJBEFNBTBZDBMPSRVFTFFGFDUÙBOTPCSFFMQMBUP QPSMPRVFFOMPTFTUVEJPTCÃTJDPTOP TFVTBFOHFOFSBM 5BNCJÊO FO FM DBQÎUVMP  TF QSFTFOUBSPO MBT FàDJFODJBT EF .VSQISFF EF WBQPS Z MÎRVJEP -B FàDJFODJBEFWBQPS.VSQISFFTFEFàOFDPNPTJHVF 

:BK 2

nhVa − nZci DBNCJPSFBMFOFMWBQPS   n hVa − nZci DBNCJPFOFMWBQPSFOFMFRVJMJCSJP



ZMBFàDJFODJBEFMÎRVJEP.VSQISFFFT 

:BA 2

DBNCJPSFBMFOFMMÎRVJEP m hVa − m Zci   mhVa − m Zci DBNCJPFOFMMÎRVJEPFOFRVJMJCSJP



&MNPEFMPGÎTJDPRVFTFVTBQBSBMBTEPTFàDJFODJBTTFWFFOMBàHVSB4FTVQPOFRVFMBTDP SSJFOUFTEFHBTZMPTMÎRVJEPTFOMPTCBKBOUFTFTUÃOQFSGFDUBNFOUFNF[DMBEPT"EFNÃT .VSQISFF TVQVTPRVFFMMÎRVJEPTPCSFFMQMBUPFTUÃQFSGFDUBNFOUFNF[DMBEP MPRVFRVJFSFEFDJSRVFYYTBM &MUÊSNJOPZ TBMFTMBGSBDDJÓONPMBSFOFMWBQPSRVFFTUBSÎBFOFRVJMJCSJPDPOMBGSBDDJÓONPMBSSFBM FOFMMÎRVJEPRVFTBMFEFMQMBUP YTBM&OMBFàDJFODJBMÎRVJEB Y TBMFTUÃFOFRVJMJCSJPDPOMBGSBDDJÓO NPMBSSFBMFOFMWBQPSRVFTBMF ZTBM-BTFàDJFODJBTEF.VSQISFFFTUÃONVZEJGVOEJEBT QPSRVFTPO SFMBUJWBNFOUFGÃDJMFTEFNFEJSZNVZGÃDJMFTEFVTBSFOMPTDÃMDVMPT WFBMBàHVSB# %FTBGPSUV

www.FreeLibros.me



$BQÎUVMP  %JTFÒPEFDPMVNOBTEFQMBUPTZFNQBDBEBT

ysal xent

yent xsal

'*(63" .0%&-01"3"&'*$*&/$*".631)3&& OBEBNFOUF TVTEFàOJDJPOFTUJFOFOBMHVOBTEJàDVMUBEFT&OMBTDPMVNOBTHSBOEFT FMMÎRVJEPTPCSFFM QMBUPOPFTUÃCJFONF[DMBEPFOTVMVHBSIBCSÃBMHPEFáVKPUSBOTWFSTBM4JMBUSBZFDUPSJBEFáVKPFT MBSHB FMDPNQPOFOUFNÃTWPMÃUJMTFSÃFMJNJOBEPEFQSFGFSFODJBDVBOEPFMMÎRVJEPáVZFBUSBWFTBOEP FMQMBUP"TÎ FOMBàHVSB YTBMYYYY 0CTFSWFRVFYTBMZ FODPOTFDVFODJB Z TBMTFCBTBOFOMBDPODFOUSBDJÓONÎOJNBTPCSFFMQMBUP&OUPO DFT FTQPTJCMFRVFZ TBMZTBM QPSRVFZTBMFTVOQSPNFEJPFOUPEPFMQMBUP&OUPODFT FMOVNFSBEPS FOMBFDVBDJÓO B TFSÃNBZPSRVFFMEFOPNJOBEPSZ&.7&TUPTFPCTFSWBDPOGSFDVFODJBFO DPMVNOBTEFHSBOEJÃNFUSP"VORVFOPTFBBCTPMVUBNFOUFOFDFTBSJP FTQSFGFSJCMFUFOFSFàDJFODJBT EFàOJEBTEFUBMNBOFSBRVFWBSÎFOFOUSFZ6OTFHVOEPQSPCMFNBNÃTTFSJPSFMBDJPOBEPDPOMBT FàDJFODJBTEF.VSQISFFFTRVFFOMPTTJTUFNBTDPOWBSJPTDPNQPOFOUFT MBTFàDJFODJBTEFMPTEJT UJOUPTDPNQPOFOUFTEFCFOTFSEJGFSFOUFT1PSGPSUVOB QBSBMPTTJTUFNBTCJOBSJPTMBTFàDJFODJBTEF .VSQISFFTPOJHVBMFTQBSBMPTEPTDPNQPOFOUFT&OMPTTJTUFNBTDPOWBSJPTDPNQPOFOUFTOPTÓMP MBTFàDJFODJBTTPOEJGFSFOUFTFOBMHVOPTQMBUPTQVFEFOTFSOFHBUJWBT&TUPFTEFTDPODFSUBOUFZBM NJTNPUJFNQPFYUSFNBEBNFOUFEJGÎDJMEFBOUJDJQBS"QFTBSEFFTUPTQSPCMFNBT TFTJHVFOVTBOEP MBTFàDJFODJBTEF.VSQISFF-BFàDJFODJBHFOFSBMZMBFàDJFODJBEFWBQPSEF.VSQISFFTFSFMBDJPOBO DPOMBTJHVJFOUFFDVBDJÓO RVFTFEFEVDJSÃFOFMQSPCMFNB$



:d 2

bK − &R A  ad\bK$ A

ad\P& :BK 



-BFàDJFODJBQVOUVBMTFEFàOFFOGPSNBNVZQBSFDJEBBMBFàDJFODJBEF.VSQISFF 

:ei 2

n′hVa − n′Zci  n′ − n′Zci



BRVÎ MBQSJNBJOEJDBRVFUPEBTMBTDPODFOUSBDJPOFTTFEFUFSNJOBOFOVOQVOUPFTQFDÎàDPEFMQMBUP -B FàDJFODJB EF .VSQISFF TF QVFEF EFUFSNJOBS JOUFHSBOEP UPEBT MBT FàDJFODJBT QVOUVBMFT RVF WBSÎBOEFVOMVHBSBPUSP TPCSFFMQMBUP&OFMDBTPUÎQJDP MBTFàDJFODJBTQVOUVBMZEF.VSQISFFOP TPOJHVBMFT&TEJGÎDJMNFEJSMBFàDJFODJBQVOUVBMFOVOBDPMVNOBDPNFSDJBM QFSPDPOGSFDVFODJBTF QVFEFEFUFSNJOBSDPODÃMDVMPTEFUSBOTGFSFODJBEFDBMPSZEFNBTB1PSMPUBOUP TFEFCFVTBSQBSB QSFEJDDJPOFTZQBSBMPTFTDBMBNJFOUPT &OHFOFSBM MBFàDJFODJBEFVOQMBUPEFQFOEFEFMBWFMPDJEBEEFMWBQPSRVFTFNVFTUSBFOMB àHVSB-PTQMBUPTTFEJTFÒBOQBSBPCUFOFSVOBFàDJFODJBNÃYJNBBMBTDPOEJDJPOFTEFEJTFÒP

www.FreeLibros.me

  &GJDJFODJBTEFQMBUPT



Eficiencia

Punto de diseño

Inundación Demasiado arrastre

Goteo Velocidad del vapor, pies/s

'*(63" &'*$*&/$*" &/'6/$*¶/%&-" 7&-0$*%"%%&-7"103

" NBZPSFT WFMPDJEBEFT EF WBQPS  BVNFOUB FM BSSBTUSF DVBOEP FM BSSBTUSF TF WVFMWF FYDFTJWP  MB FàDJFODJBTFEFTQMPNB"WFMPDJEBEFTEFWBQPSNFOPSFTRVFMBEFEJTFÒP MBUSBOTGFSFODJBEFNBTB FTNFOPTFàDJFOUF"WFMPDJEBEFTNVZCBKBT FMQMBUPDPNJFO[BBHPUFBSZMBFàDJFODJBTFEFTQMPNB UBNCJÊO-PTQMBUPTDPOCVFOBTDBSBDUFSÎTUJDBTEFSFDIB[PUJFOFOVOBODIPNÃYJNP QPSMPRVFTF QJFSEFQPDPFOMBFàDJFODJBDVBOEPEJTNJOVZFMBWFMPDJEBEEFMWBQPS -BNFKPSNBOFSBEFEFUFSNJOBSMBFàDJFODJBFTUFOFSEBUPTEFMTJTUFNBRVÎNJDPFOFMNJTNP UJQPEFDPMVNOB EFMNJTNPUBNBÒPZDPOMBNJTNBWFMPDJEBEEFWBQPS4JWBSÎBMBWFMPDJEBE MBFà DJFODJBPCFEFDFSÃBMBàHVSB&M*OTUJUVUPEF*OWFTUJHBDJÓOFO'SBDDJPOBNJFOUP 'SBDUJPOBUJPO 3FTFBSDI*OTUJUVUF '3* UJFOFJONFOTBTDBOUJEBEFTEFEBUPTEFFàDJFODJBEJTQPOJCMFTTÓMPQBSBTVT NJFNCSPT-BNBZPSQBSUFEFMBTFNQSFTBTRVÎNJDBTZQFUSPMFSBTQFSUFOFDFOBM'3*&MTFHVOEP NFKPSNÊUPEPFTUFOFSEBUPTEFFàDJFODJBQBSBFMNJTNPTJTUFNBRVÎNJDP QFSPDPOEJTUJOUPUJQPEF QMBUP(SBOQBSUFEFMPTEBUPTEJTQPOJCMFTFOMBTQVCMJDBDJPOFTTPOQBSBQMBUPTEFCBSCPUFBEPSFTP QMBUPTQFSGPSBEPT&OHFOFSBM MBFàDJFODJBEFMPTQMBUPTEFWÃMWVMBTFTJHVBMPNFKPSRVFQBSBMPT QMBUPTQFSGPSBEPT RVFFTJHVBMPNFKPSRVFMBFàDJFODJBEFQMBUPTDPOCBSCPUFBEPSFT"TÎ TJTFVTBO FàDJFODJBTDPOCBSCPUFBEPSFTQBSBVOEJTFÒPEFDPMVNOBEFQMBUPEFWÃMWVMBT FMEJTFÒPTFSÃDPOTFS WBEPS&MUFSDFSNÊUPEPNFKPSFTVTBSEBUPTEFFàDJFODJBQBSBVOTJTUFNBRVÎNJDPQBSFDJEP 4JOPTFDVFOUBDPOEBUPT TFQVFEFIBDFSVODÃMDVMPEFUBMMBEPEFMBFàDJFODJBCBTBEPFODÃMDV MPTGVOEBNFOUBMFTEFUSBOTGFSFODJBEFNBTBZDBMPS$POFTUFNÊUPEPQSJNFSPTFDBMDVMBOFàDJFO DJBTQVOUVBMFTBQBSUJSEFDÃMDVMPTEFUSBOTGFSFODJBEFDBMPSZEFNBTB ZEFTQVÊTTFEFUFSNJOBO MBTFàDJFODJBTEF.VSQISFFZHFOFSBM EFBDVFSEPDPOMBTQBVUBTEFáVKPTPCSFFMQMBUP%FTBGPS UVOBEBNFOUF DPOGSFDVFODJBMPTSFTVMUBEPTOPTPONVZFYBDUPT&OFMDBQÎUVMPTFEFTDSJCFVOB BQMJDBDJÓOTFODJMMBEFFTUFNÊUPEP &MNÊUPEPNÃTTFODJMMPFTVTBSVOBDPSSFMBDJÓOQBSBEFUFSNJOBSMBFàDJFODJB-BRVFNÃTTFVTB FTMBDPSSFMBDJÓOEF0$POOFMM 0$POOFMM  RVFTFWFFOMBàHVSB­TUBQSPQPSDJPOBVOB FTUJNBDJÓOEFMBFàDJFODJBHFOFSBMFOGVODJÓOEFMBWPMBUJMJEBESFMBUJWBEFMPTDPNQPOFOUFTDMBWF  NVMUJQMJDBEBQPSMBWJTDPTJEBEEFMMÎRVJEPBMBDPNQPTJDJÓOEFMBBMJNFOUBDJÓO5BOUP DPNP TF EFUFSNJOBOBMBUFNQFSBUVSBZQSFTJÓOQSPNFEJPEFMBDPMVNOB-BFàDJFODJBCBKBBNFEJEBRVFBV NFOUBMBWJTDPTJEBE EFCJEPBRVFMBTUBTBTEFUSBOTGFSFODJBEFNBTBTPONFOPSFT-BFàDJFODJBCBKB BNFEJEBRVFBVNFOUBMBWPMBUJMJEBESFMBUJWB QPSRVFBVNFOUBMBNBTBRVFEFCFUSBOTGFSJSTFQBSB MMFHBSBMFRVJMJCSJP-BEJTQFSTJÓOEFMPTQVOUPTEFEBUPTFTFWJEFOUFFOMBàHVSB&TQSPCBCMFRVF 0$POOFMMFTUVEJBSBDPMVNOBTEFCBSCPUFBEPSFT BTÎ MPTSFTVMUBEPTTPODPOTFSWBEPSFTQBSBMPTQMB UPTQFSGPSBEPTZEFWÃMWVMBT 8BMBT  8BMBT  SFTFÒBVOBHSBODBOUJEBEEFFàDJFODJBTEF QMBUPTEFEJWFSTPTUJQPT0#SJFOZ4DIVMU[ 

FOGFDIBSFDJFOUF JOGPSNBSPORVFNVDIBTUPSSFT QFUSPRVÎNJDBTTFEJTFÒBODPOFàDJFODJBTEFFUBQBFOMBSFHJÓOEFB"VORVFFTQSPCBCMFRVF

www.FreeLibros.me



$BQÎUVMP  %JTFÒPEFDPMVNOBTEFQMBUPTZFNQBDBEBT

O - COLUMNA COMERCIAL DE FRACCIONAMIENTO DE HIDROCARBUROS - COLUMNA COMERCIAL DE FRACCIONAMIENTO DE HIDROCARBUROS CLORADOS + - FRACCIONAMIENTO COMERCIAL DE ALCOHOL × - FRACCIONAMIENTO DE ALCOHOL ETÍLICO EN LABORATORIO

EFICIENCIA DE PLACA,%

'*(63"  $033&-"$*¶/%& 0$0//&--1"3" -"&'*$*&/$*" 505"-%& $0-6./"4%& %&45*-"$*¶/ %&0$0//&--  3&*.13&40 %&53"/4"$5*0/4 ".&3*/45 $)&.&/5   

 ¥ ".&3*$"/ */45*565&0' $)&.*$"- &/(*/&&34

u

- DIVERSOS

VOLATILIDAD RELATIVA DEL COMPONENTE CLAVE × VISCOSIDAD DE LA ALIMENTACIÓN (A CONDICIONES PROMEDIO EN LA COLUMNA)

FTBTDPMVNOBTTFBOEFQMBUPTEFWÃMWVMBT FMJOUFSWBMPEFFàDJFODJBTDPODVFSEBDPOMBDPSSFMBDJÓO EF0$POOFM-PTTJTUFNBTBMWBDÎP RVFOPTFJODMVZFOFOMBàHVSB UJFOFOFàDJFODJBTEFB  0#SJFOZ4DIVMU[   1BSBVTPTFODPNQVUBEPSBZDBMDVMBEPSBDPOWJFOFBKVTUBSMPTQVOUPTEFEBUPTBVOBFDVBDJÓO $VBOEP TF IJ[P FTUP VTBOEP VOB SVUJOB OP MJOFBM EF NÎOJNPT DVBESBEPT FM SFTVMUBEP ,FTTMFS Z 8BOLBU  GVF 

:D 2%#*',-'− %#',*&&ad\&%αμ %#%)).'(Pad\&%αμR' 



&OMBFDVBDJÓO  ZFOMBàHVSB MBWJTDPTJEBEFTUÃFODFOUJQPJTFT D1 &TUBFDVBDJÓOOP SFQSPEVDFDPOFYBDUJUVEMBàHVSBEF0$POOFMM QPSRVFBQBSFOUFNFOUF0$POOFMMVTÓVOBKVTUFB PKP-VEXJU  EFTDSJCFPUSBTDPSSFMBDJPOFTEFFàDJFODJB -BT FàDJFODJBT TF QVFEFO FTDBMBS B QBSUJS EF EBUPT EF MBCPSBUPSJP UPNBEPT FO VOB DPMVNOB 0MEFSTIBX FTVOBDPMVNOBEFQMBUPTQFSGPSBEPT BFTDBMBEFMBCPSBUPSJP  'BJSFUBM ,JTUFS   -BFàDJFODJBHFOFSBMNFEJEBFOMBDPMVNOB0MEFSTIBXDPOGSFDVFODJBTFBDFSDBNVDIPBMB FàDJFODJBQVOUVBMNFEJEBFOMBDPMVNOBDPNFSDJBMHSBOEF&TUPTFWFFOMBàHVSB EPOEFTF IBOPSNBMJ[BEPMBWFMPDJEBEEFMWBQPSDPOSFTQFDUPBMBGSBDDJÓOEFJOVOEBDJÓO 'BJSFUBM   -B FàDJFODJB QVOUVBM TF QVFEF DPOWFSUJS FO FàDJFODJB EF .VSQISFF Z FàDJFODJB HFOFSBM  VOB WF[ BEPQUBEPVONPEFMPEFMBQBVUBEFáVKPTPCSFFMQMBUP WFBMBTFDDJÓO  1BSBNF[DMBTNVZDPNQMFKBT UPEPFMEJTFÒPEFMBEFTUJMBDJÓOQVFEFIBDFSTFVTBOEPMBDPMVNOB 0MEFSTIBX DBNCJBOEPMBDBOUJEBEEFQMBUPTZMBSFMBDJÓOEFSFáVKPIBTUBFODPOUSBSVOBDPNCJOB DJÓODPORVFTFIBHBFMUSBCBKP$PNPMBDPMVNOBDPNFSDJBMUFOESÃVOBFàDJFODJBHFOFSBMJHVBMP NBZPSRVFMBDPMVNOB0MEFSTIBX FTUBDPNCJOBDJÓOUBNCJÊOGVODJPOBSÃFOMBDPMVNOBDPNFSDJBM $POFTUFNÊUPEPTFFMJNJOBMBOFDFTJEBEEFEFUFSNJOBSEBUPTEFFRVJMJCSJPWBQPSMÎRVJEP MPDVBM QVFEFTFSNVZDPTUPTP ZUBNCJÊOTFFMJNJOBMBOFDFTJEBEEFIBDFSDÃMDVMPTDPNQMFKPT5BNCJÊO MB DPMVNOB0MEFSTIBXQFSNJUFBVOPPCTFSWBSMPTQSPCMFNBTEFGPSNBDJÓOEFFTQVNB ,JTUFS   &+&.1-0 &TUJNBDJÓOEFMBFGJDJFODJBHFOFSBM $POVOBDPMVNOBEFEFTUJMBDJÓOEFQMBUPTQFSGPSBEPTTFTFQBSBVOBBMJNFOUBDJÓOGPSNBEB QPSNPMEFOIFYBOPZNPMEFOIFQUBOP-BBMJNFOUBDJÓOFTVOMÎRVJEPTBUVSB

www.FreeLibros.me

  &GJDJFODJBTEFQMBUPT



abierta abierta

EMV o Ept

Porcentaje de inundación

'*(63" &'*$*&/$*"(&/&3"-%&6/"$0-6./"0-%&4)"8%& 16-("%"%&%*¦.&530 &/$0.1"3"$*¶/$0/-"&'*$*&/$*"16/56"-%& 6/"$0-6./"'3*&-4*45&."&4$*$-0)&9"/0/)&15"/050."%0%& '"*3&5"-  3&*.13&40$0/"6503*;"$*¶/%&*/%&/(130$&44 %&4%&7&-01   

¥ ".&3*$"/$)&.*$"-40$*&5: EP-BBMUVSBFOUSFQMBUPTFTQVMHBEBT-BQSFTJÓOQSPNFEJPFOMBDPMVNOBFTBUN-B DPNQPTJDJÓOEFMEFTUJMBEPFTY% GSBDDJÓONPMBSEFOIFYBOP ZY#-BUBTB EFBMJNFOUBDJÓOFTMCNPMI-BSFMBDJÓOEFSFáVKPJOUFSOPFT-7-BDPMVNOB UJFOFVOWBQPSJ[BEPSUPUBMZVODPOEFOTBEPSUPUBM&TUJNFMBFàDJFODJBHFOFSBM 4PMVDJÓO 1BSBVTBSMBDPSSFMBDJÓOEF0$POOFMM OFDFTJUBNPTFTUJNBS Z BMBUFNQFSBUVSBZQSF TJÓOQSPNFEJPFOMBDPMVNOB-BUFNQFSBUVSBEFMBDPMVNOBTFQVFEFFTUJNBSDPOEBUPT EFFRVJMJCSJP MBHSÃàDBEF%F1SJFTUFS -PTWBMPSFTTJHVJFOUFTTFHFOFSBSPODPOGBDJMJEBE EFMBàHVSB m8+ n8+ I!° 8

% % .-#)

%#()& %#*)* -*

%#(.%#+%. -(#,

%#*% %#,% -%

&#% &#% +.

-BWPMBUJMJEBESFMBUJWBFT  ZY < −Z  −Y >-BUFNQFSBUVSBQSPNFEJPTFQVFEF FTUJNBSEFWBSJBTNBOFSBT 1SPNFEJPBSJUNÊUJDP5      1SPNFEJPFOY 5   /PIBZHSBOEJGFSFODJB6TBS  RVFDPSSFTQPOEFBQSPYJNBEBNFOUFBž$ -BWJTDPTJEBEMÎRVJEBEFMBBMJNFOUBDJÓOTFQVFEFDBMDVMBS 3FJEFUBM  1ÃH DPO 

acμbZoX 2m& acμ& m' acμ' 

B

-BTWJTDPTJEBEFTEFMPTDPNQPOFOUFTQVSPTTFQVFEFODBMDVMBSDPO 

ad\ &% μ 26P

& & − R I 7

www.FreeLibros.me

C



$BQÎUVMP  %JTFÒPEFDPMVNOBTEFQMBUPTZFNQBDBEBT

EPOEF FTUÃFOD1Z5FOLFMWJOT 3FJEFUBM  "Q"

c8+/62(+'#,.!72'%,#%c8,/62)(+#,(!72'('#*(

&TUBTFDVBDJPOFTEBODPNPSFTVMUBEP $  $Z NF[D&OUPODFT NF[D %FBDVFSEPDPOMBFDVBDJÓO 

&0 NJFOUSBTRVFEFBDVFSEPDPOMBàHV SB &01BSBTFSDPOTFSWBEPS FTQSPCBCMFRVFTFVTFFMNFOPSWBMPS 0CTFSWFRVFVOBWF[DBMDVMBEPT5QSPN  QSPNZ BMJN FTGÃDJMDBMDVMBS&0 &ONVDIPTBTQFDUPT MBQBSUFNÃTEJGÎDJMEFEFUFSNJOBSMBTDPOEJDJPOFTEFEJTFÒPQBSBDPMVN OBTEFQMBUPTZFNQBDBEBTFTEFUFSNJOBSMBTQSPQJFEBEFTGÎTJDBT1BSBMPTDÃMDVMPTBNBOP 1FSSZZ (SFFO 

3FJEFUBM 

1PMJOHFUBM 

4NJUIZ4SJWBTUSB 

4UFQIBOZ)JMEXFJO 

8PPET  Z:BXT  TPOCVFOBTGVFOUFT-PTTJNVMBEPSFTDPNFSDJBMFTUJFOFOQSP HSBNBTEFQSPQJFEBEFTGÎTJDBTRVFIBDFOFTUFDPNQMJDBEPUSBCBKP  $¦-$6-0%&-%*¦.&530%&-"$0-6./"

1BSB EJTFÒBS VOB DPMVNOB EF QMBUPT QFSGPSBEPT EFCFNPT DBMDVMBS FM EJÃNFUSP EF MB DPMVNOB RVF FWJUFMBJOVOEBDJÓO EJTFÒBSMBEJTUSJCVDJÓOEFMQMBUPZEJTFÒBSMPTCBKBOUFT&OMBTQVCMJDBDJPOFTEF EPNJOJP QÙCMJDP TF FODVFOUSBO WBSJPT QSPDFEJNJFOUPT QBSB DBMDVMBS EJÃNFUSPT EF DPMVNOB 'BJS    ,JTUFS -VEXJH .D$BCFFUBM  "EFNÃT FTDPNÙORVFDBEBGBCSJ DBOUFEFFRVJQPUFOHBTVQSPQJPQSPDFEJNJFOUP"RVÎTFHVJSFNPTFMQSPDFEJNJFOUPEF'BJSQPSRVFFT DPOPDJEPZFTVOBPQDJÓOFOFMTJNVMBEPS"TQFO1MVT WFBFMBQÊOEJDFEFMDBQÎUVMP &OFTUFQSPDF EJNJFOUPTFEFUFSNJOBQSJNFSPMBWFMPDJEBEEFWBQPSRVFDBVTBSÃJOVOEBDJÓOEFCJEBBMBSSBTUSFFYDF TJWPZBDPOUJOVBDJÓOVOBSFHMBFNQÎSJDBQBSBEFUFSNJOBSMBWFMPDJEBEEFPQFSBDJÓOEFBIÎTFDBMDVMB FMEJÃNFUSPEFMBDPMVNOB­TUFFTNVZJNQPSUBOUFQBSBDPOUSPMBSMPTDPTUPTZEFCFFTUJNBSTFBÙOFO MPTEJTFÒPTQSFMJNJOBSFT&MNÊUPEPTFBQMJDBBQMBUPTQFSGPSBEPT EFWÃMWVMBTZEFCBSCPUFBEPSFT -BWFMPDJEBEEFJOVOEBDJÓOCBTBEBFOFMÃSFBOFUBEFáVKPEFWBQPSTFEFUFSNJOBDPO 

j ^cjc 28hW![ 

σ %#' šA − šk  šk !e^Zh$h  '%



EPOEF FTMBUFOTJÓOTVQFSàDJBMFOEJOBTDNZ$TC GFTFMGBDUPSEFDBQBDJEBE&TUBFDVBDJÓOTFQBSFDF BMBFDVBDJÓO  RVFVTBNPTQBSBEJNFOTJPOBSUBNCPSFTWFSUJDBMFTEFEFTUJMBDJÓOJOTUBOUÃOFB $TC GFTVOBGVODJÓOEFMQBSÃNFUSPEFáVKP 

;E2;ak 2

LA

š

Lk

š

k





A

EPOEF8-Z8WTPOMBTUBTBTEFáVKPEFNBTBEFMÎRVJEPZWBQPS ZMBTEFOTJEBEFTTPOEFOTJEBEFTEF NBTB-BDPSSFMBDJÓOQBSB$TC GTFWFFOMBàHVSB 'BJSZ.BUUIFXT  1BSBVTBSFODPNQV UBEPSB DPOWJFOFBKVTUBSBFDVBDJPOFTMBTDVSWBTEFMBàHVSB-PTSFTVMUBEPTEFVOBOÃMJTJTEF OPMJOFBMEFSFHSFTJÓOQPSDVBESBEPTNÎOJNPT ,FTTMFSZ8BOLBU  QBSBBMUVSBFOUSFQMBUPT EFQVMHBEBT TPO 

ad\&% 8hW![ 2−&#&.,,− %#*(&)(ad\&% ;ak − %#&-,+%ad\&% ;ak' 

B

1BSBEJTUBODJBFOUSFQMBUPTEFQVMHBEBT 

ad\&% 8hW![ 2−&#&+''− %#*+%&)ad\&% ;ak − %#&-&+-ad\&% ;ak' 

www.FreeLibros.me

C



Altura entre platos

Csb,inun

pies/s

  $ÃMDVMPEFMEJÃNFUSPEFMBDPMVNOB

'*(63" '"$503%&$"1"$*%"%1"3"*/6/%"$*¶/%&1-"5041&3'03"%0450."%0 %&'"*3:."55)&84  3&*.13&40$0/"6503*;"$*¶/%&1&530-&6.3&'*/&3  

  ¥ (6-'16#$0 1BSBEJTUBODJBFOUSFQMBUPTEFQVMHBEBT 

ad\&% 8hW![ 2−&#%+,)− %#**,-%ad\&% ;ak − %#&,.&.ad\&% ;ak' 

D

1BSBEJTUBODJBFOUSFQMBUPTEFQVMHBEBT 

ad\&% 8hW![ 2−&#%'+'− %#+(*&(ad\&% ;ak − %#'%%.,ad\&% ;ak' 

E

1BSBEJTUBODJBFOUSFQMBUPTEFQVMHBEBT 

ad\&% 8hW![ 2−%#.)*%+− %#,%'()ad\&% ;ak − %#''+&-ad\&% ;ak' 

F

ZQBSBEJTUBODJBFOUSFQMBUPTEFQVMHBEBT  

ad\&% 8hW![ 2−%#-*.-)− %#,(.-%ad\&% ;ak − %#'(,(*ad\&% ;ak' 

G

-BNJTNBDPSSFMBDJÓOEFJOVOEBDJÓO QFSPFOVOJEBEFTNÊUSJDBT TFDPOTJHVFFOGPSNBHSÃàDB 'BJS    &OMBDPSSFMBDJÓOEFJOVOEBDJÓOTFTVQPOFRVF MBSFMBDJÓOEFMÃSFBEFMPTBHVKFSPT"BHVKFOUSF FMÃSFBBDUJWBEFMQMBUP "BDUJW FTJHVBMPNBZPSRVF4J  TFEFCFNVMUJQMJDBSMBWFMPDJEBEEF JOVOEBDJÓODBMDVMBEBDPOMBFDVBDJÓO  QPSVOGBDUPSEFDPSSFDDJÓO 'BJS  4J  FM GBDUPSEFDPSSFMBDJÓOFT NJFOUSBTRVFTJ  FMGBDUPSEFDPSSFDDJÓOFT0CTFSWFRVFFTVOB DPSSFMBDJÓOMJOFBMZTFQVFEFJOUFSQPMBSDPOGBDJMJEBE&MWBMPSEFMBWFMPDJEBEEFJOVOEBDJÓORVFTF PCUJFOFTFSÃDPOTFSWBEPS -BBMUVSBPEJTUBODJBFOUSFQMBUPT OFDFTBSJBFOMBDPSSFMBDJÓOEFJOVOEBDJÓO TFTFMFDDJPOBEF BDVFSEPDPOMBTOFDFTJEBEFTEFNBOUFOJNJFOUP-PTQMBUPTQFSGPSBEPTUJFOFOEJTUBODJBTFOUSFFMMPT EFBQVMHBEBTEFBQVMHBEBTTPOMPTMÎNJUFTDPNVOFTQBSBMBTUPSSFTQFRVFÒBT NFOPSFT

www.FreeLibros.me



$BQÎUVMP  %JTFÒPEFDPMVNOBTEFQMBUPTZFNQBDBEBT

EFQJFT &OHFOFSBM MBBMUVSBFOUSFQMBUPTFTNBZPSFODPMVNOBTEFHSBOEJÃNFUSP4FVTBVONÎ OJNPEFQVMHBEBTZQVMHBEBTFTMPDBSBDUFSÎTUJDPQPSTJTFOFDFTJUBRVFVOUSBCBKBEPSTFBSSBTUSF QPSMBDPMVNOBQBSBJOTQFDDJPOBSMB -BWFMPDJEBEEFPQFSBDJÓOQBSBFMWBQPSTFEFUFSNJOBDPO 

VPQ GSBDDJÓO ×VJOVO QJFTT



EPOEFMBGSBDDJÓOQVFEFJSEFB+POFTZ.FMMCPN  TVHJFSFOVTBSTJFNQSFVOWBMPSEF QBSBFTBGSBDDJÓO$PONBZPSFTGSBDDJPOFTEFJOVOEBDJÓOOPTFBGFDUBNVDIPFMDPTUPHFOFSBM EFMTJTUFNB QFSPTÎSFTUSJOHFOTVáFYJCJMJEBE-BWFMPDJEBEEFPQFSBDJÓO VPQ TFQVFEFSFMBDJPOBS DPOMBUBTBEFáVKPNPMBSEFMWBQPS jde 2



KEB k !  QJFTT šK 6cZi(+%%



EPOEFDPOTFQBTBEFIPSBT FO7 BTFHVOEPT FOVPQ &MÃSFBOFUBQBSBFMáVKPEFWBQPSFT 

6cZi 2

x9^V' )

η!

[' 



EPOEF FTMBGSBDDJÓOEFMÃSFBUSBOTWFSTBMEFMBDPMVNOBEJTQPOJCMFQBSBFMáVKPEFWBQPSTPCSFFM QMBUP&OUPODFT − FTMBGSBDDJÓOEFMÃSFBEFMBDPMVNOBPDVQBEBQPSVOCBKBOUF&OGPSNBDBSBD UFSÎTUJDB  WBMFFOUSFZÊTUFTFQVFEFDBMDVMBSDPOFYBDUJUVEVOBWF[àOBMJ[BEBMBEJTUSJCV DJÓOEFMQMBUP&MEJÃNFUSPEFMBDPMVNOBTFQVFEFEFTQFKBSEFMBTFDVBDJPOFT  Z   

9^V2

)KEB k 

x šk [gVXX^‹cj ^cjc (+%%

  QJFT



4JFTWÃMJEBMBMFZEFMHBTJEFBM 

šk 2

š EB k  GI



ZMBFDVBDJÓO  TFUSBOTGPSNBFO 

9^V2

)KGI

x η (+%%e[gVXX^‹cj^cjc

!   QJFT



5FOHBFODVFOUBRVFFTUBTFDVBDJPOFTTPOEJNFOTJPOBMFT QPSMPRVF$TCUJFOFEJNFOTJPOFT -PTUÊSNJOPTEFMBTFDVBDJPOFT  BMB  WBSÎBOEFVOBFUBQBBPUSBFOMBDPMVNOB4J TFIBDFFMDÃMDVMPFOEJTUJOUPTMVHBSFT TFDBMDVMBSÃOEJTUJOUPTEJÃNFUSPT4FEFCFVTBSFMEJÃNFUSP NÃYJNP  SFEPOEFBEP IBTUB FM JODSFNFOUP EF  QJF NÃT DFSDBOP 1PS FKFNQMP  VOB DPMVNOB EF QJFTTFSFEPOEFBBQJFT-VEXJH  Z,JTUFS  TVHJFSFOVTBSVOEJÃNFUSPNÎOJNP EFDPMVNOBEFQJFT FTUPFT TJFMEJÃNFUSPDBMDVMBEPFTQJFT VTBSNFKPSQJFT QPSRVFOP TFSÃNÃTDPTUPTP&OGPSNBDBSBDUFSÎTUJDB FTUBTDPMVNOBTQFRVFÒBTVTBOQMBUPTEFDBSUVDIPQSF GBCSJDBEPTGVFSBEFMBDPMVNOB -VEXJH  -BTDPMVNOBTDPOEJÃNFUSPTNFOPSFTBQJFTTF TVFMFODPOTUSVJSDPNPDPMVNOBTFNQBDBEBT4JMPTDÃMDVMPTEFEJÃNFUSPTFIBDFOFOMBQBSUFTVQF SJPSFJOGFSJPSEFMBDPMVNOBZBSSJCBZBCBKPEFMBBMJNFOUBDJÓO FOVOPEFFTPTMVHBSFTTFPCUFOESÃ DPONVDIBBQSPYJNBDJÓOFMEJÃNFUSPNÃYJNPZTFSÃTBUJTGBDUPSJPFMEJTFÒPCBTBEPFOFMNÃYJNP EJÃNFUSPDBMDVMBEP1BSBDPMVNOBTRVFUSBCBKFOBQSFTJÓOBUNPTGÊSJDBPNBZPSFT MBQSFTJÓOTFSÃ

www.FreeLibros.me

  $ÃMDVMPEFMEJÃNFUSPEFMBDPMVNOB



FTFODJBMNFOUFDPOTUBOUFFOMBDPMVNOB4JTVTUJUVJNPTMBTFDVBDJPOFT  Z  FOMBFDVBDJÓO  QBSBDBMDVMBSMBTDPOEJDJPOFTUBOUPFOMBQBSUFTVQFSJPSDPNPFOFMGPOEPEFMBDPMVNOB  TBDBNPTMBSFMBDJÓOFOUSFFTUBTEPTFDVBDJPOFTZTJNQMJàDBNPT FMSFTVMUBEPTFSÃ 

9^Vhje K hje &¿' 2 9^V[dcYd K [dcYd

EB K!hje &¿) EB K![dcYd

šA![dcYd &¿) Ihje &¿) σ[dcYd σhje šA!hje I[dcYd

%#&

8hW![![dcYd &¿'   

8hW![!hje

-PTEPTÙMUJNPTUÊSNJOPTEFMMBEPEFSFDIPTVFMFOFTUBSQSÓYJNPTB BVORVFDVBOEPTFTFQBSBOBHVB ZTVTUBODJBTPSHÃOJDBT FMUÊSNJOPEFMBUFOTJÓOTVQFSàDJBMQPESÎBTFS BQSPYJNBEBNFOUF TJFOEP FMBHVBFMQSPEVDUPEFGPOEPT P DVBOEPFMBHVBFTFMEFTUJMBEP -BSFMBDJÓOEFMBTUFNQFSBUVSBT TJFNQSFFTNFOPSRVFZFOMBTTFQBSBDJPOFTCJOBSJBTFTUÃEFOUSPEFVOJOUFSWBMPUÎQJDPEFB  BVORVFQVFEFTFSNFOPSQBSBEFTUJMBDJPOFTBCBKBTUFNQFSBUVSBT1BSBVOBBMJNFOUBDJÓOFOGPSNB EFWBQPSTBUVSBEP FMUÊSNJOPEFWFMPDJEBEFTEFWBQPSFTNFOPSRVFZQVFEFJSEFIBTUB  BQSPYJNBEBNFOUF1BSBVOBBMJNFOUBDJÓOFOGPSNBEFMÎRVJEPTBUVSBEP FTUFUÊSNJOPTFBQSPYJNB NVDIPB-PTUÊSNJOPTEFQFTPNPMFDVMBSZEFEFOTJEBEQVFEFOTFSNBZPSFTPNFOPSFTRVFVOP 1BSBEFTUJMBDJÓOEFTFSJFTIPNÓMPHBT FMUÊSNJOPEFQFTPTNPMFDVMBSFTFTNFOPSRVF NJFOUSBTRVF FMUÊSNJOPEFEFOTJEBEFTEFMÎRVJEPQSPCBCMFNFOUFTFBNBZPSRVF$PNPOPTFFTQFSBOHSBOEFT EJGFSFODJBT FTQSPCBCMFRVFFMQSPEVDUPEFFTPTUÊSNJOPTTFBQSPCBCMFNFOUFBQSPYJNBEBNFOUF 1BSBMBEFTUJMBDJÓOEFBHVBDPOVOBTVTUBODJBPSHÃOJDB TJFMBHVBFTFMQSPEVDUPEFGPOEPT FMUÊSNJOP EFQFTPTNPMFDVMBSFTFT NJFOUSBTRVFFMUÊSNJOPEFEFOTJEBEFTFTNBZPSRVFZFTQSPCBCMFRVF FMQSPEVDUPEFMPTEPTUÊSNJOPTTFBDFSDBOPB4JFMBHVBFTFMQSPEVDUPEFTUJMBEP TFJOUFSDBNCJBO FTUPTEPTUÊSNJOPTZFTQSPCBCMFRVFFMQSPEVDUPEFFMMPTTJHBTJFOEPDFSDBOPB $PNPSFHMBBQSPYJNBEB TJMBBMJNFOUBDJÓOFTMÎRVJEPTBUVSBEPZTFFTUÃEFTUJMBOEPVOBTFSJF IPNÓMPHB FTQSPCBCMFRVFMBSFMBDJÓOEFEJÃNFUSPTTFBNFOPSRVFZRVFFMUÊSNJOPDBMDVMBEP QBSBFMGPOEPTFBNBZPS&TUPUBNCJÊOTVDFEFDPOVOBBMJNFOUBDJÓOEFMÎRVJEPTBUVSBEPTJMBEFTUJ MBDJÓOFTBHVBDPOTVTUBODJBPSHÃOJDB TJFOEPFMBHVBFMQSPEVDUPEFTUJMBEP1FSPTJFMBHVBGPSNBMPT GPOEPT MPRVFFTNÃTDPNÙO

DVBMRVJFSBEFMPTEJÃNFUSPTTVQFSJPSPJOGFSJPSQVFEFTFSFMNBZPS 4JMBBMJNFOUBDJÓOFTVOWBQPSTBUVSBEP FTQSPCBCMFRVFMBSFMBDJÓOEFEJÃNFUSPTTFBNBZPSRVF ZTFEFCBEJTFÒBSDPOMBTDPOEJDJPOFTTVQFSJPSFT4JOFNCBSHP DVBOEPTFEFTUJMBBHVBDPOVOBTVT UBODJBPSHÃOJDBZFMBHVBFTFMQSPEVDUPEFTUJMBEP BTÎUBNCJÊODPNPQBSBEFTUJMBDJPOFTDSJPHÊOJDBT  MBSFMBDJÓOEFEJÃNFUSPTQPESÎBTFSNBZPSPNFOPSRVF 4JIBZVOHSBODBNCJPEFWFMPDJEBEEFMWBQPSFOMBDPMVNOB MPTEJÃNFUSPTDBMDVMBEPTQVFEFO TFSNVZEJGFSFOUFT"WFDFTTFDPOTUSVZFODPMVNOBTDPOEPTTFDDJPOFTEFEJTUJOUPTEJÃNFUSPTQBSB BQSPWFDIBSFTUBTJUVBDJÓO QFSPFTUBTPMVDJÓOFTFDPOÓNJDBTÓMPQBSBHSBOEFTDBNCJPTEFEJÃNFUSP 4JTFDPOTUSVZFVOBDPMVNOBDPOVOTPMPEJÃNFUSP MBTFàDJFODJBTFOMBTEJWFSTBTQBSUFTEFMBDP MVNOBQVFEFOWBSJBSNVDIP WFBMBàHVSB &TUBWBSJBDJÓOEFFàDJFODJBTFEFCFJODMVJSFOMPT DÃMDVMPTEFEJTFÒP &O FM QSPDFEJNJFOUP EF EJTFÒP TF EJNFOTJPOB MB DPMVNOB QBSB FWJUBS MB JOVOEBDJÓO DBVTBEB QPSEFNBTJBEPBSSBTUSF5BNCJÊOQVFEFIBCFSJOVOEBDJÓOFOMPTCBKBOUFTÊTUFDBTPTFEFTDSJCJSÃ NÃTBEFMBOUF&MBSSBTUSFFYDFTJWPUBNCJÊODBVTBVOBHSBODBÎEBFOMBFàDJFODJBEFMBFUBQB QPSRVF DPOFMWBQPSTFNF[DMBMÎRVJEPRVFOPIBTJEPTFQBSBEP&MFGFDUPEFMBSSBTUSFTPCSFMBFàDJFODJBEF WBQPS.VSQISFFTFQVFEFDBMDVMBSDPO 

:BL!VggVhigZ 2:BL

&  & :BL ψ $&− ψ

B

"RVÎ &.8FTMBFàDJFODJBEF.VSQISFFTJOBSSBTUSFZ FTMBGSBDDJÓOEFBSSBTUSFRVFTFEFàOFDPNP TJHVF

www.FreeLibros.me



$BQÎUVMP  %JTFÒPEFDPMVNOBTEFQMBUPTZFNQBDBEBT

Arrastre fraccionario,

Porcentaje de la inundación

'*(63" $033&-"$*¶/%&"33"453&%&'"*3  3&*.13&40$0/ "6503*;"$*¶/%&4.*5) #% %&4*(/0'&26*-*#3*6.45"(&130$&44&4 ¥  .$(3"8)*-- /6&7":03, ψ2

BSSBTUSFBCTPMVUP Z   A Z áVKPUPUBMEFMÎRVJEP

C

TJFOEPFMBTNPMFTIEFMMÎRVJEPBSSBTUSBEP&MBSSBTUSFSFMBUJWP QBSBMPTQMBUPTQFSGPSBEPTTFQVF EFFTUJNBSDPOMBàHVSB 'BJS  6OBWF[DPOPDJEPFMWBMPSDPSSFHJEPEF&.8 TFQVFEF EFUFSNJOBSMBFàDJFODJBHFOFSBMDPOMBFDVBDJÓO  &OHFOFSBM FMBSSBTUSFOPFTQSPCMFNBTJOP IBTUBRVFFMBSSBTUSFGSBDDJPOBSJPFTNBZPSRVF MPDVBMTFQSFTFOUBDVBOEPMBPQFSBDJÓOFTUÃFO MBSFHJÓOEFBEFMBJOVOEBDJÓO -VEXJH  &OUPODFT VOWBMPSEFEFJOVOEBDJÓO EFCFUFOFSVOBDPSSFDDJÓOEFTQSFDJBCMFQPSBSSBTUSF&TPTFQVFEFWFSJàDBSEVSBOUFFMQSPDFEJNJFO UPEFEJTFÒP WFBFMFKFNQMP  &+&.1-0 $ÃMDVMPEFMEJÃNFUSPQBSBVOBDPMVNOBEFQMBUPT %FUFSNJOFFMEJÃNFUSPOFDFTBSJPFOMBQBSUFTVQFSJPSEFVOBDPMVNOBEFEFTUJMBDJÓODPNP MBEFMFKFNQMP

www.FreeLibros.me

  $ÃMDVMPEFMEJÃNFUSPEFMBDPMVNOB



4PMVDJÓO 1PESFNPTVTBSMBFDVBDJÓO  DPOEFJOVOEBDJÓO$PNPFMEFTUJMBEPFTOIFYBOP DBTJ QVSP  TVT QSPQJFEBEFT TF QPESÃO BQSPYJNBS DPO MBT EFM OIFYBOP QVSP B ž$ -BT QSPQJFEBEFTGÎTJDBTTFUPNBOEF1FSSZZ(SFFO  5ž$,-BHSBWFEBEFT QFDÎàDBEFMMÎRVJEPFT Bž$ WJTDPTJEBED11. eEB  šk 2 2 GI

&Vib-+#&,

aW  aWbdaZ

Vibe^Z( ()'@ &#(&) @aWbdaZ

2%#&.&,aW$e^Z(

 -   MCQJF WBBWBSJBS QFSPOPNVDIP  LA Lk

A EB A A 2 K EB k K

-BUFOTJÓOTVQFSàDJBMFT EJOBTDN 3FJEFUBM  QÃH  1BSÃNFUSPEFáVKP ;ak 2

LA  šk %#*   2%#%*)+ Lk š A

&OMBàHVSB QBSBVOBBMUVSBFOUSFQMBUPTQVMHBEBT $TC NJFOUSBTRVF$TC DPOMBFDVBDJÓO F &OUPODFT @28hW

&(#' %#' σ %#'  2%#(+  2%#((& '% '%

,TJTFVTBMBFDVBDJÓO F 6TBSFNPTFMWBMPSNFOPSQBSBRVFFMEJTFÒPTFB DPOTFSWBEPS 4FHÙOMBFDVBDJÓO 

j ^cjc 2@

š −š A k )&#&'− %#&.&, %#*  2)#-(+ šk 2%#((& %#&.&,

$POTJEFSBSFNPTRVF -BUBTBEFáVKPEFMWBQPSFT7- %%FBDVFSEPDPO CBMBODFTFYUFSOPTEFNBTB %:BRVF-7 -7

K2

9 2 *%% 2'*%%aWbda$] &− A $ K %#'

-BFDVBDJÓOEFMEJÃNFUSP MBFDVBDJÓO  FT 9^V2

)'*%%&#(&)()' x%#.%(+%%&%#,*)#-(+

¿'

&

2&&#%(e^Zh

$PNPFTUFQSPDFEJNJFOUPGVFDPOTFSWBEPS FTQSPCBCMFRVFTFVTFVOBDPMVNOBDPOQJFT EFEJÃNFUSP4J  EJÃNFUSPQJFTBTÎ FMWBMPSEF OPUJFOFNVDIBJNQPSUBO DJB0CTFSWFRVFFTVOBDPMVNOBEFHSBOEJÃNFUSPQBSBFMáVKPEFBMJNFOUBDJÓO-BUBTB EFSFáVKPFTCBTUBOUFBMUB QPSMPRVF7FTBMUB&TUPDBVTBRVFFMEJÃNFUSPTFBNBZPS&M

www.FreeLibros.me



$BQÎUVMP  %JTFÒPEFDPMVNOBTEFQMBUPTZFNQBDBEBT

FGFDUPEFMMVHBSTPCSFFMDÃMDVMPEFMEJÃNFUSPTFQVFEFJOWFTUJHBSSFTPMWJFOEPFMQSPCMFNB %$PNPFMSFTVMUBEPPCUFOJEPFOFTFQSPCMFNBFTQJFTEFEJÃNFUSP MBDPMVNOBTF EJTFÒBSÎBSFTQFDUPBMGPOEP&TUFSFTVMUBEPDPODVFSEBDPOMBSFHMBRVFEJNPTEFTQVÊTEF MBFDVBDJÓO   FMIFYBOPZFMIFQUBOPTPOQBSUFEFMBTFSJFIPNÓMPHBEFMPTBMDBOPT  &MWBMPSEF TFSÃDPNQSPCBEPFOFMFKFNQMP&MFGFDUPEFMBQSFTJÓOEFMBDPMVNOBTF JOWFTUJHBSÃFOFMQSPCMFNB$  %  *453*#6$*¶/:$0/4*%&3"$*0/&4)*%3¦6-*$"4 1"3"1-"5041&3'03"%04

-BEJTUSJCVDJÓOEFMPTQMBUPTUJFOFTVTQSPQJBTSFHMBT&OFTUBTFDDJÓOTFHVJSFNPTMBTQSFTFOUBDJPOFT EF-VEXJH 

#PMMFT 

'BJS   

,JTUFS   Z-PDLFUU  &O FMMBTTFQVFEFOFODPOUSBSNÃTEFUBMMFT-PTBHVKFSPTEFVOQMBUPQFSGPSBEPOPTFEJTUSJCVZFOBMB[BS &OTVMVHBSTFVTBVOBQBVUBEFUBMMBEBQBSBBTFHVSBSRVFMPTáVKPTEFWBQPSZEFMÎRVJEPTPCSFFM QMBUPTFBOVOJGPSNFT&MEJÃNFUSPEFMPTBHVKFSPTUSPRVFMBEPTFOFMQMBUPWBEFBQVMHBEB -PTBHVKFSPTEF USPRVFMBEPTEFBCBKPIBDJBBSSJCB TFVTBODPOGSFDVFODJBFOPQFSBDJÓOBMWBDÎP QBSBSFEVDJSFMBSSBTUSFZNJOJNJ[BSMBDBÎEBEFQSFTJÓO&OFMGVODJPOBNJFOUPOPSNBM TFUSPRVFMBO MPTBHVKFSPTIBDJBBCBKP QPSRVFFTNÃTTFHVSPQBSBFMQFSTPOBMEFNBOUFOJNJFOUP&OBQMJDBDJPOFT DPO FOTVDJBNJFOUP  MPT BHVKFSPT TPO EF  QVMHBEB  P NBZPSFT 1BSB VO TFSWJDJP MJNQJP   EF QVMHBEBFTVOBQSJNFSBQSPQPTJDJÓOSB[POBCMFQBSBFMEJÃNFUSPEFBHVKFSPT &OMBàHVSBTFNVFTUSBVOBEJTUSJCVDJÓODPNÙOEFQMBUPDPOFMQBTPUSJBOHVMBSFRVJMÃUF SP&MVTPEFQBVUBTOPSNBMFTEFUSPRVFMBEPTFSÃNFOPTDPTUPTPRVFVTBSQBVUBTOPOPSNBMFT-B EJTUBODJBFOUSFBHVKFSPTWBEFEPBEPZEPFTVOQSPNFEJPSB[POBCMF-BSFHJÓODPOBHVKFSPT EFCFFTUBSBVOBEJTUBODJBNÎOJNBEFBQVMHBEBTMJCSFTEFMBFOWPMWFOUFEFMBDPMVNOBZEFMB FOUSBEBBMCBKBOUF4FVTBVOFTQBDJPMJCSFNÎOJNPEFBQVMHBEBTBOUFTEFMWFSUFEPSEFMCBKBOUF  QPSRVFFTJNQPSUBOUFQFSNJUJSMBTFQBSBDJÓOEFMÎRVJEPZWBQPS$PNPFMáVKPFOFMQMBUPFTBMUB NFOUFUVSCVMFOUP FMWBQPSOPWBEJSFDUPIBDJBBSSJCBEFTEFMPTBHVKFSPT&MÃSFBBDUJWBEFBHVKFSPT TFDPOTJEFSBFOUSFZQVMHBEBTEFEJTUBODJBEFMPTBHVKFSPTEFMBQFSJGFSJB FOUPODFT FMÃSFBIBTUB MBFOWPMWFOUFEFMBDPMVNOBFTBDUJWB-BGSBDDJÓOEFMBDPMVNOBPDVQBEBQPSMPTBHVKFSPTEFQFOEF EFMUBNBÒPEFMBHVKFSP TVQBTP MBEJTUBODJBFOUSFBHVKFSPT MPTFTQBDJPTMJCSFTZFMUBNBÒPEFMPT

Vertedor Entrada del bajante

Salida del bajante

'*(63" (&0.&53±"%&6/1-"50" 1"4053*"/(6-"3&26*-¦5&30 # (&0.&53±" %&-¦3&"%&-#"+"/5&

www.FreeLibros.me

  %JTUSJCVDJÓOZDPOTJEFSBDJPOFTIJESÃVMJDBTQBSBQMBUPTQFSGPSBEPT



CBKBOUFT&OFMDBTPUÎQJDP EFMBMEFUPEBFMÃSFBEFMBUPSSFFTÃSFBEFBHVKFSPT&TPDPSSFT QPOEFBVOWBMPS "BHVK"BDUJWBB&MWBMPSQSPNFEJPEF FTUÃFOUSFZ ZTFSÃ VOBQSJNFSBQSPQPTJDJÓOSB[POBCMF &MWBMPSEF TFTFMFDDJPOBQBSBRVFMBWFMPDJEBEWPEFMWBQPSQPSMPTBHVKFSPTFTUÊFOUSFFM QVOUPEFHPUFPZMBWFMPDJEBENÃYJNB4FEFCFTFMFDDJPOBSFMQVOUPFYBDUPEFEJTFÒPQBSBPCUFOFS MBNÃYJNBáFYJCJMJEBEFOMBPQFSBDJÓO"TÎ TJFTNVDIPNÃTQSPCBCMFRVFIBZBVOBSFEVDDJÓOFOFM áVKPEFBMJNFOUBDJÓORVFVOBVNFOUPEFMNJTNP MBWFMPDJEBEEFWBQPSEFEJTFÒPEFCFTFSDFSDBOBB MBNÃYJNB-BWFMPDJEBEEFMWBQPSWPQPSMPTBHVKFSPT FOQJFTQPSTFHVOEP TFQVFEFDBMDVMBSDPO kd 2



KEB k  (+%% šK 6V\j_



TJFOEP7MBTMCNPMEFWBQPSI rWMBEFOTJEBEEFMWBQPSFOMCQJFZ"BHVKFMÃSFBUPUBMEFBHVKFSPTFO FMQMBUP FOQJFT&TPCWJPRVF"BHVKTFQVFEFEFUFSNJOBSEFBDVFSEPDPOMBEJTUSJCVDJÓOEFMQMBUP "BHVK EFBHVKFSPT x



Y 'd  )

B

PCJFO 

"BHVK "BDUJWB

C

"BDUJWB "UPUBM − −h



D

&MÃSFBBDUJWBTFDBMDVMBDPO 

DPNPIBZEPTCBKBOUFT&TPCWJPRVF 

6idiVa 2

x9^V' 

E

)

-BHFPNFUSÎBEFMCBKBOUFTFNVFTUSBFOMBàHVSB#4FHÙOFMMB ZMBTSFMBDJPOFTHFPNÊUSJ DBT FMÃSFBEFMCBKBOUF "ETFQVFEFDBMDVMBSDPO 

6Y 2

& ' g θ − hZcθ  '



FTUBOEP FOSBEJBOFT5BNCJÊOTFQVFEFDBMDVMBSFMÃSFBEFMCBKBOUFDPO 6Y 2&− η6idiVa 





"MDPNCJOBSMBTFDVBDJPOFT E

  Z 

TFQVFEFEFTQFKBSFMÃOHVMP ZMBMPOHJUVE EFMWFSUFEPS"TÎPCUVWJNPTMPTSFTVMUBEPTRVFNVFTUSBMBUBCMB&OGPSNBUÎQJDB MBSFMBDJÓOEF MWFSU%JÃNFTUÃEFOUSPEFMJOUFSWBMPEFB 5"#-" 3&-"$*¶/(&0.­53*$"&/53&h:M

7&35

h MWFSU%JÃN

%#%#-,&

%#-'* %#-)(

%#-* %#-&&

%*¦.&530

%#-,* %#,,(

%#.%% %#,'+

www.FreeLibros.me

%#.'* %#++.

%#.* %#*.(

%#.,* %#),-



$BQÎUVMP  %JTFÒPEFDPMVNOBTEFQMBUPTZFNQBDBEBT

4JVOMÎRVJEPOPQVFEFCBKBSQPSFMCBKBOUFDPOMBSBQJEF[OFDFTBSJB TVCJSÃFMOJWFMEFMMÎRVJEPZ MBUPSSFTFJOVOEBSÃ TJDPOUJOÙBTVCJFOEPIBTUBRVFMMFHBBMBQBSUFTVQFSJPSEFMWFSUFEPSFOFMQMBUP EFBSSJCB%FCFFOUPODFTFWJUBSTFRVFTFJOVOEFFMCBKBOUF-PTCBKBOUFTTFEJTFÒBODPOCBTFFOMB DBÎEBEFQSFTJÓOZFMUJFNQPEFSFTJEFODJBEFMMÎRVJEP TVDPTUPFTSFMBUJWBNFOUFQFRVFÒP1PSUPEP FMMP FMEJTFÒPEFCBKBOUFTÓMPTFIBDFFOFMEJNFOTJPOBNJFOUPàOBMEFMFRVJQP &OMBàHVSBTFNVFTUSBO FOGPSNBFTRVFNÃUJDB FMQMBUPZFMCBKBOUFTFWFOMBTBMUVSBTEF QSFTJÓOEFCJEBTBEJWFSTPTFGFDUPTIJESPEJOÃNJDPT-BBMUVSBEFMÎRVJEPUSBOTQBSFOUFFOFMCBKBOUF  IED TFDBMDVMBDPOMBTVNBEFMBTBMUVSBTRVFEFCFOWFODFSTF 

IEDI

 IWFSU IDSFTUB IHSBE IEV



Q TFDP

-BBMUVSBEFMÎRVJEPOFDFTBSJBQBSBWFODFSMBDBÎEBEFQSFTJÓOEFMHBTFOVOQMBUPTFDPFTI QVFEFNFEJSFOGPSNBFYQFSJNFOUBM PTFQVFEFDBMDVMBS -VEXJH  DPO 

]Δe!hZXd 2%#%%(k d' š k 

š V\jV &− β '$8 d'  šA

ZTF

Q TFDP



EPOEFWPFTMBWFMPDJEBEEFMWBQPSQPSMPTBHVKFSPT FOQJFTT EFBDVFSEPDPOMBFDVBDJÓO  &M DPFàDJFOUFEFPSJàDJP $P TFEFUFSNJOBDPOMBDPSSFMBDJÓOEF)VHINBSLZ0$POOFMM  &TUB DPSSFMBDJÓOTFQVFEFBKVTUBSDPOMBTJHVJFOUFFDVBDJÓO ,FTTMFSZ8BOLBU   

8d 2%#-*%('− %#%)'(&

Yd ieaVid

%#%%&,.*)

Yd '   ieaVid



TJFOEPUQMBUPFMFTQFTPSEFMQMBUP&MWBMPSNÎOJNPEFEPUQMBUPFT-BFDVBDJÓO  EBDPNPSF TVMUBEPI Q TFDPFOQVMHBEBTEFMÎRVJEP -BBMUVSBEFMWFSUFEPS IWFSU FTMBBMUVSBSFBMEFMWFSUFEPS&TBBMUVSBNÎOJNBFTQVMHBEBT Z MPNÃTDPNÙOFTEFBQVMHBEBT&MWFSUFEPSEFCFUFOFSMBBMUVSBTVàDJFOUFQBSBRVFFMCBKBOUF PQVFTUPRVFEFTFMMBEPZTJFNQSFDPOUFOHBMÎRVJEP-BBMUVSBEFMBDSFTUBEFMMÎRVJEPTPCSFFMWFSUF EPS IDSFTUB TFDBMDVMBDPOMBFDVBDJÓOEF'SBODJTQBSBWFSUFEPSFT

h

p,seco

hcresta hvert

'*(63" "-563"4%&13&4*¶/&/1-"5041&3'03"%04

www.FreeLibros.me

  %JTUSJCVDJÓOZDPOTJEFSBDJPOFTIJESÃVMJDBTQBSBQMBUPTQFSGPSBEPT





IDSFTUB'WFSU -HMWFSU 



EPOEFIDSFTUBFTUÃFOQVMHBEBT&OFTUBFDVBDJÓO -HFTFMáVKPEFMÎRVJEP FOHBMNJO EFCJEPUBOUPB -DPNPBF&MBSSBTUSFFTFDBMDVMBDPOMBFDVBDJÓO-BDBOUJEBEMWFSUFTMBMPOHJUVESFDUBEFM WFSUFEPSFOQJFT&MGBDUPS'WFSUFTVOGBDUPSEFNPEJàDBDJÓOQBSBUFOFSFODVFOUBMBDVSWBUVSBEFMB QBSFEEFMBDPMVNOBFOFMCBKBOUF #PMMFT  -VEXJH  &TUFGBDUPSTFWFFOMBàHVSB  #PMMFT  )BZVOBFDVBDJÓOQBSBFTUBàHVSB #PMMFT  1BSBDPMVNOBTHSBOEFT EPO EFMWFSUFTHSBOEF 'WFSUUJFOEFB&OMPTQMBUPTQFSGPSBEPT FMHSBEJFOUFEFMÎRVJEPIHSBEBUSBWÊTEFM QMBUPTVFMFTFSNVZQFRVFÒPZDPOGSFDVFODJBOPTFUJFOFFODVFOUB )BZVOBDBÎEBQPSGSJDDJÓOEFCJEBBMáVKPFOFMZCBKPFMCBKBOUFTPCSFFMQMBUP&TUFUÊSNJOP  IEV TFQVFEFFTUJNBSDPOMBTJHVJFOUFFDVBDJÓOFNQÎSJDB -VEXJH #PMMFT   

]Yj 2%#*+

A\ )).6Yj

' 



FTUBOEPIEVFOQVMHBEBT Z"EVFTFMÃSFBEFáVKPCBKPFMNBOEJM FTEFDJS MBUFSNJOBDJÓO EFMCBKBOUF  FOQJFT&OFMDBTPUÎQJDP FMNBOEJMEFMCBKBOUFUJFOFVOFTQBDJPEFQVMHBEBTPCSFFMQMBUP 

"EV FTQBDJPMJCSF MWFSU



&MWBMPSEFIEDDBMDVMBEPDPOMBFDVBDJÓO  FTMBBMUVSBEFMMÎRVJEPUSBOTQBSFOUF FOQVMHB EBT&OVOBDPMVNOBEFEFTUJMBDJÓOFOGVODJPOBNJFOUP FMMÎRVJEPFOFMCBKBOUFUJFOFCVSCVKBT-B EFOTJEBEEFFTUFMÎRVJEPDPOCVSCVKBTTFSÃNFOPSRVFMBEFMMÎRVJEPDMBSP QPSMPRVFMBBMUVSBEFM MÎRVJEPDPOCVSCVKBTFOFMCBKBOUFTFSÃNBZPSRVFIED-BBMUVSBFTQFSBEBEFMMÎRVJEPDPOCVSCVKBT FOFMCBKBOUF IED CVSCTFQVFEFDBMDVMBS 'BJS  DPOMBFDVBDJÓO 

IED CVSCIED

ED





EPOEF EDFTMBEFOTJEBESFMBUJWBEFMBFTQVNB1BSBMBPQFSBDJÓOOPSNBM VOWBMPSEF EDFT TBUJTGBDUPSJP NJFOUSBTRVFEFBTFEFCFSÎBVTBSFODBTPTEJGÎDJMFT 'BJS  1BSBFWJUBSMB

LÍM

ITE

RE

CO

M

EN

DA

DO

RE

LA

CIÓ EN N DE TR E D LON IÁM GIT ET UD RO D DE E VE TO RTE RR DO E R

Fvert, FACTOR DE CORRECCIÓN POR CONSTRICCIÓN DEL VERTEDOR

Q/(lw)0.5 = (CARGA LÍQUIDA, GPM)/(LONGITUD DE VERTEDOR, PIES)2.5

'*(63" '"$503%&$033&$$*¶/1"3"7&35&%03 '7&35 1"3"7&35&%03&4%&4&(.&/50 50."%0%&#0--&4  3&*.13&40$0/"6503*;"$*¶/%&1&530-&6.130$&44*/(

www.FreeLibros.me



$BQÎUVMP  %JTFÒPEFDPMVNOBTEFQMBUPTZFNQBDBEBT

5"#-" 5*&.104.±/*.04%&3&4*%&/$*"&/#"+"/5&4 5FOEFODJBBFTQVNBS

&KFNQMPT

5JFNQP T EFSFTJEFODJB

1PDB

"MDPIPMFT IJESPDBSCVSPTEFCBKP1.



.FEJBOB

)JESPDBSCVSPTEF1.JOUFSNFEJP



"MUB

"CTPSCFEPSFTEFBDFJUFNJOFSBM



.VZBMUB

"NJOBT HMJDPMFT



'VFOUF,JTUFS F  Z-VEXJH  

JOVOEBDJÓOEFMCBKBOUF MBBMUVSBFOUSFQMBUPTEFCFTFSNBZPSRVFIED CVSC&OUPODFT FOFMGVODJPOB NJFOUPOPSNBM MBBMUVSBFOUSFQMBUPTEFCFTFSNBZPSRVFIED &MCBKBOUFTFEJTFÒBQBSBRVFFMUJFNQPEFSFTJEFODJBEFMMÎRVJEPTFBEFBTFHVOEPT&O MBUBCMBTFJOEJDBOMPTUJFNQPTEFSFTJEFODJBNÎOJNPT ,JTUFS F -VEXJH  &M UJFNQPEFSFTJEFODJBFOVOCBKBOUFSFDUPTFHNFOUBEPFT 

igZh 2

6Y]YX(+%%šA A ZEB A &'

!   TFHVOEPT



FMGBDUPSFTQBSBQBTBSEFIPSBTBTFHVOEPT EF- F ZFMGBDUPSDPOWJFSUFIEDEFQVMHBEBT BQJFT-BEFOTJEBEFTMBEFMMÎRVJEPUSBOTQBSFOUFZIEDFTMBBMUVSBEFMÎRVJEPUSBOTQBSFOUF4FVTB MBFDVBDJÓO  QBSBBTFHVSBSRVFIBZBUJFNQPTVàDJFOUFQBSBTFQBSBSWBQPSZMÎRVJEPFOMPT CBKBOUFT,JTUFS  SFDPNJFOEBVOÃSFBEFCBKBOUFNÎOJNBJHVBMBEFMÃSFBEFMBDPMVNOB $POBMJNFOUBDJPOFTEFMÎRVJEPTBUVSBEP FTOFDFTBSJPEJTFÒBSMPTCBKBOUFTQBSBMBTFDDJÓOEFBHPUB NJFOUP EPOEFFMáVKPEFMÎRVJEPFTNÃYJNP -BàHVSBNVFTUSBRVFMPTEPTMÎNJUFTEFMGVODJPOBNJFOUPBDFQUBCMFEFMQMBUPTPOFMBSSBT USFFYDFTJWPZFMHPUFPFYDFTJWP-PTQVOUPTEFHPUFPZEFEFTDBSHBTPOEJGÎDJMFTEFEFUFSNJOBSDPO FYBDUJUVE4FQVFEFIBDFSVOBOÃMJTJTBQSPYJNBEPQBSBBTFHVSBSRVFFMGVODJPOBNJFOUPTFBBSSJCB EFMQVOUPEFHPUFP&MMÎRVJEPOPQBTBSÃQPSMPTBHVKFSPTTJFNQSFRVFMBTVNBEFMBTBMUVSBTEFCJEBT BMBUFOTJÓOTVQFSàDJBM I ZBMáVKPEFHBT I Q TFDPTFBNBZPSRVFVOBGVODJÓORVFEFQFOEFEFMB BMUVSBIJESÃVMJDB&TUBDPOEJDJÓOQBSBFWJUBSHPUFPFYDFTJWPTFQVFEFEFUFSNJOBSDPOMBDPSSFMBDJÓO HSÃàDBEF'BJS 

PDBMDVMBS ,FTTMFSZ8BOLBU  DPO 

I

 I   Y−Y

Q TFDP



EPOEFYIWFSU IDSFTUB IHSBE-BFDVBDJÓO  FTWÃMJEBQBSBWBMPSFTEF FOUSFZ-B DBÎEBEFQSFTJÓOFOQMBUPTFDPTFDBMDVMBDPOMBTFDVBDJPOFT  Z  -BBMUVSBQPSUFOTJÓO TVQFSàDJBM I TFFTUJNB 'BJS  DPO 

]σ 2

%#%)% σ  šAYd



EPOEF FTUÃFOEJOBTDN r-FOMCQJF EFOQVMHBEBTZI FOQVMHBEBTEFMÎRVJEP-BFDVBDJÓO   FTDPOTFSWBEPSB &+&.1-0 %JTUSJCVDJÓOEFQMBUPZDÃMDVMPTIJESÃVMJDPT %FUFSNJOFMBEJTUSJCVDJÓOEFMQMBUPZMBTDBÎEBTEFQSFTJÓOQBSBMBDPMVNOBEFEFTUJMBDJÓO FOMPTFKFNQMPTZ%FUFSNJOFUBNCJÊOTJIBCSÃQSPCMFNBDPOBSSBTUSFPDPOMMPSP

www.FreeLibros.me

  %JTUSJCVDJÓOZDPOTJEFSBDJPOFTIJESÃVMJDBTQBSBQMBUPTQFSGPSBEPT



%FUFSNJOFTJMPTCBKBOUFTGVODJPOBSÃOFOGPSNBDPSSFDUB&MBCPSFFTUPTDÃMDVMPTTÓMPFOMB QBSUFTVQFSJPSEFMBDPMVNOB 4PMVDJÓO ­TUBFTVOBBQMJDBDJÓOEJSFDUBEFMBTFDVBDJPOFTWJTUBTFOFTUBTFDDJÓO1PESFNPTDPNFO[BS EFUFSNJOBOEPFMBSSBTUSF&OFMFKFNQMP PCUVWJNPT'W&OUPODFT EFBDVFS EPDPOMBàHVSB BMEFMBJOVOEBDJÓO  4FEFTQFKBF 

Z2

ψA  &− ψ



ZBRVF- -7 7MCNPMI Z2

%#%)*'%%% 2.)#')aWbda$] &− %#%)*

Z- FMCNPMI&TUBDBOUJEBEEFBSSBTUSFFTCBTUBOUFSB[POBCMF -PTDÃMDVMPTHFPNÊUSJDPTTFIBDFODPNPTFEFTDSJCFBDPOUJOVBDJÓO QBSBVOBDPMVNOB EFQJFTEFEJÃNFUSP &DVBDJÓO E

"UPUBM  QJFT &DVBDJÓO 

"E −  QJFT $POMBUBCMBTFPCUJFOFMWFSU%JÃN PMWFSUQJFT &DVBDJÓO D

"BDUJWB  − QJFT &DVBDJÓO C

"BHVK   QJFT 6TBSFNPTMÃNJOBDBMJCSFQBSBFMQMBUP UQMBUPQVMH

DPOBHVKFSPTEFQVMH &OUPODFT EPUQMBUP %FBDVFSEPDPOMBFDVBDJÓO 

kd 2

'*%%-+#&, KEB k 2)&#&e^Zh$h 2 (+%%%#&.',#+ (+%% šK 6V\j_

EPOEF WFTMBEFMFKFNQMP&TUBWFMPDJEBEFOBHVKFSPTFTSB[POBCMF &OUPODFTFTQPTJCMFDBMDVMBSMPTUÊSNJOPTJOEJWJEVBMFTEFDBÎEBEFQSFTJÓO&MDPFà DJFOUFEFPSJàDJP $P EFBDVFSEPDPOMBFDVBDJÓO 

FT $Pm      %FMBFDVBDJÓO 

]Δe!hZXd 2%#%%()&#&' %#&.'

+&#%( &−%#%&  2'#),'eja\ )&#&' %#,*.'

&O FTUB FDVBDJÓO  TF VTÓ MB rX B ž$ PCUFOJEB FO 1FSSZ Z (SFFO   QÃHT   4F TFMFDDJPOBSÃVOBBMUVSBEFWFSUFEPSIWFSUQVMH &MGBDUPSEFDPSSFMBDJÓO'WFSUTFQVFEFEFUFSNJOBSDPOMBàHVSB-HFOMBBCTDJTB FTFMáVKPEFMÎRVJEP JODMVZFOEPBSSBTUSF FOHBMPOFTQPSNJOVUP A\ 2'%.)#')-+#&,

&]g \Va aW & e^Z(  ,#) 2*),#&\Va$b^c e^Z( +%b^c aWbda )&#&'aW

www.FreeLibros.me



$BQÎUVMP  %JTFÒPEFDPMVNOBTEFQMBUPTZFNQBDBEBT

6WhX^hV2

A\ &'#* kZgi

2

*),#& -'#*

2(#%''

1BSÃNFUSPWFSU %JÃN-VFHP'WFSU 4FHÙOMBFDVBDJÓO 

]XgZhiV 2%#%.'&#%'*

*),#& ' $(  2&#*,,eja\# -

4VQPOESFNPT RVF IHSBE   &M ÃSFB CBKP FM CBKBOUF TF DBMDVMB DPO VO FTQBDJP MJCSF EF  QVMHBEB %FMBFDVBDJÓO 

"EV   QJF %FMBFDVBDJÓO 

]Yj 2%#*+

*),#& )).'$(

'

2&#-,&eja\#

"MUVSBUPUBM EFBDVFSEPDPOMBFDVBDJÓO   ]YX 2'#),' ' &#*,, % &#-,&2,#.'

4POQVMHBEBTEFMÎRVJEPUSBOTQBSFOUF1BSBFMTJTUFNBDPOCVSCVKBT ]YX!WjgW 2

,#.' 2&*#-) %#*

$PNPFTUPFTNVDIPNFOPSRVFMBBMUVSBFOUSFQMBUPTEFQVMHBEBT OPEFCFIBCFSQSP CMFNBT&MUJFNQPEFSFTJEFODJBFT TFHÙOMBFDVBDJÓO 

igZh 2

.#*&,#.'(+%%)&#&' 2*#&*h '%.)#')-+#&,&'

&TNBZPSRVFFMUJFNQPNÎOJNPEFSFTJEFODJB EFT 1PESFNPTWFSJàDBSTJIBZHPUFP DPOMBFDVBDJÓO 

]σ 2

%#%)%&(#' 2%#%+)&#&'($&+

&OUPODFT FMMBEPJ[RVJFSEPEFMBFDVBDJÓO  FT ]Δe!hZXd ]σ 2'#),' %#%+-2'#*)

-BGVODJÓOY  ZFMMBEPEFSFDIPEFMBFDVBDJÓO  FT&T PCWJPRVFTFTBUJTGBDFMBEFTJHVBMEBE/PEFCFFOUPODFTIBCFSQSPCMFNBEFHPUFP 5FOHBFODVFOUBRVFTFEFCFDPNQSPCBSFMEJTFÒPFOPUSPTMVHBSFTEFMBDPMVNOB$PNPFO FMQSPCMFNB%TFDBMDVMÓVOEJÃNFUSPEFQVMHBEBT OFDFTBSJPFOMBTFDDJÓOEFBHPUBNJFOUP  FTOFDFTBSJPSFQFUJSMPTDÃMDVMPTQBSBMBTFDDJÓOEFFOSJRVFDJNJFOUP WFBFMQSPCMFNB% &OFM QSPCMFNB%TFEFNVFTUSBRVFMBBDVNVMBDJÓOEFMÎRVJEPFOMPTCBKBOUFTQPESÎBTFSVOQSPCMFNB FOFMGPOEPEFMBDPMVNOB BÙODPOVOEJÃNFUSPEFQJFT&TPTVDFEFQPSRVF-- '

www.FreeLibros.me

  %JTFÒPTEFQMBUPTEFWÃMWVMBT



MCNPMI CBTUBOUFNBZPSRVFFMáVKPEFMÎRVJEPFOMBQBSUFTVQFSJPSEFMBDPMVNOB&TUFQSPCMFNB QVFEFNBOFKBSTFBVNFOUBOEPFMFTQBDJPMJCSFFOUSFCBKBOUFZQMBUP  %*4&µ0%&1-"504%&7¦-76-"4

-PTQMBUPTEFWÃMWVMBTRVFTFJMVTUSBOFOMBàHVSB TPOEJTQPTJUJWPTQBUFOUBEPT&MQSPWFFEPS EFCFIBDFSFMEJTFÒPàOBM4JOFNCBSHP FMQSPWFFEPSOPSNBMNFOUFOPIBSÃMPTFTUVEJPTEFPQUJNJ [BDJÓORVFRVJTJFSBFMDPNQSBEPS TJOSFDJCJSVOBDPNQFOTBDJÓOQPSFMUSBCBKPBEJDJPOBM"EFNÃT  TJFNQSFTFBDPOTFKBDPOPDFSUBOUPBDFSDBEFMFRVJQPDPNPTFBQPTJCMF BOUFTEFIBDFSVOBDPNQSB JNQPSUBOUF&OUPODFT FTNVZÙUJMFMQSPDFEJNJFOUPEFEJTFÒPQBSBQMBUPTEFWÃMWVMBTOPQBUFOUBEPT EF#PMMFT 

QBSBFTUJNBSFMGVODJPOBNJFOUP-VEXJH  EFTDSJCFFMEJTFÒPEFQMBUPTEF WÃMWVMBTQBUFOUBEPT &OFMQSPDFEJNJFOUPEFEJTFÒPEF#PMMFT  TFVTBDPNPCBTFFMEFEJTFÒPEFQMBUPTQFS GPSBEPTZTFNPEJàDBMPOFDFTBSJP6OBEFMBTQSJODJQBMFTEJGFSFODJBTFOUSFMPTQMBUPTEFWÃMWVMBTZ MPTQMBUPTQFSGPSBEPTTFEFCFBTVTDBSBDUFSÎTUJDBTEFDBÎEBEFQSFTJÓO&OVOQMBUPEFWÃMWVMBT MB DBÎEBEFQSFTJÓOFOTFDPTFNVFTUSBFOMBàHVSB #PMMFT  "MBVNFOUBSMBWFMPDJEBEEFM HBT  QQSJNFSPBVNFOUBZEFTQVÊTTFOJWFMBFOVOBQMBOJDJFIPSJ[POUBM&OMBQSJNFSBQBSUF EF Q DSFDJFOUF UPEBTMBTWÃMWVMBTFTUÃODFSSBEBT&OFMQVOUPEFFRVJMJCSJPDFSSBEP TFBCSFOBMHVOBTWÃM WVMBT&OMBSFHJÓOQMBOBBCSFONÃTWÃMWVMBT IBTUBRVFUPEBTMBTWÃMWVMBTFTUÃOBCJFSUBTFOFMQVOUP EFFRVJMJCSJPBCJFSUP$POUPEBTMBTWÃMWVMBTBCJFSUBT  QBVNFOUBBNFEJEBRVFTJHVFBVNFOUBOEP MBWFMPDJEBEEFMHBT-BDBÎEBEFQSFTJÓO FOQVMHBEBTEFMÎRVJEP QBSBWÃMWVMBTDFSSBEBTZBCJFSUBT  TFQVFEFFYQSFTBSFOGVODJÓOEFMBFOFSHÎBDJOÊUJDB 

]Δe!k{ak 2 @k

šk k d'  šA '\

B

EPOEFWPFTMBWFMPDJEBEEFMWBQPSQPSMPTBHVKFSPTFOMBQMBDB FOQJFT HQJFTZ,WFTEJTUJOUB QBSBWÃMWVMBTDFSSBEBTZBCJFSUBT1BSBMPTEBUPTEFMBàHVSB 

,W DFSSBEB   ,W BCJFSUB

C

 P W

0CTFSWFRVFMBFDVBDJÓO B UJFOFMBNJTNBEFQFOEFODJBSFTQFDUPBW  -RVFI Q TFDPQBSBMPT QMBUPTQFSGPSBEPT FOMBFDVBDJÓO   &MQVOUPEFFRVJMJCSJPDFSSBEPTFQVFEFEFUFSNJOBSQPSRVFMBQSFTJÓOEFCFTPTUFOFSFMQFTPEF MBWÃMWVMB 8WÃMW FOMJCSBT&OUPODFT MBQSFTJÓOFT8WÃMW"W EPOEF"WFTFMÃSFBEFQBTPEFMBWÃMWVMB  FOQJFTDVBESBEPT-BTDBÎEBTEFQSFTJÓO FOQJFTEFMÎRVJEPDPOEFOTJEBE -FT 

]Δe!k{ak 28k

Lk{ak  6k šA



BRVÎTFJOUSPEVDFFMDPFàDJFOUFEFMBWÃMWVMB $W QBSBUFOFSFODVFOUBMBTQÊSEJEBTQPSUVSCVMFODJB 1BSBMPTEBUPTEFMBàHVSB $W"MJHVBMBSMBTFDVBDJPOFT  Z 

TFQVFEFO EFTQFKBSMPTQVOUPTEFFRVJMJCSJPDFSSBEPZBCJFSUP 

Kd!WVa

2 8k Lk{ak '\$@k 6k šk 



FOEPOEFWP CBMFTMBWFMPDJEBEFOFMQVOUPEFFRVJMJCSJPDFSSBEP TJTFVTB,W DFSSBEP-PTWBMPSFTEF ,W DFSSBEP ,W BCJFSUPZ$WEFQFOEFOEFMFTQFTPSEFMQMBUPZ FOQFRVFÒPHSBEP EFMUJQPEFMBWÃMWVMB #PMMFT  

www.FreeLibros.me



$BQÎUVMP  %JTFÒPEFDPMVNOBTEFQMBUPTZFNQBDBEBT

h

p,válv

, pulg de agua

Datos experimentales Modelo

Punto de equilibrio cerrado Todas las válvulas cerradas

Punto de equilibrio abierto

Válvulas parcialmente abiertas

Vo

,

Todas las válvulas abiertas

pies/s

'*(63" $"±%"%&13&4*¶/&/1-"50%&7¦-76-"44&$0 %& #0--&4  3&*.13&40%&$)&.*$"-&/(*/&&3*/(130(3&44  4&15 ¥ ".&3*$"/*/45*565&0'$)&.*$"-&/(*/&&34 (SBOQBSUFEFMPRVFSFTUBEFMEJTFÒPQSFMJNJOBSEFQMBUPTEFWÃMWVMBTFTJHVBM PDPOVOBMJHFSB NPEJàDBDJÓO RVFFMEJTFÒPEFMPTQMBUPTQFSGPSBEPT ,JTUFS  -PDLFUU -BSTPOZ ,JTUFS  -PTDÃMDVMPTEFJOVOEBDJÓOZEFEJÃNFUSPTPOJHVBMFT BQBSUFEFMGBDUPSEFDPSSFDDJÓO QBSB"BHVK"B RVFTFTVTUJUVZFQPSVOGBDUPSEFDPSSFDDJÓOQBSB"SBOVSB"BDU4FVTBOMPT NJTNPTWBMPSFTQBSBMPTGBDUPSFTEFDPSSFDDJÓO&MÃSFBEFSBOVSB "SBOVSB FTFMÃSFBWFSUJDBMFOUSFFM QMBUPZMBQBSUFTVQFSJPSEFMBSBOVSB BUSBWÊTEFMBDVBMQBTBFMWBQPSFOEJSFDDJÓOIPSJ[POUBM&O MBSFHJÓOFOUSFMPTQVOUPTEFFRVJMJCSJP FMÃSFBEFSBOVSBFTWBSJBCMF ZTFQVFEFEFUFSNJOBSDPO MBGSBDDJÓOEFWÃMWVMBTRVFFTUÃOBCJFSUBT-BDBÎEBEFQSFTJÓODPOMBFDVBDJÓO  FTMBNJTNB  NJFOUSBT RVF MB FDVBDJÓO   QBSB I Q TFDP TF TVTUJUVZF QPS MB FDVBDJÓO   P   -BT FDVBDJPOFT  B  OPDBNCJBO&TQSPCBCMFRVFFMHSBEJFOUFBUSBWÊTEFMQMBUPEFWÃMWV MBT IHSBE TFBNBZPSRVFFOVOQMBUPQFSGPSBEP QFSPFTDPNÙOOPUPNBSMPFODVFOUB-PTQMBUPTEF WÃMWVMBTTVFMFOGVODJPOBSDPOWFSUFEFSPTNÃTBMUPT-POPSNBMFTVOBIWFSUEFQVMHBEBT&OGPSNB DBSBDUFSÎTUJDB IBZEFBWÃMWVMBTQPSQJFEFÃSFBBDUJWB ,JTUFS   -BFàDJFODJBEFMQMBUPEFWÃMWVMBTEFQFOEFEFMBWFMPDJEBEEFMWBQPS FMEJTFÒPEFMBTWÃMWVMBTZ FMTJTUFNBRVÎNJDPRVFTFFTUÊEFTUJMBOEP"FYDFQDJÓOEFáVKPTEFWBQPSDFSDBOPTBMBJOVOEBDJÓO  MBTFàDJFODJBTEFMPTQMBUPTEFWÃMWVMBTTPOJHVBMFTPNBZPSFTRVFMBTEFMPTQMBUPTQFSGPSBEPT RVFB

www.FreeLibros.me

  1BSUFTJOUFSOBTEFMBTDPMVNOBTFNQBDBEBT



TVWF[TPOJHVBMFTPNBZPSFTRVFMBTEFMPTQMBUPTDPOTPNCSFSPTEFCVSCVKFP"TÎ DVBOEPTFVTBO MBTDPSSFMBDJPOFTEFFàDJFODJBRVFTFEFTDSJCJFSPOBOUFTTFPCUFOESÃVOEJTFÒPDPOTFSWBEPS  */530%6$$*¶/"-%*4&µ0%&$0-6./"4&.1"$"%"4

'SFDVFOUFNFOUF  FO MVHBS EF DPMVNOBT EF QMBUPT TF VTBO DPMVNOBT FNQBDBEBT QBSB EFTUJMBDJÓO  BCTPSDJÓO BSSBTUSFZBWFDFTFYUSBDDJÓO-BTDPMVNOBTFNQBDBEBTTFVTBODPONFOPSFTEJÃNFUSPT  QPSRVFFTDPTUPTPDPOTUSVJSVOBDPMVNOBEFQMBUPTRVFGVODJPOFCJFODPOEJÃNFUSPQFRVFÒP&OEF àOJUJWB MBTDPMVNOBTFNQBDBEBTTPONÃTFDPOÓNJDBTDVBOEPUJFOFONFOPTEFQJFTEFEJÃNFUSP &OMBTDPMVNOBTFNQBDBEBTNBZPSFTFMMÎRVJEPQPESÎBUFOEFSBDBOBMJ[BSTF ZTJOVOEJTFÒPDVJEBEP TP MBTUPSSFTDPOFNQBRVFBMFBUPSJPQPESÎBOOPGVODJPOBSCJFO&ONVDIPTDBTPT MBTDPMVNOBTEF QMBUPTEFHSBOEJÃNFUSPTPONFOPTDPTUPTBT-BTDPMVNOBTFNQBDBEBTUJFOFOMBWFOUBKBEFNFOPS DBÎEBEFQSFTJÓOQPSMPRVFTPOÙUJMFTFOGSBDDJPOBNJFOUPTBMWBDÎP "MEJTFÒBSVOBUPSSFFNQBDBEB MBFMFDDJÓOEFMNBUFSJBMEFFNQBRVFTFCBTBFODPOTJEFSBDJPOFT FDPOÓNJDBT)BZEJTQPOJCMFVOBWBSJFEBEEFFNQBRVFT RVFJODMVZFOMPTBMFBUPSJPTZMPTFTUSVDUV SBEPT6OBWF[TFMFDDJPOBEPFMFNQBRVF FTOFDFTBSJPDPOPDFSFMEJÃNFUSPEFMBDPMVNOBZMBBMUVSB EF FNQBRVFOFDFTBSJB&MEJÃNFUSPEFMBDPMVNOBTFEJNFOTJPOBDPOCBTFFOFMBDFSDBNJFOUPB MBJOVOEBDJÓOPMBDBÎEBEFQSFTJÓOBDFQUBCMF-BBMUVSBEFMFNQBRVFQVFEFEFUFSNJOBSTFDPOVO BOÃMJTJTEFFUBQBTEFFRVJMJCSJPPCJFOBQBSUJSEFDPSSFMBDJPOFTEFUSBOTGFSFODJBEFNBTB"RVÎTF EFTDSJCJSÃFMBOÃMJTJTEFFUBQBTEFFRVJMJCSJP VTBOEPFMQSPDFEJNJFOUPEFMBBMUVSBFRVJWBMFOUFBVO QMBUPUFÓSJDP )&51 EFIFJHIUFRVJWBMFOUUPBUIFPSFUJDBMQMBUF FMNÊUPEPEFEJTFÒPQPSUSBOTGFSFO DJBEFNBTBTFEFTDSJCJSÃFOFMDBQÎUVMP  1"35&4*/5&3/"4%&-"4$0-6./"4&.1"$"%"4

&OVOBDPMVNOBFNQBDBEBRVFTFVTBQBSBDPOUBDUPWBQPSMÎRVJEP FMMÎRVJEPáVZFTPCSFMBTVQFS àDJFEFMFNQBRVFZFMWBQPSáVZFQPSMPTIVFDPTEFOUSPEFMFNQBRVFZFOUSFMPTFMFNFOUPTEFM FNQBRVF&MPCKFUPEFMFNQBRVFFTQSPQPSDJPOBSVODPOUBDUPÎOUJNPFOUSFFMWBQPSZFMMÎRVJEP  VOBTVQFSàDJFNVZHSBOEFQBSBMBUSBOTGFSFODJBEFNBTB"MNJTNPUJFNQP FMFNQBRVFEFCFQFS NJUJSFMWBDJBEPGÃDJMEFMMÎRVJEPZQSPEVDJSVOBCBKBDBÎEBEFQSFTJÓOFOFMáVKPEFMHBT:BRVFDPO GSFDVFODJBMPTFNQBRVFTTFEFKBODBFSBMB[BSEFOUSPEFMBDPMVNOB UBNCJÊOEFCFOEJTFÒBSTFQBSB RVFVOBQJF[BEFFNQBRVFOPDVCSBOJFONBTDBSFMBTVQFSàDJFEFPUSB -PTFNQBRVFTTFDPOTJHVFOFOVOBHSBOWBSJFEBEEFFTUJMPT BMHVOPTEFFMMPTTFNVFTUSBOFO MBàHVSB-PTFTUJMPTNÃTTFODJMMPT DPNPMPTBOJMMPT3BTDIJH TVFMFOTFSNFOPTDPTUPTPTQPS VOJEBEEFWPMVNFO QFSPDPOGSFDVFODJBTFSÃONÃTDPTUPTPTQBSBEFUFSNJOBEBFàDJFODJB ZBRVF BMHVOPTEFMPTFNQBRVFTQBUFOUBEPTTPONVDIPNÃTFàDJFOUFT-PTBOJMMPTZMBTTJMMBTJOEJWJEVBMFT TFEFTDBSHBOFOMBDPMVNOBZRVFEBOEJTUSJCVJEPTBMB[BS-PTFNQBRVFTFTUSVDUVSBEPTVPSEFOBEPT DPNPMBSFE(MJUTDI (PPEMPFZ,PDI4VM[FS TFEFQPTJUBODPODVJEBEPFOFMJOUFSJPSEFMBDPMVNOB &OHFOFSBM MPTFNQBRVFTFTUSVDUVSBEPTUJFOFONFOPSFTDBÎEBTEFQSFTJÓOZTPONÃTFàDJFOUFTRVF MPTFNQBRVFTEFTDBSHBEPT QFSPTVFMFOTFSNÃTDPTUPTPT-PTFNQBRVFTTFDPOTJHVFOFOEJWFSTPT NBUFSJBMFTDPNPQMÃTUJDPT NFUBMFT DFSÃNJDBTZWJESJPT6OBEFMBTWFOUBKBTEFMBTDPMVNOBTFNQB DBEBTFTRVFTFQVFEFOVTBSQBSBTFSWJDJPFYUSFNBEBNFOUFDPSSPTJWP &MFNQBRVFEFCFTPTUFOFSTFFOGPSNBBEFDVBEBFOMBDPMVNOBQBSBBQSPWFDIBSUPEBTVDBQB DJEBEEFTFQBSBDJÓO&OMBàHVSBTFWFVOEJBHSBNBEFVOBDPMVNOBEFEFTUJMBDJÓOFNQBDBEB "EFNÃTEFMBTTFDDJPOFTFNQBDBEBT EPOEFTFIBDFMBTFQBSBDJÓO TFOFDFTJUBOTFDDJPOFTQBSBEJTUSJ CVJSFMSFáVKP MBBMJNFOUBDJÓOZWBQPSBMGPOEP BTÎDPNPQBSBTFQBSBSFMMÎRVJEPZFMWBQPS-PTEJT

www.FreeLibros.me



$BQÎUVMP  %JTFÒPEFDPMVNOBTEFQMBUPTZFNQBDBEBT

6

7

8

9

:

'*(63" &.1"26&41"3"$0-6./"4" 4*--"*/5"-09%&$&3¦.*$"# 4*--"461&3 */5"-09%&1-¦45*$0$ "/*--01"-- % $"356$)0(&.1",& 3&+*--"(-*54$)&'" -"4'*(63"4" #:$ $035&4±"%&/0350/$)&.*$"-130$&44130%6$54 ",30/ 0)*0-"4 '*(63"4%:&$035&4±"%&(-*54$) */$ %"--"4 5&9"4 USJCVJEPSFTEFMÎRVJEPTPONVZJNQPSUBOUFTQBSBFMDPSSFDUPGVODJPOBNJFOUPEFMBDPMVNOB-PTFN QBRVFTBMFBUPSJPTZFTUSVDUVSBEPTQFRVFÒPTOFDFTJUBORVFMBEJTUSJCVDJÓOEFMÎRVJEPZWBQPSTFBNFKPS ,JTUFS   4JFMDPDJFOUF EJÃNFUSPEFDPMVNOB  EJÃNFUSPEFFNQBRVF   FTQSPCBCMF RVF IBZB NBMB EJTUSJCVDJÓO EF MÎRVJEP Z WBQPS 5BNCJÊO  MB NBMB EJTUSJCVDJÓO SFEVDF MB DBQBDJEBE EFSFDIB[PEFMFNQBRVFZDBVTBVOHSBOBVNFOUPFOMB)&51DPOCBKPTáVKPTEFMÎRVJEP&ODBTPT

www.FreeLibros.me

  "MUVSBEFMFNQBRVF.ÊUPEPEFMB)&51



Región de separación E

Placa opresora m p a q u Placa de soporte e Distribuidor de líquido

E

m Placa opresora p a q u Placa de soporte e

Distribuidor de vapor Separación

'*(63" $0-6./"&.1"$"%"%&%&45*-"$*¶/ UÎQJDPT  MPT EJTUSJCVJEPSFT EF MÎRVJEP UJFOFO WBSJBT QVOUBT EF HPUFP #POJMMB   SFDPNJFOEB TFJT EJF[QBSBGSBDDJPOBNJFOUPTEFBMUBQVSF[B QVOUBTEFHPUFPQPSQJFDVBESBEPQBSBFNQBRVFTHSBOEFT FNQBRVFTBMFBUPSJPT  QVMH PFNQBRVFTFTUSVDUVSBEPTDPOQMJFHVFTQVMH 1BSBFNQBRVFT QFRVFÒPT BMFBUPSJPTEF QVMHPFTUSVDUVSBEPTDPOQMJFHVFT EF QVMH

SFDPNJFOEBPDIP  QBSBBMUBQVSF[B QVOUBTEFHPUFPQPSQJFDVBESBEP BBMUBTDBSHBTEFMÎRVJEPZ QBSBBMUBQVSF[B  QVOUBTEFHPUFPQPSQJFDVBESBEPDPOCBKBTDBSHBTEFMÎRVJEP-BTOFDFTJEBEFTQBSBFNQBRVFTEF UBNBÒPJOUFSNFEJPRVFEBOFOUSFMBTSFDPNFOEBDJPOFTQBSBFNQBRVFTQFRVFÒPTZHSBOEFT-BTCBKBT DBSHBTEFMÎRVJEPOFDFTJUBONÃTQVOUBTEFHPUFP QPSRVFFMMÎRVJEPTFUJFOEFBSFQBSUJSNFOPT-PT FGFDUPTEFMBNBMBEJTUSJCVDJÓOEFMMÎRVJEPTFJOWFTUJHBOFOFMQSPCMFNB%&MFTDBMBNJFOUPEFMPT EJTUSJCVJEPSFTTFIBDFNBOUFOJFOEPDPOTUBOUFMBDBOUJEBEEFQVOUBTEFHPUFPQPSQJFDVBESBEP1P ESÃOOFDFTJUBSTFTJTUFNBTEFSFEJTUSJCVDJÓOFOMBTDPMVNOBTHSBOEFT&MFNQBRVFTFTPQPSUBDPOVOB QMBDBRVFQVFEFTFSVOBSFEPVOBTFSJFEFCBSSBT$POGSFDVFODJBTFFNQMFBVOBQMBDBPQSFTPSBQBSB FWJUBSFMNPWJNJFOUPEFMFNQBRVFDVBOEPTVDFEFOHPMQFTEFáVKPEFMHBT$PNPMÎRVJEPZWBQPSáV ZFOBDPOUSBDPSSJFOUFQPSMBDPMVNOB OPIBZCBKBOUFT-BTQBSUFTJOUFSOBTEFMBTUPSSFTFNQBDBEBTTF EFCFOEJTFÒBSDPODVJEBEPQBSBPCUFOFSVOCVFOGVODJPOBNJFOUP WFB'BJS ,JTUFS   -VEXJH 1FSSZZ(SFFFO Z4USJHMF  .ÃTEFUBMMFTBQBSFDFOFOMBTQVCMJDBDJPOFTEFMPT GBCSJDBOUFT-BTQBSUFTJOUFSOBTEFVOBDPMVNOBFNQBDBEBQBSBBCTPSDJÓOPBSSBTUSFTFSÎBOQBSFDJEBT BMBTEFMBDPMVNOBEFEFTUJMBDJÓOEFMBàHVSB QFSPTJOMBBMJNFOUBDJÓOBMDFOUSP FMWBQPSJ[BEPS PFMDPOEFOTBEPS  "-563"%&-&.1"26&.­50%0%&-")&51

"VODVBOEPFOVOBUPSSFFNQBDBEBFMDPOUBDUPFOUSFMÎRVJEPZWBQPSFTDPOUJOVP FOMVHBSEFEJT DPOUJOVP TFQVFEFBOBMJ[BSDPNPVOBUPSSFEFFUBQBT4VQPOESFNPTRVFMBQBSUFFNQBDBEBEFMB DPMVNOBTFQVFEFEJWJEJSFOWBSJPTTFHNFOUPTEFJHVBMBMUVSB$BEBTFHNFOUPGVODJPOBDPNPVOB

www.FreeLibros.me



$BQÎUVMP  %JTFÒPEFDPMVNOBTEFQMBUPTZFNQBDBEBT

FUBQBEFFRVJMJCSJPZFMMÎRVJEPZFMWBQPSRVFTBMFOEFMTFHNFOUPFTUÃOFOFRVJMJCSJP&TJNQPSUBOUF UFOFSFODVFOUBRVFFMNPEFMPEFFUBQBTOPFTVODVBESPFYBDUPEFMPRVFTVDFEFGÎTJDBNFOUFFOMB DPMVNOB QFSPTFQVFEFVTBSQBSBEJTFÒPT&MNPEFMPEFFUBQBTQBSBEJTFÒBSDPMVNOBTFNQBDBEBT GVFFNQMFBEPQPSQSJNFSBWF[QPS1FUFST   $BMDVMBSFNPTMBDBOUJEBEEFFUBQBTDPOVOBOÃMJTJTEF.D$BCF5IJFMFPVOPEF-FXJTZEFTQVÊT DBMDVMBSFNPTMBBMUVSBDPO 

"MUVSBDBOUJEBEEFFUBQBTEFFRVJMJCSJP×)&51

B

-B)&51 RVFTFNJEFFOGPSNBFYQFSJNFOUBM FTMBBMUVSBEFMFNQBRVFOFDFTBSJBQBSBPCUFOFSFM DBNCJPEFDPNQPTJDJÓORVFTFBMDBO[BDPOVODPOUBDUPUFÓSJDPEFFRVJMJCSJP-BT)&51QVFEFO WBSJBSEFTEFQVMHBEB áVKPTNVZQFRVFÒPTEFHBTFOFNQBRVFTBVUPIVNFDUBOUFT IBTUBWBSJPT QJFT BOJMMPT 3BTDIJOH HSBOEFT  &O FM FRVJQP JOEVTUSJBM OPSNBM  MB )&51 WBSÎB FOUSF  Z  QJFT .JFOUSBTNFOPSFTMB)&51 MBDPMVNOBFTNÃTDPSUBZFMFNQBRVFFTNÃTFàDJFOUF 1BSBNFEJSMB)&51TFEFUFSNJOBOMBTDPNQPTJDJPOFTTVQFSJPSFJOGFSJPSBSFáVKPUPUBMZEFT QVÊTTFDBMDVMBMBDBOUJEBEEFFUBQBTEFFRVJMJCSJP &OUPODFT 

)&51

BMUVSBEFMFNQBRVF DBOUJEBEEFFUBQBTUFÓSJDBT



C

4FBDPTUVNCSBVTBSVOWBQPSJ[BEPSQBSDJBM QFSPOPEFCFJODMVJSTFFOFMDÃMDVMPEFMB)&51 -B)&51EFUFSNJOBEBBSFáVKPUPUBMTFVTBFOUPODFTBMBSFMBDJÓOSFBMEFSFáVKP&MMJTZ#SPPLT  FODPOUSBSPORVFIBZVOBVNFOUPFOMB)&51QBSBSFMBDJPOFTEFSFáVKPJOUFSOPNFOPSFTRVF  QFSPFMBVNFOUPFOHFOFSBMFTCBTUBOUFQFRVFÒPIBTUBRVF-7TFBDFSDBB&OUPODFT TF QVFEFVTBSFMQSPDFEJNJFOUPOPSNBMEFNFEJDJÓOQBSBMBNBZPSQBSUFEFMBTTJUVBDJPOFTEFEJTFÒP -B)&51WBSÎBDPOFMUJQPZUBNBÒPEFFNQBRVF MBTTVTUBODJBTRVFTFWBOBTFQBSBSZDPOFMáVKP EFMHBT&OMBàHVSBTFNVFTUSBOBMHVOBTDVSWBTUÎQJDBTEF)&51-PTWBMPSFTEF)&51QBSB WBSJPTUJQPTEFFNQBRVFBQBSFDFOFOMPTCPMFUJOFTEFMPTGBCSJDBOUFTZMPTIBODPNQBSBEP1FSSZ   QÃH

&MMJTZ#SPPLT 

,JTUFSZ-BSTPO 

,JTUFSFUBM 

-VEXJH  Z8BMBT  'VSUFSZ/FXTUFBE 

-VEXJH 

1FSSZZ(SFFO  Z4USJHMF  DPNQBSBOMPT SFTVMUBEPTEFMBUSBOTGFSFODJBEFNBTB6OBTDPSSFMBDJPOFTQBSBDBMDVMBSMPTWBMPSFTEF)&51GVFSPO EFTBSSPMMBEBTQPS.VSDI  Z8IJUU 

QFSPOPTFSFàFSFOBMPTFNQBRVFTNPEFSOPT WFB

pies

Velocidad del gas, pies/s

Velocidad del gas, pies/s

'*(63" )&51&/'6/$*¶/%&7&-0$*%"%%&7"1031"3""/*--041"--.&5¦-*$04"  *400$5"/050-6&/0 # "$&50/""(6"3&*.13&40$0/"6503*;"$*¶/%&i1"--3*/(4*/."44 53"/4'&301&3"5*0/4u $035&4±"%&/0350/$)&.*$"-130$&44130%6$54 ",30/ 0)*0

www.FreeLibros.me

  *OVOEBDJÓOEFMBDPMVNOBFNQBDBEBZDÃMDVMPEFMEJÃNFUSP



-VEXJH  #PMMFTZ'BJS  QSFTFOUBOVONPEFMPNFKPSBEPEFUSBOTGFSFODJBEFNBTBQBSB EBUPT WBSJPT FNQBRVFT Z EF )&51 Z TF EFTDSJCFO FO FM DBQÎUVMP  -BT )&51 TPO EJGFSFOUFT QBSBEJTUJOUPTTJTUFNBTRVÎNJDPTZTPONBZPSFTQBSBFNQBRVFTEFNBZPSUBNBÒP-BNBZPSQBSUFEF MPTFNQBRVFTEFMNJTNPUBNBÒPUFOESÃOBQSPYJNBEBNFOUFMBNJTNB)&510CTFSWFFOMBàHVSB   RVF QBSB VO TJTUFNB Z UBNBÒP EF FNQBRVF EBEP  MB )&51 FT BQSPYJNBEBNFOUF DPOTUBOUF EFOUSPEFBNQMJPTMÎNJUFTEFáVKPTEFHBT&OUPODFT BMBQSPYJNBSTFBMBJOVOEBDJÓO EJTNJOVZFMBFà DJFODJBEFMDPOUBDUPZBVNFOUBMB)&515BNCJÊO BáVKPTNVZCBKPTEFHBT DPOGSFDVFODJBBVNFOUB MB)&51&TUPTVDFEFQPSRVFFMFNQBRVFOPFTUÃUPUBMNFOUFNPKBEP1BSBMPTFNQBRVFTBVUPNPKBO UFT EPOEFMBBDDJÓODBQJMBSMPTNBOUJFOFNPKBEPT MB)&51TVFMFCBKBSBáVKPTEFHBTNVZCBKPT -PTWBMPSFTEF)&51TPONÃTFYBDUPTTJTFEFUFSNJOBOBQBSUJSEFEBUPT4JOPIBZEBUPTEJTQP OJCMFT TFVTBODPSSFMBDJPOFTHFOFSBMJ[BEBTEFUSBOTGFSFODJBEFNBTB WFBFMDBQÎUVMP 4JOPIBZ JOGPSNBDJÓOEJTQPOJCMF -VEXJH  TVHJFSFVTBSVOQSPNFEJPEFBQJFTQBSBFNQBRVFT EFTDBSHBEPT4JFMEJÃNFUSPEFMBDPMVNOBFTNBZPSRVFQJF EFCFVTBSTFVOB)&51NBZPSRVF QJF0USPNÊUPEPBQSPYJNBEPFTJHVBMBSMB)&51BMEJÃNFUSPEFMBDPMVNOB -VEXJH  &DLFSU  IBDFOPUBSRVFMPTWBMPSFTEF)&51QBSBBOJMMPT1BMMEF ˜ZQVMHBEBTTPO ˜ZQJFT  SFTQFDUJWBNFOUF&TPTWBMPSFTEF)&51TPODBTJJOEFQFOEJFOUFTEFMTJTUFNBRVFTFEFTUJMF4FQVF EFOPCUFOFSWBMPSFTBQSPYJNBEPTEF)&51QBSBFNQBRVFTFTUSVDUVSBEPTDPOMBTJHVJFOUFFDVBDJÓO BQSPYJNBEB (FBOLPQMJT ,JTUFS   

)&51BQ 

D





EPOEF)&51FTUÃFONFUSPTZBQ MBTVQFSàDJFQPSVOJEBEEFWPMVNFO FTUÃFON N &TUFSFTVMUBEP TFSFTUSJOHFBMÎRVJEPTEFCBKBWJTDPTJEBEBQSFTJPOFTEFNPEFSBEBTBCBKBT-PTWBMPSFTUÎQJDPTEF )&51WBOEFBN-PTTJTUFNBTDPOBMUBTUFOTJPOFTTVQFSàDJBMFTUFOESÃONBZPSFTWBMPSFT EF)&511PSFKFNQMP QBSBTJTUFNBT BNJOBT HMJDPMFT DPO  EJOBTDN TFNVMUJQMJDBMB)&51 EFMBFDVBDJÓO D QPSZQBSBTJTUFNBTBDVPTPT DPO  EJOBTDN TFNVMUJQMJDBOQPS "OÓO  8BOHFUBM  SFTVNFOWBSJBTPUSBTSFMBDJPOFTTJNQMJàDBEBTQBSB)&514JMB EJTUSJCVDJÓOEFMMÎRVJEPOPFTFYDFMFOUF TFTVHJFSFVTBSVOGBDUPSEFTFHVSJEBEEFB "VORVFMBTDPMVNOBTFNQBDBEBTUSBCBKBODPOVOBWBSJBDJÓODPOUJOVBEFDPODFOUSBDJPOFTEF WBQPSZMÎRVJEP FMNPEFMPEFFUBQBTTJHVFTJFOEPVONÊUPEPEFEJTFÒPÙUJM$PNPMB)&51DPO GSFDVFODJBFTDBTJDPOTUBOUFFOUPEPFMJOUFSWBMPOPSNBMEFEJTFÒPQBSBáVKPTEFHBT DPODFOUSBDJP OFTZSFMBDJPOFTEFSFáVKP FOFMDBTPOPSNBMTFQVFEFVTBSVOBTPMB)&51QBSBDPNQBSBSNVDIPT EJTFÒPTEJGFSFOUFT&TPGBDJMJUBNVDIPFMEJTFÒP&ODJFSUPTDBTPT MB)&51QVFEFWBSJBSBQSFDJB CMFNFOUFEFOUSPEFMBDPMVNOB EFCJEPBDBNCJPTFOMBDPNQPTJDJÓOFOFTFDBTPTFQVFEFFTUJNBS QBSBDBEBFUBQBBQBSUJSEFMDPFàDJFOUFEFUSBOTGFSFODJBEFNBTB WFBVOFKFNQMPFO4IFSXPPE  FUBM  QÃHT &OGPSNBBMUFSOBUJWB TFQVFEFVTBS ZTFQSFàFSF VONÊUPEPEFEJTFÒP QPSUSBOTGFSFODJBEFNBTB WFBFMDBQÎUVMP   */6/%"$*¶/%&-"$0-6./"&.1"$"%":$¦-$6-0%&-%*¦.&530

&MEJÃNFUSPEFMBDPMVNOBTFEJNFOTJPOBQBSBRVFUSBCBKFEFMBMEFMBJOVOEBDJÓOPQBSB UFOFSEFUFSNJOBEBDBÎEBEFQSFTJÓOQPSQJFEFFNQBRVF-BJOVOEBDJÓOTFQVFEFNFEJSDPONÃT GBDJMJEBEFOVOBDPMVNOBFNQBDBEBRVFFOVOBEFQMBUPTZTVTÎOUPNBOPSNBMFTVORVJFCSFFOMB DVSWBEFDBÎEBEFQSFTJÓOFOGVODJÓOEFUBTBEFáVKPEFHBT -BDPSSFMBDJÓOHFOFSBMJ[BEBEFJOVOEBDJÓOEFTBSSPMMBEBQPS4IFSXPPEFUBM  ZNPEJàDB EBQPS&DLFSU   TFWFFOMBàHVSB0CTFSWFMBTVOJEBEFTEFMBPSEFOBEBFOMBàHVSB FTBTVOJEBEFTEFCFOVTBSTFFOFMDÃMDVMP4FQVFEFDPOTFHVJSVOBHSÃàDBEFMPTNJTNPTEBUPT DPOFTDBMBBSJUNÊUJDBFOMBTPSEFOBEBT (FBOLPQMJT 4USJHMF  &MGBDUPSEFFNQBRVF ' 

www.FreeLibros.me



$BQÎUVMP  %JTFÒPEFDPMVNOBTEFQMBUPTZFNQBDBEBT

EFQFOEFEFMUJQPZFMUBNBÒPEFMFNQBRVF.JFOUSBTNBZPSTFBFMWBMPSEF' MBDBÎEBEFQSFTJÓO TFSÃNBZPSQPSQJFEFFNQBRVF&OMBUBCMB &DLFSU  -VEXJH  TFWFOWBMPSFT 'QBSBWBSJPTUJQPTEFFNQBRVFEFTDBSHBEP ZFOMBUBCMB 'BJS (FBOLPQMJT  TFWFO WBMPSFTEF'QBSBFNQBRVFTFTUSVDUVSBEPT"MBVNFOUBSFMUBNBÒPEFMFNQBRVF EJTNJOVZFFMWBMPS EF'ZQPSDPOTJHVJFOUFCBKBMBDBÎEBEFQSFTJÓOQPSQJFEFFNQBRVF&O1FSSZT)BOECPPL 1FSSZ Z(SFFO  ZFO4USJHMF  TFFODVFOUSBOMJTUBTNÃTFYUFOTBTEFWBMPSFTEF'&MFGFDUPEFM UBNBÒPEFMFNQBRVFTPCSFFMGBDUPSEFFNQBRVF TFQVFEFSFQSFTFOUBSSB[POBCMFNFOUFCJFODPOMB FDVBDJÓO #FOOFUU 

'$Q UBNBÒP Q −





EPOEFFMGBDUPSEFUBNBÒPEFFNQBRVF $Q UBNBÒPBQBSFDFFOMBUBCMB QFTMBEJNFOTJÓODBSBD UFSÎTUJDBEFMFNQBRVFFOQVMHBEBT1BSBFNQBRVFTBMFBUPSJPT  QUBNBÒPPEJÃNFUSPOPNJOBMEFM FNQBRVF ZQBSBFNQBRVFFTUSVDUVSBEP  QBMUVSBEFMBDPSSVHBDJÓO-PTFNQBRVFTEFDFSÃNJDB UJFOFOQBSFEFTNÃTHSVFTBTRVFMPTEFQMÃTUJDP ZMPTEFQMÃTUJDPUJFOFOQBSFEFTNÃTHSVFTBTRVF MPTEFNFUBMMPTFNQBRVFTEFDFSÃNJDB FOUPODFT UJFOFONFOPSFTQBDJPMJCSF NÃYJNBTDBÎEBTEF QSFTJÓOZNÃYJNPTWBMPSFTEF'&OHFOFSBM NJFOUSBTNFOPSTFBFMWBMPSEF' FMEJÃNFUSPEFMB DPMVNOBTFSÃNFOPS-BàHVSBOPFTVOBKVTUFQFSGFDUPEFUPEPTMPTEBUPT&TQPTJCMFPCUFOFS NFKPSFT SFTVMUBEPT VTBOEP DVSWBT EF DBÎEB EF QSFTJÓO NFEJEBT QBSB EFUFSNJOBEP FNQBRVF &O GPSNBFTQFDÎàDB MBDBÎEBEFQSFTJÓODBMDVMBEBQBSBTJTUFNBTOPBDVPTPTBHSBOEFTWBMPSFTEFMQBSÃ NFUSPEFáVKP FTEFNBTJBEPCBKB ,JTUFSZ(JMM   Línea

de i n

und

aci

ón

EL PARÁMETRO DE LAS CURVAS ES CAÍDA DE PRESIÓN, PULGADAS DE AGUA/PIE DE ALTURA EMPACADA

'*(63" $033&-"$*¶/(&/&3"-*;"%"&/53&*/6/%"$*¶/:$"±%"%&13&4*¶/1"3" $0-6./"4&.1"$"%"43&*.13&40$0/"6503*;"$*¶/%&&$,&35 $)&.&/(130(  

  

¥"*$)&3&130%6$*%0$0/"6503*;"$*¶/%&-".&3*$"/*/45*565&0' $)&.*$"-&/(*/&&34

www.FreeLibros.me

  *OVOEBDJÓOEFMBDPMVNOBFNQBDBEBZDÃMDVMPEFMEJÃNFUSP



-BDVSWBEFJOVOEBDJÓOTFQVFEFSFQSFTFOUBSDPOMBFDVBDJÓO ,FTTMFSZ8BOLBU 



ad\&%

2(., HZei'%%& &%!%%%

&!%%% KZgi^XVaZh >cXa#idggZh =dg^odciVaZh

&%%

%#&

&#%

&%

&%%

&%%% (

KdajbZcYZagZX^e^ZciZ!Kb 

'*(63" $04504%&$0.13"1"3"3&$*1*&/5&4%&130$&40 56350/ &5"- 

3&*.13&40$0/"6503*;"$*¶/ ¥ 13&/5*$&)"--

www.FreeLibros.me



$BQÎUVMP  &DPOPNÎBZDPOTFSWBDJÓOEFFOFSHÎBFOMBEFTUJMBDJÓO

&MDPTUPEFMNÓEVMPàOBMDPOMPJNQSFTDJOEJCMF PNÓEVMPNÎOJNP $#. #.WJFOFEFiCBSF NPEVMVTu NÓEVMPNÎOJNP EFMFRVJQPEFEFTUJMBDJÓOTFQVFEFFTUJNBSDPOHSÃàDBTZFDVBDJPOFT &MDÃMDVMPDPNJFO[BDPOFMDPTUPCBTFEFDPNQSB $Q QBSBTJTUFNBTDPOTUSVJEPTFOBDFSPBMDBSCÓO RVFUSBCBKFOBQSFTJÓOBNCJFOUFZEFTQVÊTTFBKVTUBFTFDPTUPDPOGBDUPSFTEFDPTUPTBEJDJPOBMFT-BT HSÃàDBTRVFOFDFTJUBSFNPTQBSBFTUJNBSFMDPTUPCBTFEFDPNQSB $Q EFMPTTJTUFNBTEFEFTUJMBDJÓO  TFWFOFOMBTàHVSBTB 5VSUPOFUBM  $PNPMBFOWPMWFOUFEFMBTDPMVNOBTEFEFTUJ &!%%% 8dhidYZXdbegV!edgjc^YVYYZkdajbZc YZZbeVfjZ!8de $ K$b(

8:E8>2(., HZei'%%&

&%% %#&

8dhidhYZXdbegVedgjc^YVYYZ{gZV 8de $6$b(  YZeaVid!

%#%&

& &% &%% KdajbZcYZaZbeVfjZ!Kb(

&!%%%

&%!%%%

8:E8>2(., HZei'%%& &%!%%%

EaVidhYZk{akjaVh HZeVgVYdgYZc^ZWaVh

&!%%% EaVidheZg[dgVYdh

%#&

&

&%

ÌgZVYZaeaViddYZahZeVgVYdgYZc^ZWaV!6b '

'*(63" $04504%&$0.13"1"3"&.1"26&4 1-"504:4&1"3"%03&4%&/*&#-" 56350/&5"-  3&*.13&40$0/"6503*;"$*¶/ ¥ 13&/5*$&)"--

www.FreeLibros.me

  $PTUPTEFEFTUJMBDJÓO



8dhidYZXdbegVedgjc^YVYYZ{gZVYZigVch[ZgZcX^VYZXVadg!8 de $6$b'

&%!%%% 8:E8>2(., HZei'%%&

EVgZYgVhfjZiZVYV  IjWdYZiZ[a‹c

&!%%% IjWdYdWaZ

7VndcZiV 8VWZoV[adiVciZ IjWdhn:ck# :heZ_d[^_d IjWdhn:ck#

&%%

&

&%

&%%

ÌgZVYZigVch[ZgZcX^VYZXVadg!

&!%%%

&%!%%%

6b'

&%!%%% 8:E8>2(., HZei'%%&

IjWdZhe^gVa

&!%%%

KVedg^oVYdg YZbVgb^iV

IjWdZcJ

&%%

&

&%

&%%

&!%%%

&%!%%%

ÌgZVYZigVch[ZgZcX^VYZXVadg!6b'

'*(63" $04504%&$0.13"%&$".#*"%03&4%&$"-03 56350/&5"- 

 3&*.13&40$0/"6503*;"$*¶/ ¥ 13&/5*$&)"-- MBDJÓOFTVOSFDJQJFOUFWFSUJDBM TFQVFEFVTBSMBàHVSBQBSBEFUFSNJOBS$Q$QP× WPMVNFO

 QBSBMBTUPSSFT-PTDPTUPTCBTFEFDPNQSBQBSBQMBUPTQFSGPSBEPTZEFWÃMWVMBTZQBSBFNQBRVFT EFUPSSFTFWFOFOMBàHVSB $Q$QP× ¦SFB QBSBQMBUPTZ$Q$QP× 7PMVNFO QBSBMPTFN QBRVFT&OMPTDPTUPTEFJOUFSDBNCJBEPSFTEFDBMPS àHVSB

MPTTJTUFNBTEFEFTUJMBDJÓOTVFMFO VTBSWBQPSJ[BEPSFTUJQPNBSNJUBDPOFOWPMWFOUFEFUVCPTàKBFJOUFSDBNCJBEPSFTEFUVCPT $Q$QP × ¦SFB &MÎOEJDFEF$PTUPTEF1MBOUBT$IFNJDBM&OHJOFFSJOH $&1$* RVFNVFTUSBOFTUBTàHVSBT FTFM$&1$*FOFMNPNFOUPEFQSFQBSBSMBTàHVSBT -PT BVNFOUPT EF DPTUPT EFCJEPT B NBUFSJBMFT DPTUPTPT BGFDUBO B UPEP UJQP EF FRVJQPT Z MPT GBDUPSFTEFNBUFSJBM 'N QBSBFTPTDPTUPTJODSFNFOUBEPTFOMPTTJTUFNBTEFEFTUJMBDJÓOBQBSFDFOFO MBUBCMB 5VSUPOFUBM  4FJODMVZFO DPOFMGBDUPSEFQSFTJÓO'Q MPTFGFDUPTEFMBQSFTJÓO TPCSFMPTDPTUPTEFSFDJQJFOUFTEFQSPDFTPFJOUFSDBNCJBEPSFTEFDBMPS&MGBDUPSEFQSFTJÓOQBSB SFDJQJFOUFTEFQSPDFTPFT 5VSUPOFUBM   

;e 2

e9 %#*  &%#,&− %#%%,*+e

www.FreeLibros.me





$BQÎUVMP  &DPOPNÎBZDPOTFSWBDJÓOEFFOFSHÎBFOMBEFTUJMBDJÓO

5"#-" '"$503&4103."5&3*"- '. 1"3"&26*104&/4*45&."4%&%&45*-"$*¶/ 56350/&5"-   3FDJQJFOUFT EFQSPDFTP WFSUJDBMFT'N

.BUFSJBMEF DPOTUSVDDJÓO

"DFSPBMDBSCÓO $4



"DFSPJOPYJEBCMF "*

3FWFTUJEPTEF"* "* "MFBDJÓOEF/J 3FWFTUJEPEFBMFBDJÓOEF/J $V 5J 3FWFTUJEPEF5J 1PMJFUJMFOP $FSÃNJDB

 

$BNCJBEPSFTEF FOWPMWFOUFZUVCP  ZWBQPSJ[BEPSFTEF NBSNJUB'N

1MBUPT QFSGPSBEPT 'N

&NQBRVFT EFUPSSF 'N





&OWPMWFOUF$4 5VCPT$4 5VCPT$V 5VCPT"* 5VCPT/J "MFBDJÓO 5VCPT5J &OWPMWFOUFZUVCPT



&OWPMWFOUFZUVCPT



    

&OWPMWFOUFZUVCPT &OWPMWFOUFZUVCPT  

WÃMJEBQBSBFTQFTPSFTEFQBSFEEFMSFDJQJFOUFN EFQVMHBEB &OFTUBFDVBDJÓO  QQSFTJÓOBCTPMVUBFOCBSZ%EJÃNFUSPEFMSFDJQJFOUFFONFUSPT4J'Q TFJHVBMB'Q 1BSBPQFSBDJÓOBMWBDÎPDVBOEPQCBS VTF'Q0USBTMJNJUBDJPOFTEFFTUBFDVBDJÓOTPOMBT RVFEFTDSJCFO5VSUPOFUBM  QÃH &MGBDUPSEFQSFTJÓOQBSBDPOEFOTBEPSFTZWBQPSJ[BEP SFTUJQPNBSNJUBTFQVFEFDBMDVMBSDPO 5VSUPOFUBM   

ad\&% ;e 2%#%(--& − %#&&','ad\ &% e − 1) %#%-&-(Pad\ &% e − &R' 



&O FTUB FDVBDJÓO  Q  QSFTJÓO BCTPMVUB FO CBS Z FM SBOHP EF WBMJEBDJÓO EF MB FDVBDJÓO FT EF QCBS4JQƪ FTUBCMF[DB'Q -PTDPTUPTEFMPTQMBUPTQFSGPSBEPTZEFMFNQBRVFOPEFQFOEFOEFMBQSFTJÓOFOGPSNBEJSFDUB  QFSPTÎJOEJSFDUBNFOUF QPSRVFFMEJÃNFUSPEFMBDPMVNOBEFQFOEFEFMBQSFTJÓO-PTDPTUPTEFMPT QMBUPTQFSGPSBEPTEFQFOEFOEFMBDBOUJEBEQFEJEB BUSBWÊTEFMGBDUPSEFDBOUJEBE'R RVFTFQVFEF DBMDVMBSDPOMBTJHVJFOUFFDVBDJÓO 5VSUPOFUBM   

ad\&% ;f 2%#),,& %#%-*&+ad\&% C − 0.3473(ad\&% C' 



EPOEF/FTMBDBOUJEBEEFQMBUPT&TUBFDVBDJÓOFTWÃMJEBQBSB/1BSB/  'R5BN CJÊO  MPT DPTUPT EFM FNQBRVF EFQFOEFO EF MB DBOUJEBE EF FNQBRVF  RVF FTUÃ JODMVJEB FO GPSNB JOIFSFOUFFOMBàHVSB &MDPTUPàOBMEFMNÓEVMPNÎOJNP $#. QBSBSFDJQJFOUFTEFQSPDFTPWFSUJDBMFTFT 5VSUPOFUBM    

87B 28e'#'* &#-';b;e 

www.FreeLibros.me



  &GFDUPTEFMBPQFSBDJÓOTPCSFMPTDPTUPT



QBSBDPOEFOTBEPSFTZWBQPSJ[BEPSFTUJQPNBSNJUBFMDPTUPàOBMEFMNÓEVMPNÎOJNPFT 

87B 28e(1.63 + 1.66;b;e



1BSBQMBUPTQFSGPSBEPTZEFWÃMWVMBT FMDPTUPàOBMEFMNÓEVMPNÎOJNPFT 

87B 28e C;f ;b 



TJFOEP/DBOUJEBEEFQMBUPT1BSBFNQBRVFT FMDPTUPàOBMEFMNÓEVMPJOEJTQFOTBCMFFT 

87B 28e ;b 



&OFMFKFNQMPTFJMVTUSBFMVTPEFFTUBTHSÃàDBTZFDVBDJPOFT -PTDPTUPTUPUBMFTBOVBMFTEFPQFSBDJÓOTFEFUFSNJOBODPNP $PTUPUPUBMEFPQFSBDJÓO BÒP×  

&O MB NBZPSÎB EF MBT DPMVNOBT EF EFTUJMBDJÓO DPOUJOVB  MPT DPTUPT EF FMFDUSJDJEBE TPO NPEFTUPT ZMPTDPTUPTEFPQFSBDJÓOTPOMPTNJTNPT JOEFQFOEJFOUFNFOUFEFMPTWBMPSFTEFMBTWBSJBCMFTEF PQFSBDJÓO  &'&$504%&-"01&3"$*¶/40#3&-04$04504

1PESFNPTVTBSMPTNÊUPEPTEFTBSSPMMBEPTFOMPTDBQÎUVMPT ZQBSBDBMDVMBSMBDBOUJEBEEFFUB QBTEFFRVJMJCSJP /FRVJM RVFTFSFRVJFSFO&OUPODFT /SFBM/FRVJM&P-BBMUVSBEFVOBDPMVNOBEF QMBUPTFT 

) /SFBM BMUVSBFOUSFQMBUPT   BMUVSBTQBSBTFQBSBDJÓO 



&MEJÃNFUSPEFMBDPMVNOBTFDBMDVMBDPOMPTNÊUPEPTEFMDBQÎUVMP-BFDVBDJÓO  NVFTUSB RVF QBSBNBZPSFTQSFTJPOFT FMEJÃNFUSPTFSFEVDJSÃVOQPDP-PDPOUSBSJPPDVSSFQBSBPQFSBDJÓO BMWBDÎPFMEJÃNFUSPBVNFOUB-PTBVNFOUPTFOMBBMUVSBFOUSFQMBUPTIBDFOBVNFOUBS$TI JOVO MPRVF DBVTBRVFBVNFOUFVPQZQPSMPNJTNPEJTNJOVZFFMEJÃNFUSPBMBVNFOUBSMBBMUVSBEFMBDPMVNOB $VBOEP-%   SFáVKPUPUBM

MBDBOUJEBEEFFUBQBTUJFOEFBMNÎOJNP MPRVFNJOJNJ[BMBBM UVSBEFMBDPMVNOBQFSPBVNFOUBFMEJÃNFUSPIBTUBFMJOàOJUP$VBOEP-%  -% NÎO MBDBOUJEBE EFFUBQBTZTVBMUVSBTFWVFMWFOJOàOJUBT NJFOUBTRVFFMEJÃNFUSPEFMBDPMVNOBTFSFEVDFBMNÎOJ NP"NCPTMÎNJUFTJNQMJDBODPTUPTEFDBQJUBMJOàOJUPT"TÎ DBCFFTQFSBSRVFIBZBVOB-%ÓQUJNB  RVFNJOJNJDFMPTDPTUPTEFDBQJUBM-BBMUVSBEFMBDPMVNOBFTJOEFQFOEJFOUFEFMBUBTBEFáVKPEF BMJNFOUBDJÓO NJFOUSBTRVFFMEJÃNFUSPFTQSPQPSDJPOBMB'ZB -%  -PTFGFDUPTEFMBQSFTJÓOTPCSFMBTDPMVNOBTEFEFTUJMBDJÓOUJFOFOFYUSFNBEBJNQPSUBODJB-B FDVBDJÓO  JOEJDBRVFFMEJÃNFUSPEFMBTDPMVNOBTEFFUBQBTFTBQSPYJNBEBNFOUFQSPQPSDJP OBMB Q "MUSBCBKBSBNBZPSFTQSFTJPOFTTFSFEVDFFMEJÃNFUSPEFMBDPMVNOB QFSPMBBMUVSB QVFEFBVNFOUBSZBRVF FOGPSNBDBSBDUFSÎTUJDB MBWPMBUJMJEBEEJTNJOVZFBNFEJEBRVFMBQSFTJÓO BVNFOUB&OHFOFSBM FMFGFDUPEFMBQSFTJÓOTPCSFFMEJÃNFUSPFTBQSFDJBCMFNFOUFNBZPSRVFTV FGFDUPTPCSFMBBMUVSBEFMBDPMVNOB%FBDVFSEPDPOMBàHVSB FTEFFTQFSBSRVFEJTNJOVZBFM DPTUPCBTFEFDPNQSBEFMBDPMVNOB&OFMDBTPUÎQJDP FMGBDUPSEFQSFTJÓOFT'Q BNFOPT EFVOPTCBS ZBVNFOUBVOQPDPIBTUBQSFTJPOFTNFOPSFTRVFVOBTCBS4JMBDPMVNOBFTUÃ

www.FreeLibros.me



$BQÎUVMP  &DPOPNÎBZDPOTFSWBDJÓOEFFOFSHÎBFOMBEFTUJMBDJÓO

IFDIBEFBMHÙONBUFSJBMDPTUPTP BMUP'N

TFJODSFNFOUBOMPTGBDUPSFTEFDPTUPQPSQSFTJÓO QPSRVF FMGBDUPSQBSBNÓEVMPJOEJTQFOTBCMFEFQFOEFEFMQSPEVDUPEF'QQPS'N FDVBDJÓO  $PNPFM DPTUPEFDPNQSBEFQMBUPTQFSGPSBEPT $Q EJTNJOVZFBNFEJEBRVFBVNFOUBFMEJÃNFUSP àHVSB 

FTEFFTQFSBSTFRVFFMDPTUPEFDPNQSBQPSQMBUPCBKF BVORVFTFSFRVJFSBOBMHVOPTQMBUPTNÃT ,FMMFS  QSFTFOUÓBOÃMJTJTFDPOÓNJDPTEFUBMMBEPTZWJPRVFFMSFTVMUBEPOFUPFTRVFMPTDPTUPT EFMNÓEVMPJOEJTQFOTBCMFQBSBDPMVNOBTEFEFTUJMBDJÓO FOWPMWFOUFZQMBUPT EJTNJOVZFOFOHFOFSBM IBTUBVOBQSFTJÓOBQSPYJNBEBEFBUN QTJB 1BSBMMFHBSBFTUFSFTVMUBEPTFTVQPOFRVFOP IBZ EFHSBEBDJÓO UÊSNJDB B FTBT QSFTJPOFT -PT DPNQVFTUPT RVF EFHSBEBO EFCFO  DPO GSFDVFODJB  QSPDFTBSTFBMWBDÎP BNFOPSQSFTJÓO MPTQVOUPTEFFCVMMJDJÓOZQPSDPOTJHVJFOUFMBTUFNQFSBUVSBTEF MBDPMVNOBTPONFOPSFT

BVODVBOEPMBTDPMVNOBTTPONÃTDPTUPTBT&MFGFDUPEFMBQSFTJÓOTPCSF DPTUPTEFDPNQSB BNÃTEFBUN EFCFBOBMJ[BSTFDBTPQPSDBTP -PTUBNBÒPTEFMDPOEFOTBEPSZFMWBQPSJ[BEPSEFQFOEFOEF2DZ23&TUPTWBMPSFTTFDBMDVMBO DPOCBMBODFTFYUFSOPTEFNBTBZFOFSHÎBBMSFEFEPSEFMBDPMVNOB-BTFDVBDJPOFT  Z   QFSNJUFODBMDVMBS2DZ23QBSBDPMVNOBTDPOVOBTPMBBMJNFOUBDJÓO0CTFSWFRVF2DZQPSMPNJT NP23 BVNFOUBOFOGPSNBMJOFBMDPO-%ZDPO'-BDBOUJEBEEFBHVBEFBMJNFOUBDJÓOOFDFTBSJB TFEFUFSNJOBDPOGBDJMJEBEDPOVOCBMBODFEFFOFSHÎB 

LHBHVBEFFOGSJBNJFOUPI 2D  $Q X−5X 



EPOEF −5X  5X DBM − 5X GSÎB 6O DPOEFOTBEPS QVFEF CBKBS MB UFNQFSBUVSB GÃDJMNFOUF IBTUB ž' 0#SJFOZ4DIVMU[  &MDPTUPEFFOGSJBNJFOUPQPSBÒPFT 

$PTUPEFMBHVBEFFOGSJBNJFOUP BÒP LHBHVBI DPTUP LH IBÒP 



&TVOBGVODJÓOMJOFBMEF-%ZEF'TJFMDPTUPQPSLJMPHSBNPFTDPOTUBOUF &OFMWBQPSJ[BEPSTFTVFMFBMJNFOUBSWBQPSTPCSFDBMFOUBEPZTBDBSBHVBTBUVSBEB&OUPODFT FM áVKPEFWBQPSFT 

'MVKPEFWBQPSEFBHVB LHI

FG  =kVedg − ]a†fj^Yd

B

FG  λ

C

&ONVDIBTBQMJDBDJPOFT )WBQPS)WBQPSTBUVSBEP Z 

'MVKPEFWBQPSEFBHVB LHI

EPOEF−FTFMDBMPSMBUFOUFEFFWBQPSBDJÓOEFMBHVBBMBQSFTJÓOEFPQFSBDJÓO&MáVKPEFWBQPSBV NFOUBSÃFOGPSNBMJOFBMDPO-%ZDPO'&MWBMPSEF−TFQVFEFEFUFSNJOBSDPOMBTUBCMBTEFWBQPS &OUPODFT FMDPTUPBOVBMEFMWBQPSFT 

$PTUPEFMWBQPSEFBHVB BÒP LHWBQPSI

$PTUP  IPQFSBDJÓO



 LHEFWBQPS BÒP



0CTFSWFRVF2DZQPSMPNJTNP23 EFQFOEFOMJOFBMNFOUFEF-%ZEF'FOUPODFT MPTBVNFOUPTFO -%PEF'IBDFOBVNFOUBSMJOFBMNFOUFMPTáVKPTEFBHVBEFFOGSJBNJFOUPZEFWBQPSEFBHVB "VORVFFMEJTFÒPEFUBMMBEPEFDPOEFOTBEPSFTZFOFTQFDJBMEFWBQPSJ[BEPSFT FTFTQFDJBMJ[BEP -VEXJH .D$BSUIZZ4NJUI  ZTBMFEFMBMDBODFEFFTUFMJCSP CBTUBVOBFTUJNBDJÓOEFM ÃSFBEFUSBOTGFSFODJBEFDBMPSQBSBQPEFSIBDFSFTUJNBDJPOFTQSFMJNJOBSFTEFMPTDPTUPT-PTUBNB ÒPTEFMPTJOUFSDBNCJBEPSFTEFDBMPSTFFTUJNBODPOMBFDVBDJÓOEFUSBOTGFSFODJBEFDBMPS 

⏐ F ⏐ 2J6 Δ I 

www.FreeLibros.me



  &GFDUPTEFMBPQFSBDJÓOTPCSFMPTDPTUPT



EPOEF6DPFàDJFOUFHFOFSBMEFUSBOTGFSFODJBEFDBMPS "ÃSFBEFUSBOTGFSFODJBEFDBMPSZ −5EJGFSFODJBEFUFNQFSBUVSBFOUSFFMáVJEPRVFTFDBMJFOUBZFMáVJEPRVFTFFOGSÎB&MVTPEFMB FDVBDJÓO  TFFYQMJDBDPOEFUBMMFFOMJCSPTTPCSFGFOÓNFOPTEFUSBOTQPSUFZUSBOTGFSFODJBEF DBMPS DPNP$IFOHFM (FBOLPQMJT (SJTLFZ -VEXJH (SFFOLPSOZ,FTTMFS  Z,FSO  1BSBDPOEFOTBEPSFTZWBQPSJ[BEPSFT FMáVJEPDPOEFOTBOUFFTUÃBUFNQFSBUVSB DPOTUBOUF&OUPODFT −5−5QSPN5DBMJFOUF−5GSÎP QSPN



EPOEF5DBMJFOUFUFNQFSBUVSBEFDPOEFOTBDJÓOEFMáVJEPPEFMWBQPSEFBHVBZ5GSÎP QSPN  5GSÎP  −5GSÎP  1BSBVOWBQPSJ[BEPS MBUFNQFSBUVSBGSÎBTFSÃDPOTUBOUFFJHVBMBMBUFNQFSBUVSBEFFCVMMJ DJÓOZ−55WBQPS−51FC-PTWBMPSFTEFMDPFàDJFOUFEFUSBOTGFSFODJBEFQFOEFOEFMNBUFSJBMEFMPT UVCPTEFMPTáVJEPTRVFTFFTUÊODBMFOUBOEPZFOGSJBOEP ZEFMFTUBEPEFMPTDBNCJBEPSFTEFDBMPS -PTWBMPSFTUBCVMBEPTZMPTNÊUPEPTEFDÃMDVMPEF6TFEFTDSJCFOFOMBTSFGFSFODJBT-PTJOUFSWBMPT BQSPYJNBEPTTFWFOFOMBUBCMB 4JVTBNPTWBMPSFTQSPNFEJPEF6ZEFMBUFNQFSBUVSBEFMBHVBFOFMDPOEFOTBEPS QPESFNPT FTUJNBSFMÃSFBEFMDPOEFOTBEPS$POPDJEBMBQSFTJÓOEFMWBQPS TFQVFEFEFUFSNJOBSTVUFNQFSB UVSBFOMBTUBCMBTEFWBQPS&OUPODFT DPOVOB6QSPNFEJP TFDBMDVMBFMÃSFBEFMWBQPSJ[BEPS4F QVFEFOEFUFSNJOBSFOUPODFTMPTDPTUPTEFDPOEFOTBEPSZWBQPSJ[BEPS$PNPFMÃSFBFTEJSFDUBNFO UFQSPQPSDJPOBMB2 RVFEFQFOEFMJOFBMNFOUFEF-%ZEF' MBTÃSFBTEFMJOUFSDBNCJBEPSEFDBMPS BVNFOUBOFOGPSNBMJOFBMDPO-%PDPO' 4JTFFMFWBMBQSFTJÓOEFMBDPMVNOB MBUFNQFSBUVSBEFDPOEFOTBDJÓOFOFMDPOEFOTBEPSTFSÃ NBZPS&TPFTDPOWFOJFOUF QPSRVFBVNFOUBSÃMB−5FOMBTFDVBDJPOFT  Z 

ZTFSÃNF OPSFMÃSFBOFDFTBSJBFOFMDPOEFOTBEPS"EFNÃT DPOGSFDVFODJB DVBOEPMBTQSFTJPOFTTPONBZPSFT FMEJTFÒBEPSQVFEFFOGSJBSDPOBHVBFOMVHBSEFVTBSSFGSJHFSBDJÓO&TPQVFEFDBVTBSVOBHSBOEJT NJOVDJÓOFOMPTDPTUPTEFFOGSJBNJFOUP QPSRVFMBSFGSJHFSBDJÓOFTDPTUPTB$PONBZPSQSFTJÓOFO MBDPMVNOB BVNFOUBSÃFMQVOUPEFFCVMMJDJÓOFOFMWBQPSJ[BEPS$PNPFTMBUFNQFSBUVSBGSÎBEFMB FDVBDJÓO 

TFSFEVDJSÃFMWBMPSEF−5FOMBTFDVBDJPOFT  Z  ZBVNFOUBSÃFMÃSFB EFMWBQPSJ[BEPS6OBTPMVDJÓOBMUFSOBUJWBFTVTBSWBQPSEFNBZPSQSFTJÓO QBSBBVNFOUBSBTÎMBUFN QFSBUVSBEFMWBQPSZQBSBRVFOPTFBOFDFTBSJPVOWBQPSJ[BEPSNÃTHSBOEF&TUFNÊUPEPUBNCJÊO BVNFOUBMPTDPTUPTEFPQFSBDJÓO ZBRVFFMWBQPSEFNBZPSQSFTJÓOFTNÃTDPTUPTP &MDPTUPUPUBMBOVBMEFPQFSBDJÓOTFEFUFSNJOBDPOMBFDVBDJÓO  &TUFWBMPSTFQVFEFFT UJNBSDPNPDPTUPTEFMWBQPSEFBHVBNÃTDPTUPTEFBHVBEFFOGSJBNJFOUP6OFYBNFOEFFTUBTFDVBDJPOFTNVFTUSBMPTFGFDUPTEFEJWFSTBTWBSJBCMFT-PTDVBMFT TFSFTVNFOFOMBUBCMB 5"#-" $0&'*$*&/5&4"1309*."%04%&53"/4'&3&/$*"%&$"-03 6 #UVIQJFmž' 7BQPSJ[BEPS

$POEFOTBEPS

7BQPSBTPMVDJÓOBDVPTBIJSWJFOUF

B QSPNFEJP−

7BQPSBBDFJUFIJSWJFOEP

B

.F[DMBBDVPTBDPOEFOTBOUFBBHVB

B

7BQPSPSHÃOJDPDPOEFOTBOUFBBHVB

B

'VFOUF(SFFOLPSOBOE,FTTMFS 

www.FreeLibros.me



$BQÎUVMP  &DPOPNÎBZDPOTFSWBDJÓOEFFOFSHÎBFOMBEFTUJMBDJÓO

5"#-" &'&$50%&$".#*04&/-"47"3*"#-&4%&01&3"$*¶/ 40#3&-04$04504 &MFNFOUP EFDPTUP

$BNCJPFOMB WBSJBCMF

"HVBEFFOGSJBNJFOUP

&GFDUPTPCSFPUSBT WBSJBCMFT

&GFDUPTPCSF FMDPTUP

"VNFOUB-%

2D BVNFOUBMJOFBMNFOUF

"VNFOUB

"VNFOUB'

2D BVNFOUBMJOFBMNFOUF

"VNFOUB

"VNFOUBQSFTJÓOFO MBDPMVNOB

−5BHVBQVFEFBVNFOUBS QPSRVF #BKBPOPUJFOF FGFDUP 51&CFOFMDPOEFOTBEPS BVNFOUBPRVFEBJHVBM 4FQVFEFVTBSBHVBFOMVHBSEF #BKB SFGSJHFSBDJÓO BQSFDJBCMFNFOUF

"VNFOUBOMPTDPTUPT EFMBHVB 7BQPSEFBHVB

"VNFOUB

"VNFOUB-%

23BVNFOUBMJOFBMNFOUF

"VNFOUB

"VNFOUB'

23BVNFOUBMJOFBMNFOUF

"VNFOUB

"VNFOUBMBQSFTJÓO FOMBDPMVNOB

"VNFOUBMB5FNQFO WBQPSJ[BEPSQPESÃUFOFSRVF BVNFOUBSMBQSFTJÓOEFWBQPS

"VNFOUBTJ BVNFOUBMB QSFTJÓOEFWBQPS

"VNFOUBOMPTDPTUPT EFMWBQPS

"VNFOUB

&MDPTUPBOVBMEFDBQJUBMFT $PTUPBOVBMEFDBQJUBM UBTBEFEFQSFDJBDJÓO GBDUPSEF-BOH

× -PTDPTUPTEFMPTFRVJQPTJOEJWJEVBMFTEFQFOEFOEFMÃSFBEFMDPOEFOTBEPS ÃSFBEFMWBQPSJ[BEPS  UBNBÒPEFMBUPSSFZEJÃNFUSPEFQMBUPT"MHVOPTEFMPTFGFDUPTEFFTBTWBSJBCMFTTPCSFMPTDPTUPTEF DBQJUBMTPODPNQMFKPT4FEFTDSJCFOFOMBUBCMB&MSFTVMUBEPOFUPEFBVNFOUBS-%TFWFFOMB àHVSBFMDPTUPEFMDBQJUBMQBTBQPSVONÎOJNP &MDPTUPBOVBMUPUBMFTMBTVNBEFMPTDPTUPTEFDBQJUBMZPQFSBDJÓOZUBNCJÊOTFJMVTUSBFOMB àHVSB0CTFSWFRVFFYJTUFVOBSFMBDJÓOEFSFáVKPÓQUJNB"MBVNFOUBSMPTDPTUPTEFPQFSBDJÓO NBZPSFTDPTUPTEFFOFSHÎB

FMÓQUJNPTFBDFSDBSÃBMBSFMBDJÓOEFSFáVKPNÎOJNB"MBVNFOUBSFM DPTUPEFDBQJUBMDBVTBEPQPSNBUFSJBMFTFTQFDJBMFT PEFCJEPBMVTPEFNVZBMUBTQSFTJPOFT FMDPTUP UPUBMÓQUJNP PQFSBDJÓO DBQJUBM TFEFTQMB[BSÃIBDJBFMÓQUJNPEFMDPTUPÓQUJNPEFMDBQJUBM-B -%ÓQUJNBTVFMFFTUBSFOFMJOUFSWBMPEFB× -% NÎO 5BNCJÊOMBQSFTJÓOFOMBDPMVNOBUJFOFFGFDUPTDPNQMJDBEPTTPCSFMPTDPTUPT4JTFDPNQBSBO EPTQSFTJPOFT BNCBTNBZPSFTRVFBUNZBBNCBTQSFTJPOFTTFQVFEFVTBSBHVBEFFOGSJBNJFOUP  MPTDPTUPTUPUBMFTQVFEFOTFSNBZPSFTPNFOPSFTQBSBMBQSFTJÓONBZPS&MFGFDUPEFQFOEFEFTJ EPNJOBOMPTDPTUPTEFMBUPSSFPEFMPTQMBUPT4JTFOFDFTJUBSFGSJHFSBDJÓOQBSBFOGSJBSBMDPOEFOTB EPSBMBQSFTJÓONFOPSZBHVBBMBQSFTJÓONBZPS MPTDPTUPTEFPQFSBDJÓOZMPTDPTUPTUPUBMFTTFSÃO NFOPSFTBMBNBZPSQSFTJÓO7FBNÃTEFUBMMFTFOMBTUBCMBTZ -PTFGFDUPTEFPUSBTWBSJBCMFTTPOBMHPNÃTTJNQMFTRVFFMFGFDUPEF-%ZEFMBQSFTJÓO1PS FKFNQMP DVBOEPBVNFOUBMBUBTBEFBMJNFOUBDJÓOEFEJTFÒPTVCFOUPEPTMPTDPTUPTTJOFNCBSHP  FMDPTUPEFDBQJUBMQPSLJMPHSBNPEFBMJNFOUBDJÓOCBKBFOGPSNBBQSFDJBCMF&OUPODFT MPTDPTUPT

www.FreeLibros.me

  &GFDUPTEFMBPQFSBDJÓOTPCSFMPTDPTUPT



5"#-" &'&$50%&$".#*04&/-"47"3*"#-&4%&%*4&µ0 40#3&$04504%&$"1*5"-  &RVJQP

$POEFOTBEPS

7BQPSJ[BEPS

&OWPMWFOUFEFMB UPSSF

$PTUPTEFQMBUPT QFSGPSBEPT

$BNCJPFOWBSJBCMF EFEJTFÒP

&GFDUPTPCSFPUSBT WBSJBCMFT

&GFDUPTPCSF FMDPTUP

"VNFOUB-%

2D BVNFOUBMJOFBMNFOUF ÃSFB BVNFOUBMJOFBMNFOUF

"VNFOUB

"VNFOUB'

2D BVNFOUBMJOFBMNFOUF ÃSFB BVNFOUBMJOFBMNFOUF

"VNFOUB #BKBP BVNFOUB

"VNFOUBMBQSFTJÓOEF MBDPMVNOB

−5BVNFOUB &DTZ

 EJTNJOVZFFMÃSFBQFSPQPESÎB OFDFTJUBSTFDPOTUSVDDJÓONÃT DPTUPTB

6BVNFOUB "VNFOUB-%

%JTNJOVZFFMÃSFB 23BVNFOUBMJOFBMNFOUF ÃSFB BVNFOUBMJOFBMNFOUF

#BKB "VNFOUB

"VNFOUB'

23BVNFOUBMJOFBMNFOUF ÃSFB BVNFOUBMJOFBMNFOUF

"VNFOUB

"VNFOUBUFNQFSBUVSB EFBMJNFOUBDJÓO

I'BVNFOUBZ23CBKB

#BKB

"VNFOUBMBQSFTJÓOFO MBDPMVNOB

−5CBKB &DTZ  ZBVNFOUBFMÃSFB BQSFTJÓO DPOTUBOUFEFWBQPSEFBHVB

"VNFOUB

"VNFOUB6 "VNFOUB-%

#BKBFMÃSFBSFRVFSJEB "VNFOUBFMEJÃNFUSP BVNFOUBFM QFTP CBKBMBBMUVSB

#BKB #BKBZEFTQVÊT BVNFOUB

"VNFOUB'

"VNFOUBFMEJÃNFUSP BVNFOUBFM QFTP

"VNFOUB

"VNFOUBMBQSFTJÓOFO MBDPMVNOB

%JTNJOVZFFMEJÃNFUSP BVNFOUB FMFTQFTPS BVNFOUBFMQFTP

#BKB EFTQVÊT BVNFOUB

"VNFOUBMBBMUVSBFOUSF QMBUPT

BVNFOUBVPQ CBKBFMEJÃNFUSP  BVNFOUBMBBMUVSB BVNFOUBFMQFTP

"VNFOUB

"VNFOUB-%

#BKBMBDBOUJEBEEFQMBUPT EFTQVÊT FMEJÃNFUSPTFWVFMWFFYDFTJWP "VNFOUBFMEJÃNFUSP %JTNJOVZFFMEJÃNFUSP

#BKB EFTQVÊT TVCF "VNFOUB #BKB

"VNFOUBMBUFNQFSBUVSB EFMBBMJNFOUBDJÓO

.ÃTQMBUPTB -% DPOTUBOUF WFB FMQSPCMFNB"

"VNFOUB

"VNFOUBMBBMUVSBFOUSF QMBUPT

#BKBFMBSSBTUSF NFKPSFàDJFODJB

#BKB

1MBUPTNÃTDPNQMJDBEPT RVFMPTQMBUPT QFSGPSBEPT DPONBZPS FàDJFODJBEFQMBUP

.FOPTQMBUPT QFSPQVFEFODPTUBS NÃTQPSQMBUP

$BMDVMBSFO DBEBDBTP

"VNFOUB' "VNFOUBMBQSFTJÓOFO MBDPMVNOB

www.FreeLibros.me



$BQÎUVMP  &DPOPNÎBZDPOTFSWBDJÓOEFFOFSHÎBFOMBEFTUJMBDJÓO

Costos totales Costos de capital Costo, $/año

Costos de operación

Óptimo

'*(63" &'&$50%&-"3&-"$*¶/%& 3&'-6+040#3&-04$04504

(L/D)MÍN

L/D

UPUBMFTQPSLJMPHSBNPQVFEFOTFSCBTUBOUFNFOPSFTFOQMBOUBTHSBOEFTRVFFOQMBOUBTQFRVFÒBT 5BNCJÊOFOMBTUBCMBTZTFSFTVNFOMPTFGFDUPTEFPUSBTWBSJBCMFT &+&.1-0 &TUJNBDJÓOEFMDPTUPQBSBVOBEFTUJMBDJÓO &TUJNBSFMDPTUPEFMBDPMVNOBEFEFTUJMBDJÓO FOWPMWFOUFZQMBUPT EJTFÒBEBFOMPTFKFN QMPTB 4PMVDJÓO -BDBOUJEBEEFFUBQBTEFFRVJMJCSJPTFDBMDVMBDPOVOEJBHSBNBEF.D$BCF5IJFMFPDPO FMNÊUPEPEF'FOTLF6OEFSXPPE(JMMJMBOE6TBSFNPTFTUFÙMUJNP-BTDJGSBTFTUÃOFOEÓ MBSFTFTUBEPVOJEFOTFT&OFMFKFNQMPTFVTÓ −&OUPODFT EFBDVFSEPDPOMB FDVBDJÓOEF'FOTLF MB 

m &− m

Cb†c 2

m &− m Y^hi ac α $

%#... &− %#...

ac 2

Wdi

%#%%& &− %#%%&

ac'#(*

2&+#'

4FHÙOFMFKFNQMP ZDVBOEPY MBDPODFOUSBDJÓOEFMBBMJNFOUBDJÓO&OUPO DFT QBSBVOBBMJNFOUBDJÓOEFMÎRVJEPTBUVSBEP A K

2 b†c

A 9

%#...− %#, m9 − n 2 2%#*.. %#...− %#* m9 − o 2 b†c

A $Kb†c 2&#).* &− A $Kb†c

www.FreeLibros.me

  &GFDUPTEFMBPQFSBDJÓOTPCSFMPTDPTUPT



$PNP-7 A 9

2 gZVa

A $K %#2 2) & A $K %#'

"MVTBSMBFDVBDJÓO C

MBDPSSFMBDJÓOEF(JMMJMBOE SFTVMUB m2

A $9− A $9b†c )− &#).* 2 2%#*%& * A $9 &

Z C − Cb†c 2%#*)*-',− %#*.&)''%#*%& C & C2



%#'** Cb†c &− %#'**

%#%%',)(  2%#'** %#*%&

2''#%.ZiVeVhYZZfj^a^Wg^d

4FSFTUBQPSUFOFSVOWBQPSJ[BEPSQBSDJBM&OFMFKFNQMP MBFàDJFODJBHFOFSBMGVF &P&OUPODFT CgZVa 2

CZfj^a %#*.

2

'&#%.  %#*.

2(*#,ZhYZX^g! (+ZiVeVh

&MEJÃNFUSPEFMBDPMVNOBFSBQJFTFOFMFKFNQMPZQJFTFOFMQSPCMFNB% 6TBSFNPTFMWBMPSNBZPS $POQVMHBEBTQJFTEFBMUVSBFOUSFQMBUPT OFDFTJUBNPT   QJFT"EFNÃT  BÒBEJSFNPTVOPTQJFTQBSBTFQBSBSFMWBQPSZVOEFQÓTJUPEFMÎRVJEPFOFMGPOEP$POWFS UJSFNPTBNFUSPT QPSRVFMBTàHVSBTZFTUÃOFOVOJEBEFTNÊUSJDBT "MUVSB QJFT NQJFT NEJÃNFUSP QJFT NQJFT  NÃSFBEFMPTQMBUPT−%N ZFMWPMVNFOEFMBUPSSF −% - N %FBDVFSEPDPOMBGJHVSB $QPDPTUPWPMVNFO−NZ$Q UPSSF      4FHÙOMBàHVSB $QPDPTUPEFQMBUPTÃSFB−NZ$Q QMBUP    QMBUP "IPSBIBZRVFJODMVJSMPTGBDUPSFTBEJDJPOBMFTEFDPTUPZDBMDVMBSMPTDPTUPTEFMNÓEVMP NÎOJNP$PNPFTQSPCBCMFRVFMBDPMVNOBZMPTQMBUPTTFBOEFBDFSPBMDBSCÓO 'N" BUN 'Q$PNP/ 'RQBSBMPTQMBUPT&OUPODFT EFBDVFSEPDPOMBTFDVB DJPOFT  Z 

SFTQFDUJWBNFOUF 

$#. UPSSF      

 



$#. QMBUPT        &MDPTUPUPUBMEFMNÓEVMPNÎOJNP UPSSFZQMBUPT FT  &TUFSFTVMUBEPEFCFSÎBDPNQBSBSTFDPOFMEFMQSPCMFNB% QBSBMBNJTNBTFQBSB DJÓO QFSPDPOCBSEFQSFTJÓO&TBDPMVNOBDVFTUBBQSPYJNBEBNFOUFNÃT

www.FreeLibros.me



$BQÎUVMP  &DPOPNÎBZDPOTFSWBDJÓOEFFOFSHÎBFOMBEFTUJMBDJÓO

&TUFDPTUPOPDPNQSFOEFCPNCBT JOTUSVNFOUBDJÓOZDPOUSPMFT WBQPSJ[BEPS DPOEFOTBEPS PJOTUBMBDJÓO&MDPTUPFTBTFQUJFNCSFEF.FEJBOUFFMÎOEJDFEFDPTUPTFQVFEFBDUVB MJ[BSQBSBDPOPDFSFMDPTUPBDUVBM  $".#*04&/$"1"$*%"%&4%&-"1-"/5"

-BTQMBOUBTTFEJTFÒBOQBSBEFUFSNJOBEBDBQBDJEBEOPNJOBM QFSPDPOGSFDVFODJBQSPEVDFONFOPT &MDPTUPEFPQFSBDJÓOQPSLJMPHSBNPEFBMJNFOUBDJÓOTFDBMDVMBEJWJEJFOEPMBFDVBDJÓO  FOUSF MBUBTBEFBMJNFOUBDJÓO $PTUPEFPQFSBDJÓOLH 





LHEFBHVBI

LHEFWBQPSI '

DPTUPEFMBHVB  

' IUSBCBKBEPS×NBOPEFPCSBI '

DPTUPEFMWBQPS

L8&MFDUSI '

L8

DPTUPEFNBOPEFPCSB IIPNCSF 



-PT LH EF WBQPSI  LH EF BHVBI Z L8 EF &MFDUSI TPO EJSFDUBNFOUF QSPQPSDJPOBMFT B ' "TÎ  B FYDFQDJÓOEFMPTDPTUPTEFNBOPEFPCSB FMDPTUPEFPQFSBDJÓOQPSLJMPHSBNPTFSÃDPOTUBOUFFJO EFQFOEJFOUFEFMBUBTBEFBMJNFOUBDJÓO$PNPDPOGSFDVFODJBMPTDPTUPTEFMBNBOPEFPCSBTPOVOB GSBDDJÓOQFRVFÒBEFMPTDPTUPTUPUBMFTFOMBTQMBOUBTRVÎNJDBTDPOUJOVBTZBVUPNÃUJDBT QPESFNPT DPOTJEFSBSRVFFMDPTUPEFPQFSBDJÓOQPSLJMPHSBNPFTDPOTUBOUF &MDPTUPEFDBQJUBMEFQFOEFEFMBDBOUJEBEUPUBMEFBMJNFOUBDJÓOQSPDFTBEBQPSBÒP&OUPODFT  EFBDVFSEPDPOMBFDVBDJÓO 



$PTUPEFDBQJUBMLH

UBTBEFEFQSFDJBDJÓO GBDUPSEF-BOH TVNBEFDPTUPT

 ' LHI IPSBTEFPQFSBDJÓOBÒP



"MUSBCBKBSBMBNJUBEEFMBBMJNFOUBDJÓOEJTFÒBEBTFEVQMJDBFMDPTUPEFDBQJUBMQPSLJMPHSBNP &MDPTUPUPUBMQPSLJMPHSBNPFT 

$PTUPUPUBMLH

DPTUPEFDBQJUBMLH DPTUPEFPQFSBDJÓO  LH DPTUPTBENJOJTUSBUJWPLH



&MFGFDUPEFNFOPSFTUBTBTEFBMJNFOUBDJÓOEFQFOEFEFRVÊQPSDFOUBKFEFMDPTUPUPUBMTFEFCFBM DPTUPEFDBQJUBM 4JFMDPTUPQPSLJMPHSBNP QBSBUPEBMBQMBOUB FTNBZPSRVFFMQSFDJPEFWFOUB MBQMBOUBQFSEFSÃ EJOFSP4JOFNCBSHPFTPOPRVJFSFEFDJSRVFEFCBQBSBSTF4JFMDPTUPEFWFOUBFTNBZPSRVFFMDPTUP EFPQFSBDJÓONÃTMPTDPTUPTBENJOJTUSBUJWPT MBQMBOUBUPEBWÎBBZVEBBQBHBSMPTDPTUPTEFDBQJUBM :BRVFFTPTDPTUPTEFDBQJUBMFYJTUFOBVORVF' MPNFKPSTVFMFTFSNBOUFOFSMBPQFSBDJÓO&T PCWJPRVFCBKPFTUBTDPOEJDJPOFTOPTFDPOTUSVJSÃVOBOVFWBQMBOUB  $0/4&37"$*¶/%&-"&/&3(±"&/-"%&45*-"$*¶/

$POGSFDVFODJB FOVOBQMBOUBMBTDPMVNOBTEFEFTUJMBDJÓOTPOMBTRVFNÃTFOFSHÎBVTBO.JYFUBM  FTUJNÓRVFVOBQSPYJNBEPEFMDPOTVNPUPUBMEFFOFSHÎBFO&TUBEPT6OJEPTTFVTBFOEFT UJMBDJPOFT"TÎ UJFOFFYUSFNBJNQPSUBODJBMBDPOTFSWBDJÓOEFFOFSHÎBFOMPTTJTUFNBTEFEFTUJMBDJÓO  JOEFQFOEJFOUFNFOUFEFMQSFDJPEFMBFOFSHÎBFOFMNPNFOUP"VORVFFMDPTUPEFMBFOFSHÎBPTDJMB  BMBSHPQMB[PIBUFOEJEPBMBVNFOUPZFTQSPCBCMFRVFDPOUJOÙFIBDJÊOEPMPFOFMGVUVSP&TUP RVF PSJHJOBMNFOUFTFFTDSJCJÓFO UBNCJÊOFTDJFSUP EFTEFMVFHP QBSBFMTJHMP99*:BIFNPTEFTDSJUP

www.FreeLibros.me

  $POTFSWBDJÓOEFMBFOFSHÎBFOMBEFTUJMBDJÓO



DPOEFUBMMFBMHVOPTEFMPTFTRVFNBTEFDPOTFSWBDJÓOEFMBFOFSHÎB&OUSFFMMPT MPTNÃTJNQPSUBOUFT TPOMBPQUJNJ[BDJÓOEFMBSFMBDJÓOEFSFáVKPZMBFMFDDJÓOEFMBQSFTJÓOEFPQFSBDJÓODPSSFDUB y2VÊTFQVFEFIBDFSQBSBSFEVDJSFMDPOTVNPEFFOFSHÎBFOVOBQMBOUBFOGVODJPOBNJFOUP  $PNPZBFYJTUFFMFRVJQP IBZVOJODFOUJWPQBSBIBDFSDBNCJPTCBTUBOUFQFRVFÒPTZQPDPDPTUPTPT -BTNPEJàDBDJPOFTDPNPÊTUBTTPOVOBUBSFBRVFTFBTJHOBBMPTOVFWPTJOHFOJFSPT QPSRVFBUSBWÊT EFFMMBTTFGBNJMJBSJ[BODPOMBQMBOUB ZTJIBZVOBGBMMB OPTFSÃDSÎUJDB-PQSJNFSPQPSIBDFSFTDSJ UJDBSMBTDPOEJDJPOFTEFPQFSBDJÓO (FZFSZ,MJOF  4JQVFEFBIPSSBSTFFOFSHÎBDBNCJBOEPMBT DPOEJDJPOFTEFPQFSBDJÓO QVFEFTFSRVFMPTDBNCJPTOPSFRVJFSBODBQJUBMBMHVOP$VBOEPDBNCJB MBUBTBEFBMJNFOUBDJÓOBMBDPMVNOB yUSBCBKBMBDPMVNOBUPEBWÎBDPOáVKPTEFWBQPSDFSDBOPTBMPT EFÓQUJNBFàDJFODJB 4JOPFTBTÎ TFEFCFFYQMPSBSMBQPTJCJMJEBEEFWBSJBSMBQSFTJÓOEFMBDPMVNOB QBSBDBNCJBSMBUBTBEFáVKPEFWBQPSZBTÎUSBCBKBSNÃTDFSDBEFMQVOUPÓQUJNP%FFTFNPEPMB DPMVNOBQPESÃUFOFSFMFRVJWBMFOUFEFNÃTDPOUBDUPTEFFRVJMJCSJPZFMPQFSBEPSQPESÃSFEVDJSMB SFMBDJÓOEFSFáVKP-BSFEVDDJÓOEFÊTUBBIPSSBFOFSHÎBFOFMTJTUFNB%FTQVÊTTFEFCFOFYBNJOBS MBTFTQFDJàDBDJPOFTEFMPTQSPEVDUPTEFTUJMBEPZGPOEPT$VBOEPMPTQSPEVDUPTTPONVZQVSPT DBN CJPTCBTUBOUFQFRVFÒPTFOTVTQVSF[BTQVFEFODBVTBSHSBOEFTDBNCJPTFOMBSFMBDJÓOEFSFáVKP4J TFSFRVJFSFVOQSPEVDUPEFDPNQPTJDJÓOJOUFSNFEJB MBTTBMJEBTMBUFSBMFTSFRVJFSFONFOPTFOFSHÎB RVFNF[DMBSMPTQSPEVDUPTEFTUJMBEPZEFGPOEPT "MMFOZ4IPOOBSE   &OTFHVOEPMVHBSTFCVTDBOMBTNPEJàDBDJPOFTRVFSFRVJFSBOJOWFSTJÓOEFDBQJUBM6OBNFKPSB EFMPTDPOUSPMFTZMBJOTUSVNFOUBDJÓOQVFEFBVNFOUBSMBFàDJFODJBEFMTJTUFNB (FZFSZ,MJOF  .JYFUBM 4IJOTLFZ  6ONFKPSDPOUSPMQFSNJUFRVFFMPQFSBEPSUSBCBKFNVDIPDFSDBB MBTFTQFDJàDBDJPOFTOFDFTBSJBTFTUPJNQMJDBNFOPSSFMBDJÓOEFSFáVKP&MSFUPSOPEFFTUBJOWFSTJÓO QVFEFTFSUBODPSUPDPNPNFTFT&MDPOUSPMEFVOBDPMVNOBEFEFTUJMBDJÓOFTVOUFNBFYUSFNBEB NFOUFJNQPSUBOUF RVFTBMFEFMBMDBODFEFFTUFMJCSPEFUFYUP3PTF  QSFTFOUBVOBEFTDSJQDJÓO DVBMJUBUJWBEFMPTTJTUFNBTEFDPOUSPMEFEFTUJMBDJÓO NJFOUSBTRVF4IJOTLFZ  MPIBDFDPONÃT EFUBMMFT4JMBDPMVNOBUJFOFQMBUPTEFCVSCVKFPSFMBUJWBNFOUFJOFàDJFOUFT DPNPCBSCPUFBEPSFT P FNQBRVFT DPNPBOJMMPT3BTDIJH

FOVODBTPOPSNBMTFSÃFDPOÓNJDPJOTUBMBSQMBUPTOVFWPTEFNV DIBFàDJFODJB QPSFKFNQMP QMBUPTEFWÃMWVMBT PFNQBRVFOVFWPEFHSBOFàDJFODJB QPSFKFNQMP  BOJMMPTPTJMMBTNPEFSOBT PFNQBRVFFTUSVDUVSBEP

BVODVBOEPTFBOCBTUBOUFDPTUPTPT ,FOOFZ    $MBSP RVF IBCSÃ RVF TVTUJUVJS QMBUPT P FNQBRVFT EBÒBEPT QPS QMBUPT P FNQBRVFT EF BMUB FàDJFODJB ,FOOFZ  &OUPEBDPMVNOBDPOBJTMBNJFOUPEBÒBEPEFCFRVJUBSTFZTVTUJUVJSTFFM BJTMBNJFOUP-BJOUFHSBDJÓOEFJOUFSDBNCJBEPSFTEFDBMPSZDPMVNOBTQPESÎBFTUBSNVZBMFKBEBEFMP ÓQUJNPFOMPTTJTUFNBTFYJTUFOUFTEFEFTUJMBDJÓO4FEFCFUFOFSFODVFOUBIBDFSVONFKPSBNJFOUPEF FTBTJOTUBMBDJPOFT QBSBEFUFSNJOBSTJTPOFDPOÓNJDBT $VBOEPTFEJTFÒBOOVFWBTJOTUBMBDJPOFTTFQVFEFSFDVSSJSBNVDIPTNÊUPEPTEFDPOTFSWBDJÓO EFFOFSHÎBRVFQPESÎBOOPTFSFDPOÓNJDPTFOMBTNPEJàDBDJPOFT4FEFCFVTBSFOGPSNBFYUFOTBFM JOUFSDBNCJPEFDBMPSFOUSFMBTDPSSJFOUFTZMBJOUFHSBDJÓOEFMPTQSPDFTPT QBSBSFEVDJSBMNÎOJNPMBT OFDFTJEBEFTUPUBMFTEFFOFSHÎB&TPTNÊUPEPTZBTFDPOPDFOEFTEFIBDFNVDIPTBÒPT QPSFKFNQMP  WFB3PCJOTPOZ(JMMJMBOE  P3VEEZ8BUTPO 

QFSPOPFSBOFDPOÓNJDPTDVBOEPMPTDPT UPTEFFOFSHÎBFSBONVZCBKPT$VBOEPÊTUPTTVCJFSPOEVSBOUFMBEÊDBEBEFZMPTQSJNFSPTBÒPT EFMBEF ZWPMWJFSPOBIBDFSMPFOUSFZ NVDIBTUÊDOJDBTEFDPOTFSWBDJÓOEFFOFSHÎB TFWPMWJFSPOFDPOÓNJDBT %PIFSUZZ.BMPOF (FZFSZ,MJOF ,JOH .JYFUBM  /VMM 0#SJFO 4IJOTLFZ Z4JJSPMB  &TUBTGVFOUFTZNVDIBTSFGFSFODJBTRVF DJUBOFTUPTBVUPSFTQSFTFOUBONÃTEFUBMMFT -B JEFB CÃTJDB EFM JOUFSDBNCJP EF DBMPS FT VTBS DPSSJFOUFT DBMJFOUFT RVF OFDFTJUBO FOGSJBSTF  QBSBDBMFOUBSDPSSJFOUFTGSÎBTRVFOFDFTJUBODBMFOUBSTF-BGPSNBÓQUJNBEFIBDFSMPEFQFOEFEFMB DPOàHVSBDJÓOEFUPEBMBQMBOUB ZBRVFMPTJOUFSDBNCJPTQVFEFOEBSTFDPOMBTDPSSJFOUFTFYUFSOBT BMTJTUFNBEFEFTUJMBDJÓO4JTÓMPTFDPOTJEFSBFMTJTUFNBEFEFTUJMBDJÓO IBZEPTMVHBSFTQSJODJQBMFT

www.FreeLibros.me



$BQÎUVMP  &DPOPNÎBZDPOTFSWBDJÓOEFFOFSHÎBFOMBEFTUJMBDJÓO

EFJOUFSDBNCJPEFDBMPSRVFTFNVFTUSBOFOMBàHVSB-BBMJNFOUBDJÓOGSÎBTFQSFDBMJFOUBQPS JOUFSDBNCJPEFDBMPSDPOFMEFTUJMBEPDBMJFOUF%FFTUFNPEPTFDPOEFOTBFMEFTUJMBEPFOGPSNBQBS DJBMPUPUBM&MDPOEFOTBEPSEFBDBCBEPTFVTBQBSBUPEPFOGSJBNJFOUPBEJDJPOBMRVFTFBOFDFTBSJPZ QBSBNFKPSBSFMDPOUSPMEFMTJTUFNB&OUPODFT MBBMJNFOUBDJÓOTFTJHVFDBMFOUBOEPDPODBMPSTFOTJCMF EFMQSPEVDUPEFGPOEPT&MJOUFSDBNCJPEFDBMPSTFIBDFFOFTFPSEFO QPSRVFMPTGPOEPTFTUÃONÃT DBMJFOUFTRVFFMEFTUJMBEP&MDBMFOUBNJFOUPBEJDJPOBMEFMBBMJNFOUBDJÓOTFIBDFFOVODBMFOUBEPS EFBàOBDJÓO QBSBBZVEBSBDPOUSPMBSMBEFTUJMBDJÓO4JOFNCBSHP FMTJTUFNBRVFNVFTUSBMBàHVSB QVFEFOPTFSFMÓQUJNP FOFTQFDJBMTJTFJOUFHSBOWBSJBTDPMVNOBT4JOFNCBSHP MPTDPODFQUPT EFJOUFSDBNCJPEFDBMPSRVFNVFTUSBMBàHVSBTPOCBTUBOUFCÃTJDPT 6OBUÊDOJDBQBSFDJEBBMBEFMBàHVSBFTQSPEVDJSWBQPSEFBHVBFOFMDPOEFOTBEPS4JIBZ VTPQBSBFTFWBQPSEFCBKBQSFTJÓO QVFEFTFSVOVTPNVZFDPOÓNJDPEFMBFOFSHÎBRVFDPOUJFOFO MPT WBQPSFT EFTUJMBEPT 5BNCJÊO TF QVFEFO VTBS DPOEFOTBEPSFT JOUFSNFEJPT TFDDJÓO   QBSB QSPEVDJSWBQPSEFBHVBZTVWBQPSFTNÃTDBMJFOUF -BJOUFHSBDJÓOEFMJOUFSDBNCJPUÊSNJDPFOMBTDPMVNOBTFTVOJNQPSUBOUFDPODFQUPQBSBSFEVDJS FMVTPEFMBFOFSHÎB "OESFDPWJDIZ8FTUFSCFSH #JFHMFSFUBM %PIFSUZZ.BMPOF  %PVHMBT ,JOH -JOOIPGFUBM 3PCJOTPOZ(JMMJMBOE  -BJEFBCÃTJDBFTDPOEFO TBSFMWBQPSEFTUJMBEPEFVOBDPMVNOBFOFMWBQPSJ[BEPSEFVOBTFHVOEBDPMVNOB&TPTFNVFTUSBFO MBàHVSB FOMBQSÃDUJDBUBNCJÊOTFVTBODBNCJBEPSFTEFDBMPSDPNPMPTEFMBàHVSB QFSPRVF OPTFJODMVZFSPOEFMBàHVSBQBSBNBOUFOFSMBTFODJMMB &TPCWJPRVFMBUFNQFSBUVSBEFDPOEFO TBDJÓOEFMBDPSSJFOUF%EFCFTFSNBZPSRVFMBUFNQFSBUVSBEFFCVMMJDJÓOEFMBDPSSJFOUF#$VBOEP TFVTBEFTUJMBDJÓOQBSBEPTTFQBSBDJPOFTNVZEJTUJOUBT TFQVFEFVTBSFMTJTUFNBEFMBàHVSBTJO NPEJàDBDJÓO4JOFNCBSHP FONVDIPTDBTPTMBDPSSJFOUF%FTMBBMJNFOUBDJÓOBMBTFHVOEBDPMVNOB &MTJTUFNBEFMBàHVSBUSBCBKBTJMBQSJNFSBDPMVNOBFTUÃBNBZPSQSFTJÓORVFMBTFHVOEB QBSB RVFMBDPSSJFOUF%TFDPOEFOTFBVOBUFNQFSBUVSBNBZPSRVFBRVFMMBBMBRVFIJFSWFMBDPSSJFOUF# 4FIBOEFTBSSPMMBEPNVDIBTWBSJBDJPOFTEFMBJEFBCÃTJDBRVFNVFTUSBMBàHVSBTJTFSFDV QFSBVOTPMWFOUFTFQBSÃOEPMPEFJNQVSF[BTDPOTJEFSBCMFNFOUFNÃTQFTBEBT FTÙUJMBMHVOBWBSJBOUF EFMTJTUFNBEFWBSJPTFGFDUPTRVFTFWFFOMBàHVSB "HSBXBM "OESFDPWJDIZ8FTUFSCFSH  Condensador de acabado

Calentador de acabado

'*(63" */5&3$".#*0%&$"-031"3"6/"$0-6./" %&%&45*-"$*¶/*/%&1&/%*&/5&

www.FreeLibros.me

Intercambiador de calor

  $POTFSWBDJÓOEFMBFOFSHÎBFOMBEFTUJMBDJÓO



'*(63" */5&(3"$*¶/%& $0-6./"4%&%&45*-"$*¶/ %PIFSUZZ.BMPOF ,JOH 0#SJFO 3PCJOTPOZ(JMMJMBOE 4JJSPMB  8BOLBU  %FTQVÊTEFQSFDBMFOUBSTFSFDVQFSBFMTPMWFOUFDPNPQSPEVDUPEFTUJMBEPFOMBQSJNF SBDPMVNOB RVFUSBCBKBBCBKBQSFTJÓO-PTGPOEPTEFÊTUBTFCPNCFBOBNBZPSQSFTJÓO TFQSFDBMJFO UBOZTFBMJNFOUBOBMBTFHVOEBDPMVNOB$PNPMBTFHVOEBDPMVNOBFTUÃBNBZPSQSFTJÓO TFQVFEFO

Reflujo

'*(63" 4*45&."%&%&45*-"$*¶/ $0/7"3*04&'&$504

www.FreeLibros.me



$BQÎUVMP  &DPOPNÎBZDPOTFSWBDJÓOEFFOFSHÎBFOMBEFTUJMBDJÓO

Válvula de expansión Condensador de acabado

'*(63" 4*45&."%&3&$0.13&4*¶/%& 7"103 0%&#0.#"5­3.*$"

Compresor

VTBSMPTEFTUJMBEPTFOFMWBQPSJ[BEPSEFMBDPMVNOBBCBKBQSFTJÓO"TÎ FMWBQPSEFBHVBVTBEPFOFM WBQPSJ[BEPSEFMBDPMVNOBEFNBZPSQSFTJÓOTJSWFQBSBDBMFOUBSBNCBTCPNCBT$BTJTFEVQMJDBMB FàDJFODJBEFFTFWBQPS$PNPMBTFQBSBDJÓOFTTFODJMMB OPTFSFRVJFSFOEFNBTJBEPTQMBUPTZMPTEPT QSPEVDUPT EFTUJMBEP TPO FO FTFODJB TPMWFOUF QVSP "EJDJPOBMNFOUF  MPT TJTUFNBT EF WBSJPT FGFDUPT QVFEFOUFOFSMBBMJNFOUBDJÓOBMBDPMVNOBEFBMUBQSFTJÓO BEFNÃTPFOMVHBSEFBMJNFOUBDJÓOBMB DPMVNOBEFCBKBQSFTJÓO&MPYÎHFOPZFMOJUSÓHFOPMÎRVJEPTTFQSPEVDFOBQBSUJSEFMBJSFBNVZHSBO FTDBMB FODPMVNOBTEPCMFTEF-JOEF RVFTPODPMVNOBTEFEFTUJMBDJÓOEFWBSJPTFGFDUPT&TDMBSPRVF MBEFTUJMBDJÓOEFWBSJPTFGFDUPTTFSFMBDJPOBDPOMBFWBQPSBDJÓOFOWBSJPTFGFDUPT .FISB   &MWBQPSEFTUJMBEPDPOEFOTBOUFTFQVFEFVTBSQBSBDBMFOUBSFMWBQPSJ[BEPSEFMBNJTNBDPMVNOB  TJTFVTBSFDPNQSFTJÓOEFWBQPS PVOBCPNCBEFDBMPS )VNQISFZZ,FMMFS ,JOH .FJMJ  /VMM 3PCJOTPOZ(JMMJMBOE  -BàHVSBNVFTUSBVOBSSFHMPEFFTUFDBTP-PTWB QPSFTEFTUJMBEPTTFDPOEFOTBOBVOBQSFTJÓOBEFDVBEBQBSBRVFMBTUFNQFSBUVSBTTFBONBZPSFTRVF MBTEFFCVMMJDJÓOEFMPTGPOEPT-BSFDPNQSFTJÓOEFMPTWBQPSFTGVODJPOBNFKPSQBSBEFTUJMBDJPOFTDPO QVOUPTEFFCVMMJDJÓODFSDBOPT QPSRVFTFSFRVJFSFOBVNFOUPTQFRVFÒPTEFMBQSFTJÓO&OHFOFSBM MB SFDPNQSFTJÓOEFWBQPSFTFTNÃTDPTUPTBRVFMBJOUFHSBDJÓOUÊSNJDBPMBPQFSBDJÓOEFDPMVNOBTDPO WBSJPTFGFDUPT"TÎ MBSFDPNQSFTJÓOEFWBQPSTFVTBDVBOEPMBDPMVNOBFTVOBJOTUBMBDJÓOBJTMBEB P CJFODVBOEPFTUÃUSBCBKBOEPBUFNQFSBUVSBTBMUBTPCBKBTFYUSFNBT0#SJFOZ4DIVMU[  EJDFO RVF601 BOUFT6OJWFSTBM0JM1SPEVDUT *OD VTBCPNCBTEFDBMPSQBSBMBTFQBSBDJÓOEFQSPQBOPZ QSPQJMFOP MBDVBMFTEJGÎDJM  4  ±/5&4*4%&4&$6&/$*"4%&$0-6./"41"3"%&45*-"$*¶/ %&7"3*04$0.10/&/5&4$"4**%&"-&4

6OB DPMVNOB EF EFTUJMBDJÓO DPOUJOVB FT  FO FTFODJB  VO TFQBSBEPS CJOBSJP &T EFDJS  TFQBSB VOB BMJNFOUBDJÓOFOEPTQBSUFT&OMPTTJTUFNBTCJOBSJPT BNCBTQBSUFTQVFEFOTFSMPTQSPEVDUPTQVSPT RVF TF EFTFBO 4JO FNCBSHP  QBSB TJTUFNBT EF WBSJPT DPNQPOFOUFT  VOB TPMB DPMVNOB OP QVFEF TFQBSBSMPTUPEPT1BSBTJTUFNBTUFSOBSJPTTFOFDFTJUBOEPTDPMVNOBTQBSBPCUFOFSQSPEVDUPTQVSPT QBSBTJTUFNBTEFDVBUSPDPNQPOFOUFT TFSFRVJFSFOUSFTDPMVNOBTZBTÎTVDFTJWBNFOUF)BZNVDIBT GPSNBTFOMBTRVFTFQVFEFOBDPQMBSDPMVNOBTNÙMUJQMFTDPOFMàOEFIBDFSTFQBSBDJPOFTEFWBSJPT DPNQPOFOUFT-BFMFDDJÓOEFMBDBTDBEBQVFEFUFOFSVOHSBOFGFDUPTPCSFMPTDPTUPTEFDBQJUBMZ EF PQFSBDJÓO &O FTUB TFDDJÓO EFTDSJCJSFNPT FO GPSNB CSFWF FM BDPQMBNJFOUP EF DPMVNOBT QBSB

www.FreeLibros.me

  4ÎOUFTJTEFTFDVFODJBTEFDPMVNOBTQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFTDBTJJEFBMFT



TJTUFNBTRVFTFBODBTJJEFBMFT&OPUSPTMJCSPTTFQSFTFOUBOEFTDSJQDJPOFTNÃTEFUBMMBEBT #JFHMFS FUBM %PIFSUZZ.BMPOF %PVHMBT ,JOH 3VEEFUBM Z8PPET 

 PFOSFTFÒBT /JTIJEBFUBM 4JJSPMB 

BTÎDPNPFOVOBFOPSNFDBOUJEBEEFUSBCBKPT EF MPTDVBMFTTÓMPBMHVOPTTFDJUBOBRVÎ "HSBXBM (BSHFUBM ,JNZ8BOLBU 4IVMU[ FUBM  4IBI 5BEEFSZ3VEE 5IPNQTPOZ,JOH  &OMBQSÓYJNBTFDDJÓOTF EFTDSJCJSÃOTÎOUFTJTEFTFDVFODJBTQBSBTJTUFNBTOPJEFBMFT y&O DVÃOUBT GPSNBT QVFEFO BDPQMBSTF DPMVNOBT QBSB EFTUJMBS WBSJPT DPNQPOFOUFT  `&O NV DIBT1PSFKFNQMP MBàHVSBNVFTUSBOVFWFGPSNBTFOMBTRVFTFQVFEFOBDPQMBSMBTDPMVNOBT QBSBVOTJTUFNBUFSOBSJPRVFOPGPSNFB[FÓUSPQPT$PONÃTDPNQPOFOUFT MBDBOUJEBEEFQPTJCJ MJEBEFTBVNFOUBFOGPSNBHFPNÊUSJDB-BàHVSB"NVFTUSBMBTFDVFODJBiOPSNBMu EPOEFMPT DPNQPOFOUFTNÃTWPMÃUJMFTTBMFOFOFMEFTUJMBEPVOPQPSVOP&TQSPCBCMFRVFFTUBTFDVFODJBTFBMB NÃTVTBEB FOFTQFDJBMFOMBTQMBOUBTNÃTBOUJHVBT&MFTRVFNB#NVFTUSBVOBTFDVFODJBJOWFSUJEB  EPOEFTFTBDBOMPTQSPEVDUPT VOPQPSVOP FOMPTGPOEPT$PONÃTDPNQPOFOUFTFTQPTJCMFVOB HSBOWBSJFEBEEFDPNCJOBDJPOFTEFFTUPTFTRVFNBT&MFTRVFNBEFMBàHVSB$TFQBSFDFBMEF MBQBSUF" QFSPTFIBFMJNJOBEPFMWBQPSJ[BEPSZVOBDPSSJFOUFEFSFUPSOPEFWBQPSEFMBTFHVOEB DPMVNOBQSPEVDFMBWBQPSJ[BDJÓOBMBQSJNFSBDPMVNOB4FSFEVDFOMPTDPTUPTEFDBQJUBM QFSPMBT

'*(63" 4&$6&/$*"4 %&%&45*-"$*¶/%&.&;$-"4 5&3/"3*"4 4*/";&¶530104 &-$0.10/&/5&"&4&-.¦4 70-¦5*-:&-$0.10/&/5&$ &4&-.&/0470-¦5*-

Destilación instantánea

www.FreeLibros.me



$BQÎUVMP  &DPOPNÎBZDPOTFSWBDJÓOEFFOFSHÎBFOMBEFTUJMBDJÓO

DPMVNOBTFTUÃOBDPQMBEBT MPDVBMEJàDVMUBFMDPOUSPMZFMBSSBORVF&MFTRVFNB%TFQBSFDFBM#  QFSPVOBDPSSJFOUFEFMÎRVJEPEFSFUPSOPFTFMSFáVKP &MFTRVFNBEFMBàHVSB&VTBVOFOSJRVFDFEPSMBUFSBM NJFOUSBTRVFFMEFMBQBSUF'VTBVO BHPUBEPSMBUFSBM QBSBQVSJàDBSFMDPNQPOFOUFJOUFSNFEJP#-BDPSSJFOUFTFUPNBEFMMVHBSEPOEFMB DPODFOUSBDJÓOEF#FTNÃYJNB$POGSFDVFODJB FTUPTFTRVFNBTTFVTBOFOMBTSFàOFSÎBTQFUSPMFSBT -BàHVSB(NVFTUSBVOTJTUFNBUÊSNJDBNFOUFBDPQMBEP RVFBWFDFTTFDPOPDFDPNPDPMVNOBT 1FUZMVL-BQSJNFSBDPMVNOBTFQBSB"EF$ RVFFTMBTFQBSBDJÓONÃTTFODJMMBZEFTQVÊTFOMBTFHVOEB DPMVNOB TFPCUJFOFOUSFTQSPEVDUPTQVSPT$POGSFDVFODJB FMTJTUFNBUJFOFQPDBTOFDFTJEBEFTFOFS HÊUJDBT QFSPFTNÃTEJGÎDJMEFBSSBODBSZDPOUSPMBS"EFNÃT FTUFTJTUFNBQVFEFOFDFTJUBSVOBDBOUJEBE FYDFTJWBEFFUBQBT DVBOEPMBTTFQBSBDJPOFTEF"#PEF#$TPOEJGÎDJMFT"WFDFT TFQVFEFUFOFS FTUFFTRVFNBFOVOBTPMBDPMVNOBEFiQBSFEEJWJEJEBu 4DIVMU[FUBM  &TUBDPMVNOBEFDVBUSP TFDDJPOFTUJFOFVOBQBSFEWFSUJDBMFOUSFEPTQBSUFTEFMBDPMVNOBFOMBTEPTTFDDJPOFTJOUFSNFEJBT -BBMJNFOUBDJÓOFOUSBFOFMMBEPJ[RVJFSEPEFMBQBSFEZMBTEPTTFDDJPOFTFOFMMBEPJ[RVJFSEPEFMB QBSFEIBDFOMBNJTNBTFQBSBDJÓORVFIBDFMBQSJNFSBDPMVNOBEFMBàHVSB(&OMBQBSUFTVQFSJPS EFMBQBSFEVOBNF[DMBEF"Z#TFEJWJEFTPCSFMBQBSFEZFOUSBBMBTTFDDJPOFTEFSFDUJàDBDJÓOZMB JOUFSNFEJBTVQFSJPS&OMBQBSUFJOGFSJPSEFMBQBSFE QBTBVOBNF[DMBEF#Z$CBKPMBQBSFEZWBBMBT TFDDJPOFTJOUFSNFEJBTEFBHPUBNJFOUPZEFGPOEPT"TÎ MBTEPTTFDDJPOFTJOUFSNFEJBTBMMBEPEFSFDIP EFMBQBSFEIBDFOMBTFQBSBDJÓORVFTFIBDFFOMBTEPTTFDDJPOFTJOUFSNFEJBTEFMBTFHVOEBDPMVNOB FOMBàHVSB(&TQPTJCMFEJTFÒBSDPMVNOBTEFQBSFEEJWJEJEBDPNPTJTFUSBUBSBEFUSFTDPMVNOBT TJNQMFTQPSFKFNQMP DPOFMNÊUPEPEF'FOTLF6OEFSXPPE(JMMJMBOE .VSBMJLSJTIOBFUBM  4F EJDFRVF FODPNQBSBDJÓODPOMBàHVSB( MBTDPMVNOBTEFQBSFEEJWJEJEB BIPSSBOIBTUBFMEF MBFOFSHÎBZEFMDBQJUBM 0#SJFOZ4DIVMU[  0CTFSWFRVFQBSFDFRVFFTUFBSSFHMPFTNFOPT TFOTJCMFBBMUFSBDJPOFT&OMBàHVSB)TFNVFTUSBPUSBWBSJBOUF EPOEFMBTFQBSBDJÓOEF"$FTUBO GÃDJMRVFQVFEFVTBSTFVOUBNCPSEFEFTUJMBDJÓOJOTUBOUÃOFBFOMVHBSEFMBQSJNFSBDPMVNOB &MFTRVFNBEFMBàHVSB*FTCBTUBOUFEJTUJOUPEFMPTEFNÃT QPSRVFTFVTBVOBTPMBDPMVNOB DPOVOBTBMJEBMBUFSBM 5FEEFSZ3VEE  -BTBMJEBMBUFSBMOPQVFEFTFS#UPUBMNFOUFQVSP QFSP TÎQVFEFUFOFSMBQVSF[BTVàDJFOUFQBSBDVNQMJSMBTFTQFDJàDBDJPOFTEFMQSPEVDUP&TUFFTRVFNB Z PUSPTNVZQBSFDJEPT TFVTBODPONVDIBGSFDVFODJBDVBOEPMBDPODFOUSBDJÓOEF$FOMBBMJNFOUBDJÓO FTCBTUBOUFCBKB&OUPODFT FOFMQVOUPEFNÃYJNBDPODFOUSBDJÓOEF#OPIBCSÃNVDIP$QSFTFOUF 5BNCJÊOTFQVFEFOVTBSNÊUPEPTDPOTBMJEBTMBUFSBMFT RVFTFDPOFDUBOBPUSBTDPMVNOBT %PIFSUZ Z.BMPOF  ZQBSBTFQBSBDJPOFTEFDVBUSPDPNQPOFOUFT ,JNZ8BOLBU   &TUBTTFDVFODJBTTÓMPTPOFMQSJODJQJPEFMPRVFTFQVFEFIBDFS1PSFKFNQMP MPTFTRVFNBTEF JOUFSDBNCJPEFDBMPSZEFJOUFHSBDJÓOEFFOFSHÎBEFTDSJUPTFOMBTFDDJÓOBOUFSJPSTFQVFEFOJOUFSDB MBSFOFMFTRVFNBEFTFQBSBDJÓO"HSBXBM  QSFTFOUBDBTDBEBTEFWBSJPTFGFDUPTQBSBTFQBSB DJPOFTUFSOBSJBT&OMBBDUVBMJEBE FTPTFTRVFNBTTPOMPTNÊUPEPTNÃTFDPOÓNJDPTQBSBQSPEVDJS PYÎHFOP  OJUSÓHFOP Z BSHÓO QPS EFTUJMBDJÓO DSJPHÊOJDB EF BJSF &T PCWJP RVF FM TJTUFNB TF WVFMWF CBTUBOUFDPNQMFKP &MNFKPSNÊUPEPBVTBSEFQFOEFEFMQSPCMFNBEFMBTFQBSBDJÓO-BGBDJMJEBEEFMBTEJWFSTBTTFQB SBDJPOFT MBTQVSF[BTOFDFTBSJBTZMBTDPODFOUSBDJPOFTEFMBBMJNFOUBDJÓOTPOJNQPSUBOUFTQBSBEFUFS NJOBSMBDPOàHVSBDJÓOÓQUJNB&TUBDPOàHVSBDJÓOÓQUJNBUBNCJÊOQVFEFEFQFOEFSEFDÓNPTFEFàOF iMPNFKPSu&MJOHFOJFSPBDBSHPEFMBPQFSBDJÓOEFMBQMBOUBQSFGFSJSÃTJTUFNBTEFTBDPQMBEPT NJFOUSBT RVFFMRVFFTUÊBDBSHPEFNJOJNJ[BSFMDPOTVNPEFFOFSHÎBQPESÃQSFGFSJSMPTTJTUFNBTBDPQMBEPTF JOUFHSBEPT-BÙOJDBGPSNBEFFTUBSTFHVSPEFIBCFSFODPOUSBEPFMNFKPSNÊUPEPFTNPEFMBSUPEPT MPTTJTUFNBTZIBDFSQSVFCBTDPOFMMPT&TUPFTEJGÎDJM ZBRVFJNQMJDBVOBHSBODBOUJEBEEFDPMVNOBT EFEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFTJOUFSDPOFDUBEBT$POGSFDVFODJBTFVTBONÊUPEPTBCSFWJBEPTEF DÃMDVMP QBSBBIPSSBSUJFNQPZDPTUPEFDÓNQVUP%FTBGPSUVOBEBNFOUF QPESÃTFSRVFFMSFTVMUBEPOP

www.FreeLibros.me

  4ÎOUFTJTEFTFDVFODJBTEFDPMVNOBTQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFTDBTJJEFBMFT



TFBFMÓQUJNP&ONVDIPTFTUVEJPTOPTFIBOUPNBEPFODVFOUBBMHVOPTEFMPTBSSFHMPTRVFNVFTUSB MBàHVSB&OUPODFT QPESÃTFSRVFOPQSFTFOUFOFMFTRVFNBÓQUJNP-BTDPOEJDJPOFTTJFNQSF DBNCJBOZVOBDBTDBEBEFEFTUJMBDJÓOTFQVFEFWPMWFSOPÓQUJNBQPSMPTDBNCJPTFOMBTDPOEJDJPOFTEF PQFSBDJÓOEFMBQMBOUB DPNPáVKPTZDPODFOUSBDJPOFTEFBMJNFOUBDJÓOPEFQSPEVDUPT-PTDBNCJPT FDPOÓNJDPT DPNPMPTDPTUPTEFFOFSHÎBPMBTUBTBTEFJOUFSÊT UBNCJÊOQVFEFOBMUFSBSFMTJTUFNBÓQUJ NP"WFDFTFTNFKPSDPOTUSVJSVOTJTUFNBOPÓQUJNPDVBOEPÊTUFSFTVMUBNÃTWFSTÃUJM 6ONÊUPEPBMUFSOBUJWPQBSBFMEJTFÒPFTBQMJDBSMBIFVSÎTUJDB UBOUFPT DPOPDJNJFOUPTVCKFUJWP  QSFTFOUJNJFOUPT SFHMBTHFOFSBMFTZPUSPTNÊUPEPTJOGPSNBMFT

RVFDPOTJTUFFOSFHMBTGÃDJMFTQBSB FYDMVJSNVDIPTEFMPTTJTUFNBTQPTJCMFT&MNÊUPEPIFVSÎTUJDPQPESÃOPMMFHBSBMFTRVFNBÓQUJNP EFTFQBSBDJÓO QFSPTVFMFQSPEVDJSVOFTRVFNBDFSDBOPBMÓQUJNP4FIBEFTBSSPMMBEPMBIFVSÎTUJDB IBDJFOEP VOB HSBO DBOUJEBE EF TJNVMBDJPOFT  QBSB EFTQVÊT CVTDBS DPODFQUPT RVF SFMBDJPOFO MPT NFKPSFTFTRVFNBT"MHVOBTEFMBTIFVSÎTUJDBTNÃTDPNVOFT DJUBEBTBQSPYJNBEBNFOUFFOPSEFOEF JNQPSUBODJB #JFHMFSFUBM %PIFSUZZ.BMPOF %PVHMBT (BSHFUBM ,JOH  5IPNQTPOZ,JOH  JODMVZFO                  

1SJNFSPTBDBSDPNQPOFOUFTQFMJHSPTPT DPSSPTJWPTZSFBDUJWPT /PVTBSEFTUJMBDJÓOTJ− -,),− NÎO TJ− NÎO−B 4BDBSQSJNFSPMPTDPNQPOFOUFTRVFSFRVJFSBOUFNQFSBUVSBTNVZBMUBTPNVZCBKBT )BDFSQSJNFSPMPTDPSUFTGÃDJMFT −HSBOEF  -BTJHVJFOUFGSBDDJÓOEFCFFMJNJOBSMPTDPNQPOFOUFTFOFYDFTP -BTJHVJFOUFGSBDDJÓOEFCFTBDBSFMDPNQPOFOUFNÃTWPMÃUJM )BDFSMBTTFQBSBDJPOFTNÃTEJGÎDJMFTDPNPTFQBSBDJPOFTCJOBSJBT 'BWPSFDFSMPTGSBDDJPOBNJFOUPT 4JFTQPTJCMF MBTFMJNJOBDJPOFTEFQSPEVDUPTàOBMFTEFCFOTFSDPNPQSPEVDUPTEFTUJMBEPT

%PTIFVSÎTUJDBTBEJDJPOBMFTRVFOPBQBSFDFOFOPSEFOEFJNQPSUBODJB QFSPRVFQVFEFOGPS[BSBM EJTFÒBEPSQBSBCVTDBSTFDVFODJBTBEJDJPOBMFTTPO  5FOFSFODVFOUBTBMJEBTMBUFSBMFTQBSBTFQBSBDJPOFTEJGÎDJMFT  5FOFSFODVFOUBDPMVNOBTUÊSNJDBNFOUFBDPQMBEBTZEFWBSJPTFGFDUPT FOFTQFDJBMTJMBFOFSHÎB FTDPTUPTB &YJTUFOSB[POFTGVOEBEBTQBSBDBEBVOBEFMBTIFVSÎTUJDBT-BIFVSÎTUJDBSFEVDJSÃBMNÎOJNP MPTSJFTHPTEFTFHVSJEBE TBDBSÃMPTDPNQVFTUPTJOFTUBCMFTZSFEVDJSÃMBOFDFTJEBEEFVTBSNBUFSJB MFTEFDPOTUSVDDJÓODPTUPTPTFOMBTDPMVNOBTQPTUFSJPSFT-BIFVSÎTUJDBFMJNJOBMBOFDFTJEBEEF DPMVNOBTDPTUPTBT$PNPMBTUFNQFSBUVSBTZQSFTJPOFTNVZBMUBTZNVZCBKBTSFRVJFSFODPMVNOBT BMUBT ZP DPOEJDJPOFT EF PQFSBDJÓO DPTUPTBT  MB IFVSÎTUJDB  NBOUFOESÃ CBKPT MPT DPTUPT $PNP FM GSBDDJPOBNJFOUPNÃTGÃDJMFTFMRVFSFRVJFSFVOBDPMVNOBNÃTDPSUBZCBKBTSFMBDJPOFTEFSFáVKP  MBIFVSÎTUJDBJOEJDBIBDFSMBDVBOEPIBZWBSJPTDPNQPOFOUFTQSFTFOUFTZMBTUBTBTEFBMJNFOUBDJÓO TPOHSBOEFT-BTJHVJFOUFIFVSÎTUJDBTVHJFSFSFEVDJSMBTUBTBTEFBMJNFOUBDJÓOMPNÃTSÃQJEPRVFTFB QPTJCMF"MFMJNJOBSFMDPNQPOFOUFNÃTWPMÃUJM IFVSÎTUJDB TFFMJNJOBOMPTNBUFSJBMFTEJGÎDJMFTEF DPOEFOTBS FTQSPCBCMFRVFTFDPOTJHBOSFEVDDJPOFTFOMBTQSFTJPOFTEFMBDPMVNOB-BIFVSÎTUJDB IBDFRVFTFUFOHBOMBNÎOJNBUBTBEFBMJNFOUBDJÓOZFODPOTFDVFODJBFMEJÃNFUSPNÎOJNPEFMB DPMVNOBHSBOEFOFDFTBSJBQBSBMBTFQBSBDJÓONÃTEJGÎDJM-BIFVSÎTUJDBCBMBODFBBMBTDPMVNOBTEF UBMNPEPRVFOPDBNCJFOMPTáVKPTFOGPSNBESÃTUJDB:BRVFMPTQSPEVDUPTEFEFHSBEBDJÓOUÊSNJDB TVFMFOTFSSFMBUJWBNFOUFOPWPMÃUJMFT FTQSPCBCMFRVFMBIFVSÎTUJDBEÊDPNPSFTVMUBEPQSPEVDUPT NÃTQVSPT&MPCKFUPEFMBTIFVSÎTUJDBTZFTGPS[BSBMEJTFÒBEPSBJNBHJOBSDPTBTFYDFQDJPOBMFT ZCVTDBSFTRVFNBTRVFTFDPOP[DBODPNPFGFDUJWPTFODJFSUPTDBTPT

www.FreeLibros.me



$BQÎUVMP  &DPOPNÎBZDPOTFSWBDJÓOEFFOFSHÎBFOMBEFTUJMBDJÓO

"DBEBIFVSÎTUJDBEFCFOBOUFDFEFSMBTQBMBCSBTiFOJHVBMEBEEFPUSBTDPOEJDJPOFTu%FTBGPSUV OBEBNFOUF FOFMDBTPHFOFSBMMBTEFNÃTDPOEJDJPOFTOPTPOJHVBMFTZGSFDVFOUFNFOUFMBTIFVSÎTUJ DBTTFPQPOFOFOUSFTÎ1PSFKFNQMP QVFEFTFSRVFFMDPNQPOFOUFNÃTDPODFOUSBEPOPTFBFMNÃT WPMÃUJM$VBOEPFYJTUFDPOáJDUPFOUSFMBTIFVSÎTUJDBT FTOFDFTBSJPHFOFSBSMPTFTRVFNBTEFDBTDBEB TVHFSJEPTQPSFTBTIFVSÎTUJDBTQBSBDPNQBSBSMPTDPODÃMDVMPTNÃTFYBDUPT &+&.1-0 4FDVFODJBDJÓOEFDPMVNOBTDPOIFVSÎTUJDBT 4FEFCFEFTUJMBSVOBBMJNFOUBDJÓODPONPMEFFUBOPM NPMEFJTPQSPQBOPM  NPMEFOQSPQBOPM NPMEFJTPCVUBOPMZNPMEFOCVUBOPM4FEFTFBPCUFOFSDBEB BMDPIPMDPOEFQVSF[B%FUFSNJOBSMBTDPOàHVSBDJPOFTÓQUJNBTEFMBTDPMVNOBT 4PMVDJÓO " # $%FGJOB FYQMPSF QMBOFF$PODJODPDPNQPOFOUFTIBZVOBHSBODBOUJEBEEFQPTJ CJMJEBEFT"QMJDBSFNPTFOUPODFTMBIFVSÎTUJDBQBSBHFOFSBSDPOàHVSBDJPOFTQPTJCMFT -PTEBUPTEFFRVJMJCSJPTFQVFEFOBQSPYJNBSDPNPWPMBUJMJEBEFTSFMBUJWBTDPOTUBOUFT ,JOH 

DPOOQSPQBOPMDPNPDPNQVFTUPEFSFGFSFODJBFUBOPM  JTPQSP QBOPM  OQSPQBOPM  JTPCVUBOPM  ZOCVUBOPM    1BSBBQMJDBSMBIFVSÎTUJDBTFBDPOTFKBEFUFSNJOBSMBTWPMBUJMJEBEFTSFMBUJWBTEFUPEPTMPT QBSFTBEZBDFOUFTEFDPNQVFTUPT 

α:">E 2'#%.$&#-'2&#&*!α>E"cE 2&#-'$&#%2&#-'!αcE">7 2&#%$%#+,,2&#)-!α>7"c7 2%#+,,$%#)'-2&#*-#



$PNPMBTFQBSBDJÓONÃTGÃDJM MBEFJTPQSPQBOPMOQSPQBOPM OPFTNVDIPNÃTTFODJMMB RVFMBTEFNÃTTFQBSBDJPOFT FTQSPCBCMFRVFTFQVFEBJHOPSBSMBIFVSÎTUJDB % )ÃHBMP  $BTP$POMBTIFVSÎTUJDBTZTFPCUJFOFMBTFDVFODJBEJSFDUB

 

/PTFNVFTUSBOWBQPSJ[BEPSFTOJDPOEFOTBEPSFT &TTFHVSPRVFFTUFFTRVFNBGVO DJPOB QFSPOPFTNVZOPWFEPTP $BTP&TGSFDVFOUFRVFMBIFVSÎTUJDBTFBJNQPSUBOUFy$VÃMFTMBTFQBSBDJÓONÃT EJGÎDJM %FBDVFSEPDPOMBMJTUBEFWPMBUJMJEBEFTSFMBUJWBTEFQBSFTBEZBDFOUFTEFDPN QVFTUPT MBNÃTEJGÎDJMFTMBEFFUBOPMJTPQSPQBOPM4JUBNCJÊOBQMJDBNPTMBIFVSÎTUJDB QBSBMBDPMVNOB" ZMBZMBQBSBMBDPMVNOB$ PCUFOESFNPTFMFTRVFNBRVF NVFTUSBMBàHVSBTJHVJFOUF

www.FreeLibros.me

  4ÎOUFTJTEFTFDVFODJBTEFDPMVNOBTQBSBEFTUJMBDJÓOEFWBSJPTDPNQPOFOUFTDBTJJEFBMFT

 

&TDMBSPRVFIBZPUSBTBMUFSOBUJWBTQPTJCMFT $BTP4FQVFEFVTBSMBIFVSÎTUJDBQBSBHFOFSBSVOTJTUFNBUPUBMNFOUFBDPQMBEP UÊSNJDBNFOUF WFBFMQSPCMFNB" 4FSÎBEJGÎDJMEFPQFSBS4JOFNCBSHP VTBOEP MBTIFVSÎTUJDBT ZTFQVFEFPCUFOFSVOBNPEJàDBDJÓOEFMDBTP WFBMBàHVSB 



$BTP5BNCJÊOTFQVFEFBQMJDBSMBIFVSÎTUJDBQBSBEFTBSSPMMBSVOTJTUFNBDPOVOB PNÃTDPMVNOBTEFWBSJPTFGFDUPT4JBQMJDBNPTMBIFVSÎTUJDBQBSBIBDFSMBTFQBSBDJÓO FUBOPMJTPQSPQBOPM  VOB PQDJÓO FT FMFWBS MB QSFTJÓO EF MB BMJNFOUBDJÓO MÎRVJEB B MB DPMVNOB% FOFMDBTPZUSBCBKBSMBDPMVNOB%BNBZPSQSFTJÓO&TUFBSSFHMPDPOWB SJPTFGFDUPTTFNVFTUSBBDPOUJOVBDJÓO)BZNVDIBTPUSBTPQDJPOFTQPTJCMFTQBSBVTBS DPMVNOBTEFWBSJPTFGFDUPTQBSBIBDFSFTUBTFQBSBDJÓO c−E

: ;

6

8 EA

7

^E ^7 9 E=

c7



4FQVFEFOHFOFSBSPUSPTTJTUFNBT QFSPFTQSPCBCMFRVFBMHVOPEFMPTDVBUSPRVFNPT USBNPTFTUÊSB[POBCMFNFOUFDFSDBOPBMÓQUJNP & $PNQSVFCF1BSBEFUFSNJOBSMBDPOàHVSBDJÓOÓQUJNBTFSFRVJFSFTJNVMBSDBEBBMUFS OBUJWB&TPTFQVFEFIBDFSQBSBMPTDBTPTZDPOFMNÊUPEPEF'FOTLF6OEFSXPPE (JMMJMBOE1BSBMPTDBTPTZ MBTDPMVNOBTEFWBSJPTFGFDUPTZUÊSNJDBNFOUFBDPQMBEBT TPONÃTDPNQMJDBEBTZFTQSPCBCMFRVFTFEFCBOTJNVMBSFOGPSNBEFUBMMBEB ' (FOFSBMJDF &T QSPCBCMF RVF VOP EF FTUPT EJTFÒPT TFB DFSDBOP BM ÓQUJNP 1PS MB CBKB WPMBUJMJEBESFMBUJWBFOUSFFMFUBOPMZFMJTPQSPQBOPM MBIFVSÎTUJDBFTJNQPSUBOUF-BBQMJ DBDJÓOEFMBIFVSÎTUJDBTÎFWJUBUFOFSRVFFYBNJOBSWBSJPTDJFOUPTEFPUSBTBMUFSOBUJWBT &TUBTIFVSÎTUJDBTTFIBOEFTBSSPMMBEPQBSBTJTUFNBTTJOB[FÓUSPQPT$VBOEPIBZB[FÓUSPQPT QSFTFOUFT FTOFDFTBSJPVTBSMPTNÊUPEPTEFTDSJUPTFOFMDBQÎUVMP

www.FreeLibros.me





$BQÎUVMP  &DPOPNÎBZDPOTFSWBDJÓOEFFOFSHÎBFOMBEFTUJMBDJÓO

 4  ±/5&4*4%&4*45&."4%&%&45*-"$*¶/1"3".&;$-"4 5&3/"3*"4/0*%&"-&4

&OMBTFDDJÓOBOUFSJPSQSFTFOUBNPTIFVSÎTUJDBTQBSBTJOUFUJ[BSTFDVFODJBTEFEFTUJMBDJÓOQBSBTJTUFNBT DBTJJEFBMFTEFTBGPSUVOBEBNFOUF MBNBZPSÎBEFFTBTIFVSÎTUJDBTOPTFBQMJDBOBTJTUFNBTOPJEFBMFT &OMVHBSEFFMMBT QSFTFOUBSFNPTVODPOKVOUPEJGFSFOUFEFTVHFSFODJBTEFPQFSBDJÓOZMPTNÊUPEPT EFTBSSPMMBEPTFOMBTFDDJÓO DVSWBTEFEFTUJMBDJÓOZEFSFTJEVP&MPCKFUJWPEFMBTTVHFSFODJBTEF PQFSBDJÓOFTEFTBSSPMMBSQSJNFSPVOFTRVFNBEFTFQBSBDJÓOQBSBMVFHPUSBUBSEFNFKPSBSMP -BTIFVSÎTUJDBTQBSBTJTUFNBTOPJEFBMFTOPTFIBOGPSNBMJ[BEPOJDPOWFOJEPDPOFMNJTNPHSB EPRVFQBSBTJTUFNBTJEFBMFT-BTTJHVJFOUFTTVHFSFODJBTEFPQFSBDJÓOTPOEF#JFHMFSFUBM 

 %PIFSUZZ.BMPOF  ZEFMTFOUJEPDPNÙO 4VHFSFODJBTEFPQFSBDJÓO1SFMJNJOBSFT  0CUFOHBEBUPTZPDPSSFMBDJPOFTàBCMFTEFFRVJMJCSJPQBSBFMTJTUFNB  5SBDFDVSWBTEFSFTJEVPPDVSWBTEFEFTUJMBDJÓOQBSBFMTJTUFNB  $MBTJàRVFFMTJTUFNBFO" DBTJJEFBM# OPJEFBMTJOB[FÓUSPQPT$ VOB[FÓUSPQPCJOBSJPIP NPHÊOFPDPOVOBGSPOUFSBEFEFTUJMBDJÓO& EPTPNÃTB[FÓUSPQPTCJOBSJPTIPNPHÊOFPT QP TJCMFNFOUF DPO VO B[FÓUSPQP UFSOBSJP '  B[FÓUSPQP IFUFSPHÊOFP  RVF QVFEF DPOUFOFS WBSJPT B[FÓUSPQPTCJOBSJPTZUFSDJBSJPT"VORVFMBTTPMVDJPOFTQBSBMPTDBTPT%B'TBMFOEFMBMDBODFEF FTUBFYQPTJDJÓOJOUSPEVDUPSJB TFEFTDSJCJSÃOFOGPSNBCSFWF " $BTJJEFBM4JFMTJTUFNBFTSB[POBCMFNFOUFDFSDBOPBMJEFBM àHVSB

BMÊHSFTFZVTFMBT IFVSÎTUJDBTEFMBTFDDJÓO # 4JTUFNBTOPJEFBMFTTJOB[FÓUSPQPT&TUPTTJTUFNBTDPOGSFDVFODJBTFBDFSDBOBMPTJEFBMFTZ FTQSPCBCMFRVFWBSJBTTFDVFODJBTEFDPMVNOBTGVODJPOFO4JOFNCBSHP MPNÃTGÃDJMQPESÃ TFSIBDFSMBTFQBSBDJÓONÃTEJGÎDJMDPOMBOPDMBWFQSFTFOUF FOMVHBSEFMBTFQBSBDJÓOCJOBSJB SFDPNFOEBEBQBSBMBTNF[DMBTJEFBMFT%PIFSUZZ.BMPOF  QSFTFOUBOVOFKFNQMPEFUB MMBEPQBSBFMTJTUFNBBDFUBMEFIÎEPNFUBOPMBHVB  (FOFSBSMBTDVSWBTZYQBSBDBEBQBSCJOBSJP4JUPEBTMBTTFQBSBDJPOFTTPOSFMBUJWBNFOUF GÃDJMFT WPMBUJMJEBEFTSFMBUJWBTSB[POBCMFTTJOQVOUPTEFJOáFYJÓORVFDBVTFOFTUSJDDJPOFT UBOHFOUFTQBSBVOPEFMPTDPNQPOFOUFTQVSPT

VTFMBIFVSÎTUJDBJEFBMEFMBTFDDJÓO  4JVOPEFMPTQBSFTCJOBSJPTUJFOFWPMBUJMJEBESFMBUJWBQFRVFÒBPVOBFTUSJDDJÓOUBOHFOUF  EFUFSNJOF TJ FTB TFQBSBDJÓO FT NÃT GÃDJM FO MB QSFTFODJB EFM UFSDFS DPNQPOFOUF &TP TF QVFEF IBDFS HFOFSBOEP DVSWBT EF EFTUJMBDJÓO P EF FRVJMJCSJP iCJOBSJPu ZY B EJGFSFOUFT DPODFOUSBDJPOFTDPOTUBOUFTEFMUFSDFSDPNQPOFOUF4JMBQSFTFODJBEFMUFSDFSDPNQPOFOUF BZVEBBMBTFQBSBDJÓO TFQBSBSQSJNFSPFMQBSEJGÎDJM-BDPODFOUSBDJÓOEFMUFSDFSDPNQP OFOUFTFQVFEFBKVTUBSSFDJSDVMÃOEPMPEFTEFMBDPMVNOBEPOEFTFQVSJàDB0CTFSWFRVF FTUFNÊUPEPTFQBSFDFNVDIPBVTBSFMUFSDFSDPNQPOFOUFDPNPTPMWFOUFEFEFTUJMBDJÓO FYUSBDUJWBQBSBTFQBSBSDPNQPOFOUFTEFQVOUPTEFFCVMMJDJÓODFSDBOPT TFDDJÓO  $ 6OB[FÓUSPQPCJOBSJPIPNPHÊOFP TJOGSPOUFSBEFEFTUJMBDJÓO-PTNBQBTEFDVSWBEFSFTJEVP TFQBSFDFOBMPTEFMBàHVSBBVD  4JFMB[FÓUSPQPCJOBSJPFTUÃFOUSFMPTDPNQPOFOUFTMJHFSPFJOUFSNFEJP àHVSBD

MBTJUVB DJÓOTFQBSFDFNVDIPBDVBOEPTFVTBEFTUJMBDJÓOFYUSBDUJWBQBSBTFQBSBSVOB[FÓUSPQPCJOBSJP ZTFVTBFMDPNQPOFOUFQFTBEPFOMVHBSEFVOTPMWFOUFBHSFHBEP&OHFOFSBM FMEJBHSBNBEF áVKPTFQBSFDFBMEFMBàHVSB DPOMBFYDFQDJÓORVFFMQSPEVDUPEFDPNQPOFOUFQFTBEPTF SFUJSBEPOEFTFBHSFHBFMTPMWFOUFEFSFMMFOP4JFOMBBMJNFOUBDJÓOIBZTVàDJFOUFDPNQPOFOUF QFTBEP QPESÃOPOFDFTJUBSTFMBSFDJSDVMBDJÓOEFMDPNQPOFOUFQFTBEP&MNBQBEFMBDVSWB EFSFTJEVPTFQBSFDFSÃBMNBQBEFSFTJEVPEFEFTUJMBDJÓOFYUSBDUJWB àHVSB QFSPDPNPMB BMJNFOUBDJÓODPOUJFOFMPTUSFTDPNQPOFOUFT FMQVOUP'FTUBSÃEFOUSPEFMUSJÃOHVMP

www.FreeLibros.me

  4ÎOUFTJTEFTJTUFNBTEFEFTUJMBDJÓOQBSBNF[DMBTUFSOBSJBTOPJEFBMFT



 4JFMB[FÓUSPQPCJOBSJPFTUÃFOUSFMPTDPNQPOFOUFTQFTBEPZMJHFSP àHVSBB

TFQVFEF IBDFSVOBTFQBSBDJÓODPOVOBSFDJSDVMBDJÓOJOUFSNFEJB DPNPNVFTUSBOMBTàHVSBTBZ C4JIBZTVàDJFOUFDPNQPOFOUFJOUFSNFEJPFOMBBMJNFOUBDJÓO QPESÎBOPOFDFTJUBSTF MBSFDJSDVMBDJÓOJOUFSNFEJB&OFMFKFNQMPTFJMVTUSBMBTFQBSBDJÓOVTBOEPFMEJBHSBNB EFáVKPEFMBàHVSBB % 6OB[FÓUSPQPCJOBSJPIPNPHÊOFPDPOGSPOUFSBEFTFQBSBDJÓO1VFEFTFSVOB[FÓUSPQPEF FCVMMJDJÓONÃYJNB àHVSB

PVOPEFFCVMMJDJÓONÎOJNB àHVSBC   4JMBGSPOUFSBEFEFTUJMBDJÓOFTSFDUB OPFTQPTJCMFMBTFQBSBDJÓODPNQMFUBEFMBBMJNFOUBDJÓO UFSOBSJB TJOPTFBHSFHBVOBTVTUBODJBTFQBSBEPSBEFNBTBT %PIFSUZZ.BMPOF    4JMBGSPOUFSBEFEFTUJMBDJÓOFTDVSWB TFQPESÃIBDFSVOBTFQBSBDJÓODPNQMFUBEFMBBMJNFO UBDJÓOUFSOBSJB$POGSFDVFODJB MBTGSPOUFSBTEFEFTUJMBDJÓOQVFEFODSV[BSTFBMNF[DMBSVOB BMJNFOUBDJÓODPOVOBDPSSJFOUFEFSFDJSDVMBDJÓO#JFHMFSFUBM  QSFTFOUBOVOFKFNQMP EFMBTÎOUFTJTEFEJBHSBNBTEFáVKPQPTJCMFTQBSBFMTJTUFNBEFMBàHVSB-BTPMVDJÓO EFUBMMBEBEFFTUFDBTPZMPTEPTDBTPTRVFSFTUBO TBMFEFMBMDBODFEFFTUBTFDDJÓO & %PTPNÃTB[FÓUSPQPTCJOBSJPTIPNPHÊOFPT QPTJCMFNFOUFDPOVOB[FÓUSPQPUFSOBSJP&TPT TJTUFNBTTPONPMFTUPTFJOWBSJBCMFNFOUFIBZVOBPNÃTGSPOUFSBTEFEFTUJMBDJÓO4JTÓMPIBZ VOBGSPOUFSBEFEFTUJMBDJÓO QPESÎBEFTBSSPMMBSTFVOFTRVFNBRVFTFQBSFMBNF[DMBTJOBHSF HBSVOBTVTUBODJBTFQBSBEPSBEFNBTBT4JTÓMPIBZEPTB[FÓUSPQPTCJOBSJPT TJOB[FÓUSPQPT UFSDJBSJPT  CVTDBS VO NÊUPEP EF TFQBSBDJÓO QPS FKFNQMP  FYUSBDDJÓO  RVF FMJNJOF FM DPN QVFTUPQSFTFOUFFOBNCPTB[FÓUSPQPT

7#

6#

>GZX^gXjaVX^‹c A

>

A ;

&

'

;

= >GZX^gXjaVX^‹c

= >

'*(63" $"4$"%"4%&%&45*-"$*¶/1"3""-*.&/5"$*¶/5&3/"3*"$0/";&¶53010 #*/"3*0&/53&-04$0.10/&/5&4-*(&30 - :1&4"%0 )" 4&$6&/$*"*/%*3&$5"  # 4&$6&/$*"%*3&$5"

www.FreeLibros.me



$BQÎUVMP  &DPOPNÎBZDPOTFSWBDJÓOEFFOFSHÎBFOMBEFTUJMBDJÓO

' "[FÓUSPQPIFUFSPHÊOFP RVFQVFEFDPOUFOFSWBSJPTB[FÓUSPQPTCJOBSJPTZUFSOBSJPT&OMB àHVSBTFNPTUSÓVOFKFNQMP QBSBVOFTRVFNBEFEFTUJMBDJÓOB[FPUSÓQJDB&TQSPCBCMF RVF FM NBQB EF DVSWB EF SFTJEVP  PCUFOJEP DPO VO TJNVMBEPS EF QSPDFTPT  OP NVFTUSF MB FOWPMWFOUFEFMBSFHJÓOEFEPTGBTFTZIBCSÃRVFBHSFHBSFTBSFHJÓO:BRVFMPTTFQBSBEPSFT MÎRVJEPMÎRVJEPQVFEFODSV[BSGSPOUFSBTEFEFTUJMBDJÓO FYJTUFOBMUBTQSPCBCJMJEBEFTEFMPHSBS VOBTFQBSBDJÓOTJOVTBSVOBTVTUBODJBTFQBSBEPSBEFNBTBT-BTGSPOUFSBTEFEFTUJMBDJÓOQVF EFODSV[BSTFDPONF[DMBEP EFDBOUBDJÓOZSFBDDJÓO4JFTQPTJCMF VTBSDPNQPOFOUFTRVFZB FYJTUBOFOMBBMJNFOUBDJÓO DPNPTPMWFOUFEFEFTUJMBDJÓOFYUSBDUJWBPDPNPQPSUBEPSFOEFT UJMBDJÓOB[FPUSÓQJDB5BNCJÊO JOWFTUJHBSFMVTPEFMPTDPNQPOFOUFTEFMBBMJNFOUBDJÓODPNP TPMWFOUFTEFFYUSBDDJÓO&TUPTTJTUFNBTTFEFTDSJCFODPOEFUBMMFFO%PIFSUZZ.BMPOF   Z#JFHMFSFUBM  EFTDSJCFOVOFKFNQMPEFMQSPDFTP &+&.1-0 %FTBSSPMMPEFQSPDFTPTQBSBTFQBSBSVOBNF[DMBUFSOBSJBDPNQMFKB 4FUJFOFOLHNPMIEFVOBBMJNFOUBDJÓOMÎRVJEBTBUVSBEBGPSNBEBQPSNPMEF NFUBOPM NPMEFCVUJSBUPEFNFUJMPZNPMEFUPMVFOP%FTFBNPTTFQBSBSFTUB BMJNFOUBDJÓOFOUSFTQSPEVDUPTQVSPT QVSF[BTEF 1SPQPOFSVOBDBTDBEBEFEFTUJ MBDJÓOGBDUJCMFQBSBFTUFTJTUFNB%FNPTUSBSRVFFTFTJTUFNBFTGBDUJCMF 4PMVDJÓO " %FGJOB%FTFBNPTQSPQPOFSVOBTFDVFODJBEFDPMVNOBTEFEFTUJMBDJÓORVFUFOHBSFDJS DVMBDJÓO QBSBQPEFSQSPEVDJSNFUBOPM CVUJSBUPEFNFUJMPZUPMVFOPDPOQVSF[BTNBZP SFTRVF-BEFNPTUSBDJÓOSFRVJFSFUSBCBKBSDPOVOTJNVMBEPSEFQSPDFTPTQBSB EFNPTUSBSRVFTFBMDBO[BMBTFQBSBDJÓO0CTFSWFRVFOPTFSFRVJFSFVOBPQUJNJ[BDJÓO # &YQMPSF&TUPTDPNQPOFOUFTFTUÃOFOFMCBODPEFEBUPTEF"TQFO1MVTZMBTDVSWBTEF SFTJEVPTFHFOFSBSPODPO"TQFO1MVT VTBOEP/35- àHVSB  FTPCWJPRVFTF QVFEFOVTBSPUSPTTJNVMBEPSFTEFQSPDFTPT $PNPIBZVOB[FÓUSPQPCJOBSJPFOUSFFM NFUBOPM DPNQPOFOUFMJHFSP ZFMUPMVFOP DPNQPOFOUFQFTBEP

TJOGSPOUFSBEFEFT UJMBDJÓO FTUFNBQBEFDVSWBEFSFTJEVPFTQBSFDJEPBMEFMBàHVSBB$BCFFTQFSBS RVFFMEJBHSBNBEFáVKPEFMBàHVSBBPMBCIBHBMBTFQBSBDJÓO $ 1MBOFF&MQVOUPEFBMJNFOUBDJÓOGSFTDBTFJOEJDBFOMBàHVSB$PNPMBDPODFO USBDJÓOEFCVUJSBUPEFNFUJMPFOMBBMJNFOUBDJÓOGSFTDBFTCBKB FTFQVOUPFTDFSDBOPB MBMÎOFBCJOBSJBUPMVFOPNFUBOPM4JOPSFDJSDVMBNPTFMDPNQVFTUPJOUFSNFEJP CVUJSB UPEFNFUJMP QPESFNPTUFOFSQSPCMFNBDPOFMB[FÓUSPQPCJOBSJP&OUPODFT QBSBUFOFS VOEJTFÒPGBDUJCMF MPNÃTTFHVSPFTDPNFO[BSSFDJSDVMBOEPFMDPNQVFTUPJOUFSNFEJP y&TQSPCBCMFRVFTFBNFKPSMBàHVSBBPMBC 2VJ[ÃBNCBTUSBCBKFO"M DPNQBSBSMPTQVOUPTEFFCVMMJDJÓO FTQSPCBCMFRVFMBTFQBSBDJÓOEFMNFUBOPMZFMCVUJSBUP EFNFUJMPTFBNVDIPNÃTTFODJMMBRVFTFQBSBSCVUJSBUPEFNFUJMPZUPMVFOP"TÎ FTQSP CBCMFRVFMBTFHVOEBDPMVNOBTFBCBTUBOUFNÃTQFRVFÒB TJVTBNPTFMEJBHSBNBEFáVKP EFMBàHVSBB BVORVFMBQSJNFSBDPMVNOBTFSÃNBZPS6TBSFNPTMBàHVSBBZ EFKBSFNPTQBSBMPTQSPCMFNBT%Z(MBJOWFTUJHBDJÓOEFMBàHVSBC % )ÃHBMP6TFFMEJBHSBNBEFáVKPFOMBàHVSBBDPOSFDJSDVMBDJÓOEFMDPNQVFTUP JOUFSNFEJP&OGPSNBBSCJUSBSJB TFMFDDJPOBSVOBUBTBEFSFDJSDVMBDJÓOEFLHNPMI FMPCKFUPEFFTUFFKFNQMPFTEFNPTUSBSMBGBDUJCJMJEBEEFTQVÊTTFIBSÎBWBSJBSFTUBQSP QPTJDJÓOJOJDJBMQBSBQVMJSFMEJTFÒP $PNPFMCVUJSBUPEFNFUJMPEFCFUFOFS EF QVSF[B TVQPOESFNPTRVFMBDPSSJFOUFEFSFDJSDVMBDJÓOFTQVSB"MNF[DMBSMBBMJNFOUB DJÓOGSFTDBZMBDPSSJFOUFEFSFDJSDVMBDJÓOZBQMJDBSMBSFHMBEFMBQBMBODB TFEFUFSNJOBFM QVOUP. DPNPTFWFFOMBàHVSB&TUBBMJNFOUBDJÓODPNCJOBEBTFQVFEFEJWJEJS

www.FreeLibros.me

  4ÎOUFTJTEFTJTUFNBTEFEFTUJMBDJÓOQBSBNF[DMBTUFSOBSJBTOPJEFBMFT



;g VX X^ %#* ‹cb %#) daB 7 %#( %#' %#+ %#-

%#,

;

%#.

B

%#'

%#& CD J: %#' DA I %#( YZ da %#) cb * X^‹ %# VX ;g %#+ %#,

%#&

%#-

B7 &%'#,°8 >ciZgbZY^d

%#.

%#&

7 I&&%#+°8 EZhVYd

%#(9 %#) %#* %#+ %#, %#;gVXX^‹cbdaYZB:I6CDA

%#.

B+)#*°8 A^\Zgd

'*(63" $637"4%& 3&4*%60:#"-"/$&4%&."4" 1"3"-"%&45*-"$*¶/%&.&5"/0-  50-6&/0:#65*3"50%&.&5*-0 ..&5"/0- .##65*3"50%& .&5*-0 550-6&/0

FOUPODFTFOVOEFTUJMBEPRVFQSÃDUJDBNFOUFOPDPOUFOHBUPMVFOPZVOQSPEVDUPEFGPO EPTRVFTFBUPMVFOP QVSP&TUBUSBZFDUPSJBFTGBDUJCMF QPSRVFMBTSFDUBTRVFWBO EF%B.#ZB# UPMVFOPQVSP TJFNQSFUJFOFOMBEJSFDDJÓOEFUFNQFSBUVSBTDSFDJFO UFT ZSFQSFTFOUBOVOBDVSWBWÃMJEBEFSFTJEVP&MQSPEVDUPEFTUJMBEPTFQPESÃTFQBSBS EFTQVÊTFOMBTFHVOEBDPMVNOB FOVOEFTUJMBEPEFNFUBOPM QVSPZGPOEPTEF CVUJSBUPEFNFUJMP QVSP1PSMPNJTNP QBSFDFRVFMBTFQBSBDJÓOFTGBDUJCMF 

%FNPTUSBDJÓO-BBMJNFOUBDJÓONJYUBBMBDPMVNOBDPOUJFOFEFCVUJSBUPEFNF UJMP EFUPMVFOPZEFNFUBOPM&MáVKPFTLHNPMIZTFTVQVTPRVFFTVO MÎRVJEPTBUVSBEP&MTJTUFNBEFMBàHVSB"GVFTJNVMBEPDPO"TQFO1MVTVTBOEP /35-DPNPEBUPTEFFRVJMJCSJP1BSBFMFTUVEJPEFGBDUJCJMJEBETFNF[DMBSPOCVUJSBUP EFNFUJMPQVSP FOMVHBSEFMBDPSSJFOUFEFSFDJSDVMBDJÓO DPOBMJNFOUBDJÓOGSFTDBZTF JOZFDUBSPOFOMBNJTNBFUBQBEFMBDPMVNOB%FTQVÊTEFBMHVOPTUBOUFPT TFPCUVWJF SPOMPTTJHVJFOUFTSFTVMUBEPT

$PMVNOB/ JODMVZFOEPDPOEFOTBEPSUPUBMZWBQPSJ[BEPSQBSDJBM

/BMJN  %LHNPMI -% QBUN  'SBDDJPOFT NPMBSFT FO EFTUJMBEP NFUBOPM    CVUJSBUP EF NFUJMP    UPMVFOP  'SBDDJPOFTNPMFOMPTGPOEPTNFUBOPM& CVUJSBUPEFNFUJMP  UPMVFOP  $PMVNOB/ JODMVZFOEPDPOEFOTBEPSUPUBMZWBQPSJ[BEPSQBSDJBM

/BMJN  %LHNPMI -% QBUN  'SBDDJPOFTNPMFOEFTUJMBEPNFUBOPM CVUJSBUPEFNFUJMP UPMVFOP   'SBDDJPOFTNPMBSFTFOMPTGPOEPTNFUBOPM CVUJSBUPEFNFUJMP  UPMVFOP 1PSMPBOUFSJPS MBTFQBSBDJÓOFTGBDUJCMF & $PNQSVFCF&MNBQBEFDVSWBEFSFTJEVPUSB[BEPDPOFMTJNVMBEPSEFQSPDFTPTDPO DVFSEBDPOFMNBQBFO%PIFSUZZ.BMPOF  -BDPNQPTJDJÓODBMDVMBEBEFMEFTUJ MBEPEFMBQSJNFSBDPMVNOB EFUFSNJOBEBDPODÃMDVMPEFCBMBODFEFNBTBFOMBàHVSB  FTEFNFUBOPMZEFCVUJSBUPEFNFUJMP&TUPDPODVFSEBCBTUBOUFCJFO 

www.FreeLibros.me



$BQÎUVMP  &DPOPNÎBZDPOTFSWBDJÓOEFFOFSHÎBFOMBEFTUJMBDJÓO

DPOMPTSFTVMUBEPTEFMTJNVMBEPS&OMBTQVCMJDBDJPOFTTFJOEJDBRVFMBàHVSB" EFCFTFSBEFDVBEBQBSBTFQBSBSFTUFUJQPEFNF[DMB1PSMPNJTNP DPOàBNPTCBTUBOUF FORVFFMQSPDFTPTFBGBDUJCMF ' (FOFSBMJDF&MEFTBSSPMMPEFVOQSPDFTPGBDUJCMFFTFMQSJNFSQBTPQSJODJQBMFOFMEJ TFÒP5BNCJÊOTFOFDFTJUBSÎBIBDFSVOEJTFÒPQSFMJNJOBSTPCSFMBàHVSBCQBSB BTFHVSBSOPTRVFFMQSPDFTPOPFTNFKPS WFBMPTQSPCMFNBT%Z( /FDFTJUB NPTPQUJNJ[BSFMQSPDFTPNFKPSQBSBEFUFSNJOBSMPTWBMPSFTBEFDVBEPTQBSBFMáVKP EFSFDJSDVMBDJÓOZWBMPSFTÓQUJNPTQBSB/ /BMJNZ-%QBSBDBEBDPMVNOB5BNCJÊO EFCFNPTQSPCBSMPTQSPDFTPTTJOSFDJSDVMBDJÓOEFCVUJSBUP QBSBWFSTJBMHVOPEFFMMPT FTGBDUJCMF WFBMPTQSPCMFNBT%BZ( &OMBQSJNFSBDPMVNOBTEFCFJOWFT UJHBSTFFMVTPEFMVHBSFTTFQBSBEPTEFMBBMJNFOUBDJÓOGSFTDBZEFMBSFDJSDVMBDJÓO4J OJOHVOPEFFTUPTQSPDFTPTFTDMBSBNFOUFNFKPSRVFPUSP EFCFNPTPQUJNJ[BSBNCPT  QBSBEFUFSNJOBSDVÃMFTFMNÃTFDPOÓNJDP  3&46.&/m0#+&5*704

&OFTUFDBQÎUVMPIFNPTFYBNJOBEPFOGPSNBCSFWFMBFDPOPNÎBEFMBEFTUJMBDJÓOZMPTFGFDUPTEF DBNCJBSMBTWBSJBCMFTEFPQFSBDJÓO"MàOBMJ[BSFTUFDBQÎUVMP VTUFEEFCFSÃTFSDBQB[EFBMDBO[BSMPT TJHVJFOUFTPCKFUJWPT  &TUJNBSMPTDPTUPTEFDBQJUBMZEFPQFSBDJÓOQBSBVOBDPMVNOBEFEFTUJMBDJÓO  *OEJDBSFMFGFDUPEFMBTWBSJBCMFTTJHVJFOUFTTPCSFMPTDPTUPTEFDBQJUBMZEFPQFSBDJÓO B 5BTBEFBMJNFOUBDJÓO C 1SFTJÓOFOMBDPMVNOB D 3FMBDJÓOEFSFáVKPFYUFSOP  &TUJNBSMPTFGFDUPTRVFUJFOFOMPTGBDUPSFTFYUFSOPTTPCSFMPTDPTUPTEFDBQJUBMZEFPQFSBDJÓO FOUSFMPTGBDUPSFTFYUFSOPTFTUÃO B $PTUPTEFMBFOFSHÎB C &TUBEPHFOFSBMEFMBFDPOPNÎB  %FTDSJCJSNÊUPEPTQBSBSFEVDJSFMVTPEFFOFSHÎBFOTJTUFNBTEFEFTUJMBDJÓO5SB[BSEJBHSBNBTEF áVKPDPOMPTJOUFSDBNCJPTBEFDVBEPTEFDBMPS  6TBSIFVSÎTUJDBTQBSBEFTBSSPMMBSDBTDBEBTBMUFSOBUJWBTQBSBMBEFTUJMBDJÓOEFNF[DMBTDBTJJEFBMFT EFWBSJPTDPNQPOFOUFT  6TBSMBTDVSWBTEFEFTUJMBDJÓOPEFSFTJEVPQBSBEFTBSSPMMBSVOFTRVFNBEFTFQBSBDJÓOGBDUJCMF QBSBNF[DMBTOPJEFBMFT 3&'&3&/$*"4

"HSBXBM 3 i.VMUJFGGFDU%JTUJMMBUJPOGPS5IFSNBMMZ$PVQMFE$POàHVSBUJPOTu "*$I&+   /PW  "MMFO %5Z%34IPOOBSE (SFFO&OHJOFFSJOH&OWJSPONFOUBMMZ$POTDJPVT%FTJHOPG$IFNJDBM 1SPDFTTFT 1SFOUJDF)BMM153 6QQFS4BEEMF3JWFS /FX+FSTFZ  "OESFDPWJDI .+Z"88FTUFSCFSH i"TJNQMF4ZOUIFTJT#BTFEPO6UJMJUZ#PVOEJOHPG)FBU *OUFHSBUFE%JTUJMMBUJPO4FRVFODFTu "*$I&+     #JFHMFS -5 *&(SPTTNBOOZ"88FTUFSCFSH 4ZTUFNBUJD.FUIPETPG$IFNJDBM1SPDFTT%F TJHO 1SFOUJDF)BMM 6QQFS4BEEMF3JWFS /FX+FSTFZ   $IFOHFM :" )FBU5SBOTGFS"1SBDUJDBM"QQSPBDI .D(SBX)JMM /VFWB:PSL  %PIFSUZ .'Z.'.BMPOF $PODFQUVBM%FTJHOPG%JTUJMMBUJPO4ZTUFNT .D(SBX)JMM /VFWB :PSL 

www.FreeLibros.me

3FGFSFODJBT



%PVHMBT +. 5IF$PODFQUVBM%FTJHOPG$IFNJDBM1SPDFTTFT .D(SBX)JMM /VFWB:PSL  (BSH ., 1-%PVHMBTZ+(-JOEFST i"O&YQFSU4ZTUFNGPS*EFOUJGZJOH4FQBSBUJPO1SPDFT TFTu $BO+$IFN&OH   'FC  (FBOLPQMJT $+ 5SBOTQPSU1SPDFTTFTBOE4FQBSBUJPO1SPDFTT1SJODJQMFT ‰&E 1SFOUJDF)BMM153  6QQFS4BEEMF3JWFS /FX+FSTFZ  (FZFS (3Z1&,MJOF i&OFSHZ$POTFSWBUJPO4DIFNFTGPS%JTUJMMBUJPO1SPDFTTFTu $IFN&OH 1SPHSFTT   

 NBZPEF  (SFFOLPSO 3"Z%1,FTTMFS 5SBOTGFS0QFSBUJPOT .D(SBX)JMM /VFWB:PSL  (SJTLFZ 3( 5SBOTQPSU1IFOPNFOBBOE6OJU0QFSBUJPOT"$PNCJOFE"QQSPBDI 8JMFZ /VFWB :PSL  )VNQISFZ +-Z(&,FMMFS** 4FQBSBUJPO1SPDFTT5FDIOPMPHZ .D(SBX)JMM /VFWB:PSL  ,FMMFS  ( &  **  4FQBSBUJPOT /FX %JSFDUJPOT GPS BO 0ME 'JFME  "*$I& .POPHSBQI 4FSJFT      ,FOOFZ 8' i4USBUFHJFTGPS$POTFSWJOH&OFSHZu $IFN&OH1SPHSFTT  

 NBS[PEF  ,FSO %2 1SPDFTT)FBU5SBOTGFS .D(SBX)JMM /VFWB:PSL  ,JN +,Z1$8BOLBU i2VBUFSOBSZ%JTUJMMBUJPO4ZTUFNTXJUI-FTTUIBO/$PMVNOTu  *OE&OH$IFN3FT     ,JOH $+ 4FQBSBUJPO1SPDFTTFT ‰&E .D(SBX)JMM /VFWB:PSL  -JOOIPGG # %85PXOTFOE %#PMBOEZ(')FXJUU "6TFST(VJEFPO1SPDFTT*OUFHSBUJPOGPS UIF&GGJDJFOU6TFPG&OFSHZ *OTUJUVUJPOPG$IFNJDBM&OHJOFFST 3VHCZ 6OJUFE,JOHEPN  -VEXJH && "QQMJFE1SPDFTT%FTJHO ‰&E 7PM (VMG1VC$P #PTUPO  .D$BSUZ "+Z#34NJUI i3FCPJMFS4ZTUFN%FTJHO5IF5SJDLTPGUIF5SBEFu $IFN&OH 1SPHSFTT   

 .BZPEF  .FISB %, i4FMFDUJOH&WBQPSBUPSTu $IFN&OH  

 'FC   .FJMJ " i)FBU1VNQTGPS%JTUJMMBUJPO$PMVNOTu $IFN&OH1SPHSFTT   

 KVOJPEF  .JY  5 +  + 4 %XFDL  . 8FJOCFSH Z 3 $ "SNTUSPOH  i&OFSHZ $POTFSWBUJPO JO %JTUJMMBUJPOu  $IFN&OH1SPHSFTT   

 BCSJMEF  .VSBMJLSJTIOB  ,  , 1 .BEIBWBO BOE 4 4 4IBI  i%FWFMPQNFOU PG %JWJEJOH 8BMM %JTUJMMBUJPO $PMVNO%FTJHO4QBDFGPSB4QFDJàFE4FQBSBUJPOu $IFN&OH3FT%FT  "  NBS[P EF  /JTIJEB / (4UFQIBOPQPVMPVTZ888FTUFSCFSH i"3FWJFXPG1SPDFTT4ZOUIFTJTu "*$I& +     /VMM )3 i)FBU1VNQTJO%JTUJMMBUJPOu $IFN&OH1SPHSFTT   

 KVMJPEF  0#SJFO %Z."4DIVMU[ i"TLUIF&YQFSUT%JTUJMMBUJPOu $IFN&OH1SPHSFTT  

 'FC   0#SJFO /( i3FEVDJOH$PMVNO4UFBN$POTVNQUJPOu $IFN&OH1SPHSFTT   

 KVMJP EF  1FSSZ 3) $)$IJMUPOBOE4%,JSLQBUSJDL &ET

$IFNJDBM&OHJOFFST)BOECPPL ‰ &E  .D(SBX)JMM /VFWB:PSL  1FUFST .4 ,%5JNNFSIBVTZ3&8FTU 1MBOU%FTJHOBOE&DPOPNJDTGPS$IFNJDBM&OHJOFFST  ‰&E .D(SBX)JMM /VFWB:PSL  3PCJOTPO $4Z&3(JMMJMBOE &MFNFOUTPG'SBDUJPOBM%JTUJMMBUJPO .D(SBX)JMM /VFWB:PSL   3PTF -. %JTUJMMBUJPO%FTJHOJO1SBDUJDF &MTFWJFS "NTUFSEBN  3VEE %' '+1PXFSTZ++4JJSPMB 1SPDFTT4ZOUIFTJT 1SFOUJDF)BMM 6QQFS4BEEMF3JWFS /FX +FSTFZ  3VEE %'Z$$8BUTPO 4USBUFHZPG1SPDFTT&OHJOFFSJOH 8JMFZ /VFWB:PSL 

www.FreeLibros.me



$BQÎUVMP  &DPOPNÎBZDPOTFSWBDJÓOEFFOFSHÎBFOMBEFTUJMBDJÓO

4DIVMU[ ." %(4UFXBSU +.)BSSJT 413PTFOCMVN .44IBLVS %&0#SJFO i3FEVDF $PTUTXJUI%JWJEJOH8BMM$PMVNOT i$IFN&OH1SPHSFTT     NBZPEF  4FJEFS 8% +%4FBEFSZ%3-FXJO %FTJHO1SPDFTT1SJODJQMFT ‰FE 8JMFZ /VFWB:PSL  4IBI 1# i4RVFF[F.PSF0VUPG$PNQMFY$PMVNOTu $IFN&OH1SPHSFTT     KVMJPEF  4IJOTLFZ '( %JTUJMMBUJPO$POUSPM 'PS1SPEVDUJWJUZBOE&OFSHZ$POTFSWBUJPO ‰&E .D(SBX)JMM  /VFWB:PSL  4JJSPMB ++ i*OEVTUSJBM"QQMJDBUJPOTPG$IFNJDBM1SPDFTT4ZOUIFTJTu "EW$IFN&OH     5FEEFS %8Z%'3VEE i1BSBNFUSJD4UVEJFTJO*OEVTUSJBM%JTUJMMBUJPO1BSU%FTJHO$PNQBSJ TPOTu "*$I&+     5IPNQTPO 38Z$+,JOH i4ZTUFNBUJD4ZOUIFTJTPG4FQBSBUJPO4ZTUFNTu "*$I&+    5VSUPO 3 3$#BJMJF 8#8IJUJOHZ+"4IBFJXJU[ "OBMZTJT 4ZOUIFTJT BOE%FTJHOPG$IFNJDBM 1SPDFTTFT ‰&E 1SFOUJDF)BMM153 6QQFS4BEEMF3JWFS /FX+FSTFZ  6MSJDI  ( %  " (VJEF UP $IFNJDBM &OHJOFFSJOH 1SPDFTT %FTJHO BOE &DPOPNJDT  8JMFZ  /VFWB :PSL  8BOLBU 1$ i.VMUJFGGFDU%JTUJMMBUJPO1SPDFTTFTu *OE&OH$IFN3FT     8PPET %3 'JOBODJBM%FDJTJPO.BLJOHJOUIF1SPDFTT*OEVTUSJFT 1SFOUJDF)BMM 6QQFS4BEEMF3JWFS  /FX+FSTFZ  8PPET %3 1SPDFTT%FTJHOBOE&OHJOFFSJOH1SBDUJDF 1SFOUJDF)BMM153 6QQFS4BEEMF3JWFS /FX +FSTFZ  5"3&"

" 1SPCMFNBTQBSBEJTDVTJÓO " 4JMPTQMBUPTEFWÃMWVMBTDVFTUBONÃTRVFMPTQMBUPTQFSGPSBEPT yQPSRVÊTFBOVODJBODPNP VOBGPSNBQBSBSFEVDJSMPTDPTUPTEFMBTUPSSFT " 'PSNFTVQSPQJBUBCMBEFSFMBDJPOFTDMBWFQBSBFTUFDBQÎUVMP " y2VÊFGFDUPUJFOFBVNFOUBSMBUFNQFSBUVSBEFMBBMJNFOUBDJÓODVBOEP B -%FTDPOTUBOUF C -% -% NÎO 0CTFSWFRVF -% NÎODBNCJB *ODMVZBMPTFGFDUPTTPCSF23ZMBDBOUJEBEEFFUBQBT6TFVOEJBHSBNBEF.D$BCF5IJFMF " -PTQVOUPTÓQUJNPTTVFMFOQSFTFOUBSTFQPSRVFIBZEPTFGFDUPTQSJODJQBMFTRVFDPNQJUFO1BSB MB-%ÓQUJNB FTPTEPTFGFDUPTQSJODJQBMFTTPCSFFMDPTUPEFDBQJUBMTPO TFMFDDJPOFEPTSFT QVFTUBT  B -BDBOUJEBEEFFUBQBTFTJOàOJUBDVBOEP-%TVCFBMJOàOJUP ZUJFOFVOWBMPSNÎOJNPFO -% NÎO C -BDBOUJEBEEFFUBQBTFTJOàOJUBDVBOEP-% -% NÎOZUJFOEFBVOWBMPSNÎOJNPDVBOEP -%TVCFBMJOàOJUP D &MEJÃNFUSPEFMBDPMVNOBTFWVFMWFJOàOJUPFO -% NÎOZUJFOEFBVOWBMPSNÎOJNPDVBOEP -%UJFOEFBJOàOJUP E &MEJÃNFUSPEFMBDPMVNOBTFWVFMWFJOàOJUPDVBOEP-%UJFOEFBJOàOJUPZUJFOFVOWBMPS NÎOJNPFO -% NÎO " &MDBQJUBMEFUSBCBKPFTFMEJOFSPRVFTFSFRVJFSFQBSBFMGVODJPOBNJFOUPEJBSJPEFMBQMBOUBZ FMJOUFSÊTTPCSFFMDBQJUBMEFUSBCBKPFTVODPTUPEFPQFSBDJÓO4JCBKBMBUBTBEFBMJNFOUBDJÓO  yFTDPOTUBOUFFMDPTUPEFDBQJUBMQPSLJMPHSBNP y2VÊTVDFEFDPOFMDBQJUBMEFUSBCBKPTJMPT DMJFOUFTUBSEBOFOQBHBSTVTGBDUVSBT "MHVOBTFNQSFTBTEBOVOEFEFTDVFOUPQPSQBHP JONFEJBUPEFMBTGBDUVSBTFYQMJRVFQPSRVÊFTPQPESÎBTFSCVFOPPNBMP " y$ÓNPBGFDUBFMFTUBEPHFOFSBMEFMBFDPOPNÎBBM B EJTFÒPEFOVFWBTQMBOUBT

www.FreeLibros.me

5BSFB

" "

" " " "

" "

"

"

" "

# # # #

#

#



C MBPQFSBDJÓOEFMBTQMBOUBTFYJTUFOUFT y1PSRVÊMBEFQFOEFODJBEFMUBNBÒPTVFMFTFSNFOPTRVFMJOFBM &OPUSBTQBMBCSBT yQPSRVÊ FMFYQPOFOUFEFMBFDVBDJÓO  FTNFOPSRVF &TGSFDVFOUFEJTFÒBSDPMVNOBTDPOSFMBDJPOFTEFSFáVKPVOQPDPNBZPSFTRVF -% ÓQU6TF VOBDVSWBEFDPTUPUPUBMBÒPFOGVODJÓOEF-%QBSBFYQMJDBSQPSRVÊTFVTBVOB-% -% ÓQUy1PSRVÊOPIBZVOHSBOBVNFOUPFOFMDPTUP %FTDSJCBFMDPODFQUPEFFDPOPNÎBTEFFTDBMBy2VÊQBTBDPOMBTFDPOPNÎBTEFFTDBMBTJMB UBTBEFBMJNFOUBDJÓOFTMBNJUBEEFMWBMPSEFEJTFÒP 6TFVOEJBHSBNBEF.D$BCF5IJFMFQBSBFYQMJDBSDÓNPBMSFEVDJSMBDPODFOUSBDJÓOEFMQSP EVDUPTFQVFEFVTBSNFOPS-%FOVOBDPMVNOBFYJTUFOUF 3FTQFDUPBMBàHVSB TJ%FTMBBMJNFOUBDJÓOBMBDPMVNOB FYQMJRVFRVÊDPOEJDJPOFTTF OFDFTJUBOQBSBRVFUSBCBKFFTUFTJTUFNB -BàHVSB*NVFTUSBVOBSSFHMPRVFTFVTBDVBOEPFTCBKBMBDPODFOUSBDJÓOEFMDPNQP OFOUFQFTBEP $ FOMBBMJNFOUBDJÓO5SBDFVOBSSFHMPRVFTFVTFDVBOEPMBDPODFOUSBDJÓOEFM DPNQPOFOUFMJHFSP " TFBCBKBFOMBBMJNFOUBDJÓO y1PSRVÊFMDPTUPEFMFNQBRVFQPSNZFMDPTUPQPSQMBUPFTNFOPSDVBOEPTFDPNQSBONÃT FNQBRVFPNÃTQMBUPT 4FSFDPNJFOEBVTBSDPNQPOFOUFTFOMBBMJNFOUBDJÓODPNPTPMWFOUFTQBSBEFTUJMBDJÓOFYUSBD UJWBPEFTUJMBDJÓOB[FPUSÓQJDB PFYUSBDDJÓO BVODVBOEPOPTFBOMPTNFKPSFTTPMWFOUFTQBSB TFQBSBDJPOFTJOEFQFOEJFOUFT&YQMJRVFFMSB[POBNJFOUPFORVFTFCBTBFTUBSFDPNFOEBDJÓO -BTDVSWBTEFSFTJEVPZMBTDVSWBTEFEFTUJMBDJÓOUJFOFOGPSNBTQBSFDJEBT QFSPOPJEÊOUJDBT "VODVBOEPMBTDVSWBTEFSFTJEVPQVFEBODPOGVOEJSFOBMHVOPTDBTPTTPOÙUJMFTQBSBTFMFD DJPOBSQPTJCMFTTFQBSBDJPOFTDPOEFTUJMBDJÓO&YQMJRVFQPSRVÊ -BàHVSBNVFTUSBVOTJTUFNBEFCPNCBEFDBMPSFOFMRVFFMWBQPSEFTUJMBEPTFVTBDPNP áVJEPEFUSBCBKP1PESÎBTFSQSFGFSJCMFVTBSVOáVJEPEFUSBCBKPTFQBSBEP)BHBVOFTRVFNB EFFTPy$VÃMFTTPOMBTWFOUBKBTZMBTEFTWFOUBKBT 5SBDFFMTJTUFNBUPUBMNFOUFBDPQMBEP VOBFYUFOTJÓOEFMBàHVSB( QBSBFMFKFNQMP $POGSFDVFODJB BMQSFDBMFOUBSMBBMJNFOUBDJÓOBVNFOUBMBDBOUJEBEEFFUBQBTOFDFTBSJBTQBSB MBTFQBSBDJÓO ' [ Y% Y# -%DPOTUBOUFT 6TFVOEJBHSBNBEF.D$BCF5IJFMFQBSBFYQMJDBS QPSRVÊTVDFEFBTÎ (FOFSBDJÓOEFBMUFSOBUJWBT 5SBDFBSSFHMPTEFDPMVNOBTQPTJCMFTQBSBTFQBSBSVOTJTUFNBEFDVBUSPDPNQPOFOUFT5FOHB FODVFOUBRVFFYJTUFVOBHSBODBOUJEBEEFQPTJCJMJEBEFT 3FQJUBFMFKFNQMP QFSPQBSBSFDVQFSBSFMEFOQSPQBOPM-BTQVSF[BTQVFEFOTFS NFOPSFT -BEFTUJMBDJÓOEFWBSJPTFGFDUPTPMBJOUFHSBDJÓOEFDPMVNOBTQVFEFOIBDFSTFDPONÃTEFEPT DPMVNOBT"QMJRVFMBTJEFBTCÃTJDBTEFMBTàHVSBTZQBSBUSB[BSUBOUBTGPSNBTDPNP QVFEBEFDPOFDUBSUÊSNJDBNFOUFUSFTDPMVNOBT 4FEFTFBTFQBSBSVOBBMJNFOUBDJÓORVFDPOUJFOFNPMEFCFODFOP NPMEFUPMVFOP  NPMEFYJMFOPZNPMEFDVNFOP"QMJRVFIFVSÎTUJDBTQBSBHFOFSBSBMUFSOBUJWBTDPO WFOJFOUFT-BTWPMBUJMJEBEFTSFMBUJWBTQSPNFEJPTPO #5  55  95  $5 4FSFRVJFSFVOBQVSF[BEFFOUPEPTMPTQSPEVDUPT 3FQJUBFMQSPCMFNB#QBSBVOBQVSF[BEFFOFMYJMFOPQSPEVDJEP

$ %FEVDDJPOFT $ %FNVFTUSF RVF MPT DPTUPT EFM BHVB EF FOGSJBNJFOUP Z EFM WBQPS EF BHVB TPO EJSFDUBNFOUF QSPQPSDJPOBMFTBMBUBTBEFBMJNFOUBDJÓO

www.FreeLibros.me



$BQÎUVMP  &DPOPNÎBZDPOTFSWBDJÓOEFFOFSHÎBFOMBEFTUJMBDJÓO

$ 1BSBHSBOEFTWPMÙNFOFT MBàHVSBJOEJDBRVFMPTDPTUPTEFFNQBRVFTPOEJSFDUBNFOUF QSPQPSDJPOBMFTBMWPMVNFOEFMFNQBRVF%FNVFTUSFRVFMPTDPTUPTEFMFNQBRVFQBTBOQPS VONÎOJNPBMBVNFOUBS-% % 1SPCMFNBT  -BTSFTQVFTUBTEFQSPCMFNBTNBSDBEPTDPOVOBTUFSJTDPFTUÃOBMGJOBMEFMMJCSP %  3FQJUBFMFKFNQMP QFSPBVOBQSFTJÓOEFL1B"FTUBQSFTJÓO &P %QJFTZ MBWPMBUJMJEBESFMBUJWBFTVOBGVODJÓOEFMBQSFTJÓO B  $BMDVMF -% NÎO C  $BMDVMF/NÎO D  &TUJNF/FRVJM E  &TUJNF/SFBM F  $BMDVMFFMDPTUPEFMBTFOWPMWFOUFTZMPTQMBUPTFOTFQUJFNCSFEF G "DUVBMJDFFMDPTUPEFFOWPMWFOUFTZQMBUPTBMBGFDIBEFIPZ %  &TUJNFFMDPTUPEFMDPOEFOTBEPSZFMWBQPSJ[BEPS BNCPTEFFTQFKPàKP FOWPMWFOUFZUVCPT  QBSBMBEFTUJMBDJÓOEFMFKFNQMP-BQSFTJÓOFTL1B$1- $#UVMCNPMž'  $  #UVMCNPM-PTEBUPTQBSBFMIFYBOPFTUÃOFOFMQSPCMFNB%&MWBQPSEFBHVBTBUV SBEPFOFMWBQPSJ[BEPSFTUÃBž$  WBQPS#UVMC&MBHVBEFFOGSJBNJFOUPFOUSBBž' ZTBMFBž'$1 X#UVMCž'6TFMPTDPFàDJFOUFTEFUSBOTGFSFODJBEFDBMPSEFMBUBCMB 5FOHBDVJEBEPDPOMBTVOJEBEFT % %FUFSNJOFMPTDPTUPTEFPQFSBDJÓOQPSWBQPSEFBHVBZQPSBHVB QPSIPSB QBSBFMQSPCMFNB %&MDPTUPEFMWBQPSEFBHVBFTMC ZFMDPTUPEFMBHVBEFFOGSJBNJFOUPFT HBM % &OFMFKFNQMPZFMQSPCMFNB%TFDBMDVMBFMEJÃNFUSPEFVOBDPMVNOBFNQBDBEB QBSBMBTFQBSBDJÓOEFMFKFNQMP4VQPOHBRVFTFWBBVTBSVOBDPMVNOBEFQJFTEFEJÃ NFUSP-BTTJMMBT*OUBMPYEFQVMHBEBUJFOFOQJFTEF)&51&TUJNFMPTDPTUPTEFMFNQBRVF ZMBUPSSF-BQSFTJÓOFTL1B % 6OBDPMVNOBEFQJFTEFEJÃNFUSPFTBEFDVBEBQBSBFMFKFNQMPBL1B6TFMPTNJT NPTEBUPTRVFMPTEFMQSPCMFNB%ZMBDBOUJEBEEFDPOUBDUPTEFFRVJMJCSJPFTUJNBEBFOFM QSPCMFNB% QBSBFTUJNBSMPTDPTUPTEFMFNQBRVFZEFMBUPSSF % 3FQJUBFMBOÃMJTJTEFDVSWBEFSFTJEVPQBSBFMFKFNQMP QFSPVTBOEPFMEJBHSBNBEFáVKP EFMBàHVSBC6TFVOáVKPEFSFDJSDVMBDJÓOBSCJUSBSJPEFLHNPMI % 3FQJUBFMBOÃMJTJTEFDVSWBEFSFTJEVPQBSBFMFKFNQMP QFSPTJOSFDJSDVMBDJÓO B 1BSBFMQSPDFTPEFMBàHVSBB C 1BSBFMQSPDFTPEFMBàHVSBC ' 1SPCMFNBTRVFSFRVJFSFOPUSPTSFDVSTPT ' #VTRVFFMÎOEJDFEFDPTUPBDUVBMFOMBSFWJTUB$IFNJDBM&OHJOFFSJOH¼TFMPQBSBBDUVBMJ[BSMBT PSEFOBEBTFOMBTàHVSBTB ( 1SPCMFNBTQBSBDPNQVUBEPSB ( 3FQJUBMBTJNVMBDJÓOFODPNQVUBEPSBQBSBEFNPTUSBSMBGBDUJCJMJEBEFOFMFKFNQMP QFSP VTFFMEJBHSBNBEFáVKPEFMBàHVSBC-PTEBUPTQBSBFMTJNVMBEPSTFEFCFOCBTBSFOMB TPMVDJÓOQBSBFMQSPCMFNB%4JMPEFTFB QVFEFJOHSFTBSMBDPSSJFOUFEFSFáVKPZMBBMJ NFOUBDJÓOGSFTDBFOEJTUJOUBTFUBQBTEFMBQSJNFSBDPMVNOB ( 3FQJUBMBTJNVMBDJÓOFODPNQVUBEPSBQBSBEFNPTUSBSMBGBDUJCJMJEBEFOFMFKFNQMP QFSPTJO SFDJSDVMBDJÓO-PTEBUPTQBSBFMTJNVMBEPSEFCFOCBTBSTFFOMBTPMVDJÓOEFMQSPCMFNB% B 1BSBFMQSPDFTPEFMBàHVSBB C 1BSBFMQSPDFTPEFMBàHVSBC

www.FreeLibros.me

$"1±56-0 

Absorción y arrastre

)BTUBBIPSBIFNPTIBCMBEPDBTJQPSDPNQMFUPTPCSFEFTUJMBDJÓO4JOFNCBSHP FYJTUFOPUSBTPQFSB DJPOFTVOJUBSJBTNVZÙUJMFTFOFMQSPDFTBNJFOUPEFTVTUBODJBTRVÎNJDBTZFMDPOUSPMEFMBDPOUBNJ OBDJÓO-BBCTPSDJÓOFTMBPQFSBDJÓOVOJUBSJBFOMBRVFTFFMJNJOBOVOPPNÃTDPNQPOFOUFTEFVOB DPSSJFOUFEFHBTBMTFSUPNBEPT PBCTPSCJEPT QPSVOMÎRVJEPOPWPMÃUJM TPMWFOUF &OFTUFDBTP FM TPMWFOUFMÎRVJEPEFCFBHSFHBSTFDPNPBHFOUFTFQBSBEPS-BBCTPSDJÓOFTVOPEFMPTNÊUPEPTQBSB FMJNJOBSFM$0FOFMHBTOBUVSBMZFOMPTHBTFTEFDPNCVTUJÓO QBSBRVFFM$0OPFOUSFBMBBUNÓT GFSBZDPOUSJCVZBBMDBMFOUBNJFOUPHMPCBM 4PDPMPX   &MBSSBTUSFFTMPDPOUSBSJPEFMBBCTPSDJÓO&OFMBSSBTUSF VOPPNÃTDPNQPOFOUFTEFVOBDP SSJFOUFMÎRVJEBTFFMJNJOBOBMTFSFWBQPSBEPTZQBTBSBVOBDPSSJFOUFJOTPMVCMFEFHBT&OFTUFDBTP  MBDPSSJFOUFEFHBT FMBHFOUFEFBSSBTUSF TFEFCFBHSFHBSDPNPBHFOUFTFQBSBEPS y$VÃMGVFFMBHFOUFTFQBSBEPSQBSBMBEFTUJMBDJÓO &MDBMPS -BBCTPSDJÓOQVFEFTFSGÎTJDBPRVÎNJDB&OFMDBTPEFBCTPSDJÓOGÎTJDB FMHBTTFFMJNJOBQPS UFOFSNBZPSTPMVCJMJEBEFOFMTPMWFOUFRVFPUSPTHBTFT6OFKFNQMPFTMBFMJNJOBDJÓO DPOVOBDFJUF QFTBEP EFCVUBOPZQFOUBOP $Z$ EFVOBNF[DMBHBTFPTBEFSFàOFSÎB&OMBBCTPSDJÓORVÎNJDB  FMHBTRVFTFWBBFMJNJOBSSFBDDJPOBDPOFMTPMWFOUFZRVFEBFOTPMVDJÓO6OFKFNQMPFTMBFMJNJOB DJÓOEF$0PEF)4QPSSFBDDJÓODPO/B0) PDPONPOPFUBOPMBNJOB .&" 1BSBMBTSFBDDJPOFT JSSFWFSTJCMFT FMMÎRVJEPRVFSFTVMUBEFCFEFTFDIBSTF NJFOUSBTRVFFOMBTSFBDDJPOFTSFWFSTJCMFTFM TPMWFOUFTFQVFEFSFHFOFSBS FODPMVNOBTEFBHPUBNJFOUPPEFEFTUJMBDJÓO "TÎ DPOGSFDVFODJBTF QSFàFSFOMBTSFBDDJPOFTSFWFSTJCMFT-PTTJTUFNBTEFBCTPSDJÓORVÎNJDBTFEFTDSJCFODPONÃTEFUBMMF FO"TUBSJUBFUBM 

,PIM 

,PIMZ/JFMTFO  Z;BSZDLJZ$IBDVL   &ODBTPTUÎQJDPT MBBCTPSDJÓORVÎNJDBUJFOFVOBSFMBDJÓOEFFRVJMJCSJPNVDIPNÃTGBWPSBCMFRVF MBBCTPSDJÓOGÎTJDB MBTPMVCJMJEBEEFMBNBZPSQBSUFEFMPTHBTFTTVFMFTFSNVZQFRVFÒB QPSMP RVFDPOGSFDVFODJBTFQSFàFSF4JOFNCBSHP MBFàDJFODJBEF.VSQISFFTVFMFTFSCBTUBOUFCBKB OPFT SBSPFM

MPDVBMEFCFUFOFSTFFODVFOUB -BBCTPSDJÓOZFMBSSBTUSFQVFEFONBOFKBSTFDPNPPQFSBDJPOFTEFFUBQBTEFFRVJMJCSJPDPODPO UBDUPEFMÎRVJEPZWBQPS$PNPMBEFTUJMBDJÓOUBNCJÊOFTVOBPQFSBDJÓOEFFUBQBTEFFRVJMJCSJPDPO DPOUBDUPEFMÎRVJEPWBQPS DBCFFTQFSBSRVFMPTFRVJQPTTFBOCBTUBOUFQBSFDJEPT:FTPFTMPRVFTV DFEFUBOUPMBBCTPSDJÓODPNPFMBSSBTUSFTFFGFDUÙBOFOUPSSFTFNQBDBEBTZEFQMBUPT-BTUPSSFTEF QMBUPTTFEFCFOEJTFÒBSDPOVOBBEBQUBDJÓOEFMNÊUPEPEF.D$BCF5IJFMF-BTUPSSFTFNQBDBEBT 

www.FreeLibros.me



$BQÎUVMP  "CTPSDJÓOZBSSBTUSF

L, X0 (Solvente alimentado)

(Gas tratado) G, Y1

(Gas que entra)

'*(63" "#403#&%03%&("4

TFQVFEFOEJTFÒBSNFEJBOUF)&51 PEFQSFGFSFODJB BQBSUJSEFDPOTJEFSBDJPOFTEFUSBOTGFSFODJB EFNBTB WFBFMDBQÎUVMP  5BOUPFOMBBCTPSDJÓODPNPFOFMBSSBTUSFTFBHSFHBVOBGBTFTFQBSBEBDPNPBHFOUFTFQBSBEPS &OUPODFTMBTDPMVNOBTTPONÃTTFODJMMBTRVFMBTEFEFTUJMBDJÓO QPSRVFFODBTPTOPSNBMFTOPTFVTB OJDPOEFOTBEPSOJWBQPSJ[BEPS-BàHVSBFTVOFTRVFNBDBSBDUFSÎTUJDPQBSBVOBDPMVNOBEF BCTPSDJÓO&OÊTUB FMTPMVUP#RVFFOUSBDPOFMHBTQPSUBEPS$JOTPMVCMF FOVOBDPSSJFOUF:/ FT BCTPSCJEPZQBTBBMTPMWFOUFOPWPMÃUJM" &TDPNÙORVFFOVOBQMBOUBUSBUBEPSBEFHBTFTUFOHBDPMVNOBTUBOUPEFBCTPSDJÓODPNPEF BSSBTUSF DPNPNVFTUSBMBàHVSB&OFTUBPQFSBDJÓO FMTPMWFOUFTFSFDJSDVMBFOGPSNBDPOUJOVB &MJOUFSDBNCJBEPSEFDBMPSDBMJFOUBBMTPMWFOUFTBUVSBEPQBSBDBNCJBSMBTDBSBDUFSÎTUJDBTEFFRVJMJCSJP EFMTJTUFNBQBSBRVFQVFEBBSSBTUSBSTFFMTPMWFOUF6OBGPSNBNVZDPNÙOEFQMBOUBEFUSBUBNJFOUP EFHBTFTFTMBRVFTFVTBQBSBFMJNJOBS$0Z)4EFHBTFTEFSFàOFSÎBPEFHBTOBUVSBM&OFTUFDBTP  .&"VPUSPTTPMWFOUFTBNJOBEPTEJTVFMUPTFOBHVBTFVTBODPNPTPMWFOUFZDPNPHBTEFBSSBTUSFTF VTBWBQPSEFBHVB WFBNÃTEFUBMMFTFO,PIMZ/JFMTFO  PFO#BMMZ7FMENBO  

Gas tratado

Recirculación de solvente " C T P S C F E P S

Gas por tratar

Gas Conc.

Enfriador

4 F Q B S B E P S

Solvente agotado Calentador

'*(63" 1-"/5"%&53"5".*&/50%&("4&4

www.FreeLibros.me

Gas de arrastre

  &RVJMJCSJPTEFBCTPSDJÓOZBSSBTUSF



 &26*-*#3*04%&"#403$*¶/:"33"453&

&OMPTTJTUFNBTEFBCTPSDJÓOZBSSBTUSFDPOUSFTDPNQPOFOUFTDPOGSFDVFODJBTFTVQPOESÃRVF  &MHBTEFBSSBTUSF PQPSUBEPS FTJOTPMVCMF  &MTPMWFOUFFTOPWPMÃUJM  &MTJTUFNBFTJTPUÊSNJDPFJTPCÃSJDP  -BSFHMBEFMBTGBTFTEF(JCCTFOFTUFDBTPFT '$−1  " #Z$ − WBQPSZMÎRVJEP   4JIBDFNPTRVF5ZQTFBODPOTUBOUFTRVFEBVOHSBEPEFMJCFSUBE&OHFOFSBM MPTEBUPTEFFRVJ MJCSJPTFSFQSFTFOUBODPOVOBHSÃàDBEFMBDPODFOUSBDJÓOEFMTPMVUPFOFMWBQPSFOGVODJÓOEFMBDPO DFOUSBDJÓOEFMTPMVUPFOFMMÎRVJEP PJOEJDBOEPVOBDPOTUBOUFEFMFZEF)FOSZ-BMFZEF)FOSZFT 

e7 2=7m7 



EPOEF)#FTMBDPOTUBOUFEFMFZEF)FOSZFOBUNGSBDDNPM )) Q 5 DPNQPTJDJÓO Y#FTMB GSBDDJÓONPMEF#FOFMMÎRVJEP ZQ#FTMBQSFTJÓOQBSDJBMEF#FOFMWBQPS -BMFZEF)FOSZTÓMPFTWÃMJEBBCBKBTDPODFOUSBDJPOFTEF#$PNPMBQSFTJÓOQBSDJBMTFEFàOF DPNP 

n7

e7  eidi



MBMFZEF)FOSZFT 

= n72 e 7 m7  idi



&TUPQSPEVDFVOBHSÃàDBFOGPSNBEFMÎOFBSFDUBTJ)#FTDPOTUBOUF4JFMDPNQPOFOUFFTQVSP  Z#ZQ#QUPU)XBOH 

)XBOHFUBM B C

,PIM 

,PIMZ/JFMTFO 

1FSSZ FUBM  1ÃHTB

1FSSZZ$IJMUPO  1ÃH

1FSSZZ(SFFO  1ÃHT B Z:BXTFUBM  QSFTFOUBOEBUPTQBSBBCTPSDJÓO1PSFKFNQMP MPTWBMPSFTJOEJDBEPT QBSB$0 $0Z)4TFWFOFOMBUBCMB 1FSSZFUBM  -PTWBMPSFTHSBOEFTEF)FOMBUBCMB JOEJDBORVFFM$0ZFM)4TPONVZQPDPTPMVCMFTFOBHVB$PNP)FTBQSPYJNBEBNFOUF JOEFQFOEJFOUFEFQUPU FTUPRVJFSFEFDJSRVFTFBCTPSCFNÃTHBTBNBZPSQSFTJÓO&TUFGFOÓNFOPTF BQSPWFDIBQBSBGBCSJDBSCFCJEBTDBSCPOBUBEBT$VBOEPTFBCSFMBCPUFMMBPMBMBUB CBKBMBQSFTJÓOZ TFEFTPSCFFMHBTGPSNBOEPQFRVFÒBTCVSCVKBT&OMBUBCMB :BXTFUBM  TFNVFTUSBOWB MPSFTTFMFDDJPOBEPTEFDPOTUBOUFTEFMFZEF)FOSZ QBSBDPNQVFTUPTDMPSBEPTFOBHVBBž$&TPT WBMPSFTTPOÙUJMFTQBSBEFTBSSPMMBSQSPDFTPTQBSBFMJNJOBSFTUPTDPNQVFTUPTEFBHVBDPOUBNJOBEB QPSNFEJPEFBSSBTUSF0CTFSWFRVFFTPTDPNQVFTUPTTPONVDIPNÃTTPMVCMFTRVFMPTHBTFTRVF BQBSFDFOFOMBUBCMB -BTDPOTUBOUFTEFMFZEF)FOSZEFQFOEFOEFMBUFNQFSBUVSBZTVFMFOBQFHBSTFBMBFDVBDJÓOEF "SSIFOJVT&TEFDJS 

=2=% Zme

−:  GI

6OBHSÃàDBEFMPH)FOGVODJÓOEF5QSPEVDFDPOGSFDVFODJBVOBMÎOFBSFDUB

www.FreeLibros.me





$BQÎUVMP  "CTPSDJÓOZBSSBTUSF

5"#-" $0/45"/5&4)%&-&:%& )&/3:1"3"$0 $0:)4&/"(6") &45¦&/"5.'3"$$*¶/.0-"3 I° 8

8D'

8D

='H

% * &% &* '% '* (% (* )% )* *% +% ,% -% .% &%%

,'-,+ &%)% &''% &)'% &+)% &-+% '%.% '((% '*,% '-(% ()&% · · · ·

(*!'%% (.!+%% ))!'%% )-!.%% *(!+%% *-!%%% +'!%%% +*!.%% +.!+%% ,'!.%% ,+!&%% -'!&%% -)!*%% -)!*%% -)!+%% -)!+%%

'+!-%% (&!*%% (+!,%% )'!(%% )-!(%% *)!*%% +%!.%% +,!+%% ,)!*%% -&!)%% --!)%% &%(!%%% &&.!%%% &(*!%%% &))!%%% &)-!%%%

'VFOUF1FSSZFUBM 

QÃHTZ

&MFGFDUPEFMBDPODFOUSBDJÓOTFNVFTUSBFOMBUBCMB EPOEFTFJMVTUSBMBBCTPSDJÓOEFBNP OJBDPFOBHVB 1FSSZFUBM  0CTFSWFRVFMBTTPMVCJMJEBEFTTPOOPMJOFBMFTZRVF)Q/)YOP FTDPOTUBOUF&TUFDPNQPSUBNJFOUPFTCBTUBOUFDPNÙOQBSBHBTFTTPMVCMFT 4FSÃOFDFTBSJPDPOWFSUJSMPTEBUPTEFFRVJMJCSJPBMBTVOJEBEFTEFDPODFOUSBDJÓORVFTFSFRVJF SFOFOMPTDÃMDVMPT4JTFVTBOGSBDDJPOFTNPMBSFTPEFNBTB EFCFODPOWFSUJSTFMPTEBUPTEFFRVJMJ CSJPFOSFMBDJPOFTNPMBSFT

5"#-" $0/45"/5&4%&-&:%&)&/3::40-6#*-*%"%&41"3"$0.16&4504$-03"%04&/"(6" "ž$:"5. :"84&5"-  

$PNQVFTUP )

BUN GSBDDJÓONPMBS

4PMVCJMJEBE QQN NPMBS

5FUSBDMP SVSPEF DBSCPOP 88l)

$MPSP GPSNP 8=8l(

%JDMPSP NFUBOP 8='8l'

$MPSVSPEF WJOJMP 8'='8l

  USJDMP SPQSPQBOP 8(=*8l(

DMPSP IFQUBOP 8,=&*8l

DMPSP OBGUBMFOP 8&%=,8l

&*-.#(+

'&&#&.

&(,#%%

&')(#-)

'(#,-

'&(%#'-

&%#.+

.(#+-

&&.%#&

)&,*#)

,,-#.

'&(#..

&#-&.+

'#)-

www.FreeLibros.me

  -ÎOFBTEFPQFSBDJÓOQBSBBCTPSDJÓO



5"#-" "#403$*¶/%&".0/*"$0&/"(6" 1FTPEF /)FO  QBSUFT EF)0 FOQFTP ='D

1SFTJÓOQBSDJBMEFM/) NN)H %°8 &%°8 '%°8

(%°8

)%°8

*%°8

+%°8

&%% .% -% ,% +% *% )% (% '* '% &* &% ,#* * ) ( '#* ' &#+ &#' &#% %#*

.), ,-* +(+ *%% (-% ',* &.% &&. -.#* +) )'#, '*#& &,#, &&#' · · · · · · · ·

· · · · · · · · · · · · · '(#* &.#) &*#( &'#% .#& ,#) (#)

· · · · ,&. )*) (*' '+% &,. &&% ,.#, *&#% )%#& '.#+ ')#) &.#( &*#( &&#* ·

((%% ',+% '&(% &*'% &%+* +.' *() (.* ',( &+, &'% ,+#* +%#)* (,#+ (%#% ')#& &-#( &*#)

-'* *.+ )%* '), &,. &&* .&#& +,#& **#, ))#* (*#* '+#, ''#'

.-, ,-% +%% )(. (%& &.% &)) &%(#* ,%#& )&#'.#. &.#& &+#& &&#( · · · · · ·

&)*% &&,% .)* +-+ ),% '.'', &++ &&) +.#+ *%#% (&#, ')#. &-#' &*#% &'#% · · · ·

7BMPSFTFYUSBQPMBEPT 'VFOUF1FSSZFUBM  ¥3FJNQSFTPDPOBVUPSJ[BDJÓOEF.D(SBX)JMM

 -±/&"4%&01&3"$*¶/1"3""#403$*¶/

&MEJBHSBNBEF.D$BCF5IJFMFFTNVZÙUJMDVBOEPMBMÎOFBEFPQFSBDJÓOFTVOBSFDUB1BSBFTPTF SFRVJFSFRVFTFTBUJTGBHBOMPTCBMBODFEFFOFSHÎBZRVFMBSFMBDJÓOEFáVKPEFMÎRVJEPáVKPEFWBQPS TFBDPOTUBOUF1BSBRVFMPTCBMBODFTEFFOFSHÎBRVFEFOTBUJTGFDIPTBVUPNÃUJDBNFOUF EFCFNPTTV QPOFSRVF  &MDBMPSEFBCTPSDJÓOFTEFTQSFDJBCMF  -BPQFSBDJÓOFTJTPUÊSNJDB $POFTUBTEPTIJQÓUFTJTTFHBSBOUJ[BMBTBUJTGBDDJÓOEFMPTCBMBODFTEFFOFSHÎB$VBOEPMBTDPSSJFOUFT EFHBTZMÎRVJEPTPOCBTUBOUFEJMVJEBT FTQSPCBCMFRVFFTBTIJQÓUFTJTRVFEFOTBUJTGFDIBT

www.FreeLibros.me



$BQÎUVMP  "CTPSDJÓOZBSSBTUSF

5BNCJÊOTFEFTFBRVFMBMÎOFBEFPQFSBDJÓOTFBVOBSFDUB&TPTVDFEFSÃEFNBOFSBBVUPNÃUJDB TJEFàOJNPTRVF -(

NPMFTEFTPMWFOUFOPWPMÃUJMI NPMFTEFHBTJOTPMVCMFQPSUBEPSI

ZTJBEFNÃTTVQPOFNPTRVF  &MTPMWFOUFFTOPWPMÃUJM  &MHBTQPSUBEPSFTJOTPMVCMF &TDPNÙORVFMBTIJQÓUFTJTZTFDVNQMBOCJFO-PTSFTVMUBEPTEFFTUBTEPTÙMUJNBTIJQÓUFTJTTPO RVFFMCBMBODFEFNBTBQBSBFMTPMWFOUFFT -/-K--DPOTUBOUF





NJFOUSBTRVFFMCBMBODFEFNBTBQBSBFMHBTQPSUBEPSFT (/ (K((DPOTUBOUF





5PNFFODVFOUBRVFOPTFQVFEFOVTBSáVKPTUPUBMFTEFHBTZEFMÎRVJEPFONF[DMBTDPODFOUSBEBT  QPSRVFTFQVFEFBCTPSCFSVOBDBOUJEBEBQSFDJBCMFEFTPMVUPZFTUPDBNCJBSÎBMPTáVKPTEFHBTZMÎRVJ EP ZMBMÎOFBEFPQFSBDJÓOTFSÃFOUPODFTVOBDVSWB1BSBTPMVDJPOFTNVZEJMVJEBT EFTPMVUP

 TFQVFEFOVTBSáVKPTUPUBMFTZQVFEFOVTBSTFGSBDDJPOFTEFNBTBPNPMBSFTFOMBTFDVBDJPOFTEF PQFSBDJÓOZEFFRVJMJCSJP$PNPTFRVJFSFVTBS-NPMFTEFTPMWFOUFOPWPMÃUJM 4 I Z(NPMFT EFHBTQPSUBEPSJOTPMVCMF $ I EFCFNPTEFàOJSOVFTUSBTDPNQPTJDJPOFTEFUBMNBOFSBRVFQPEBNPT GPSNVMBSVOCBMBODFEFNBTBQBSBFMTPMVUP#y$ÓNPIBDFSMP %FTQVÊTEFBMHVOBTNBOJQVMBDJPOFTWFNPTRVFMBGPSNBDPSSFDUBEFEFàOJSOVFTUSBTDPNQPTJ DJPOFTFTDPNPSFMBDJPOFTNPMBSFT4FEFàOFO 

N2

bdaZhYZ7ZcZa\Vh bdaZhYZ\VhedgiVYdgejgd!8

n

M2

bdaZhYZ7Zca†fj^Yd    B

bdaZhYZhdakZciZejgdH

-BTSFMBDJPOFTNPMBSFT:Z9TFSFMBDJPOBODPOMBTGSBDDJPOFTNPMBSFTBDPTUVNCSBEBTNFEJBOUF 

N2

n &−n

n

M2

m  &−m

C

0CTFSWFRVF:Z9QVFEFOTFSNBZPSFTRVF$POMBTVOJEBEFTEFSFMBDJPOFTNPMBSFT   molesde B en la corriente de gasj   molesde gasportador  molesde B en la corriente de gasj Yj G     h moless de portador h   

Z  molesde B en la corriente líquida j   molesde solvente  molesde B en la corriente de solvente j Xj L     h moleesde solvente h   

&OUPODFT QPEFNPTFTDSJCJSFMCBMBODFEFNBTBFOFTUBEPFTUBCMF FOUSBEBTTBMJEBT FOFTUBTVOJ EBEFT&MCBMBODFEFNBTBFOUPSOPBMBQBSUFTVQFSJPSEFMBDPMVNOB DPOMBFOWPMWFOUFEFCBMBODF RVFNVFTUSBMBàHVSBFT 

N_ &   &−n6 ac  &−n6>



1BSBTJTUFNBTNVZEJMVJEPT  −Z" MN ZL ZBLZB 3FQFUJSFNPTBIPSBFMBOÃMJTJTEFVOBTFDDJÓOFNQBDBEBDPOMBFDVBDJÓO  FJODMVJSFNPT MBTUBTBTEFáVKPUPUBMFTOPDPOTUBOUFT-BàHVSB"FTVOFTRVFNBEFVOBCTPSCFEPS4FTVQPOF RVFFMBCTPSCFEPSFTJTPUÊSNJDPZRVFUJFOFáVKPUBQÓO-BWFMPDJEBEEFUSBOTGFSFODJBEFNBTBFO VOTFHNFOUPEFMBDPMVNOBE[FT 

C6 V6X Yo2`′n Vn6 − n6>6X Yo 

www.FreeLibros.me





$BQÎUVMP  "OÃMJTJTEFMBUSBOTGFSFODJBEFNBTB

"MDPNQBSBSFTUBFDVBDJÓODPOMB  TFWFRVFTFIBDBNCJBEPFMTJHOPEFMBEJGFSFODJBEFGSBD DJPOFTNPMBSFT QPSRVFMBEJSFDDJÓOEFUSBOTGFSFODJBEFTPMVUPFOMPTBCTPSCFEPSFTFTDPOUSBSJBB MBEFMBUSBOTGFSFODJBEFMDPNQPOFOUFNÃTWPMÃUJMFOMBEFTUJMBDJÓO"EFNÃT TFVTBFMDPFàDJFOUF NPEJàDBEPEFUSBOTGFSFODJBEFNBTB L Z5BNCJÊOTFQVFEFSFMBDJPOBSMBUSBOTGFSFODJBEFNBTBEFM TPMVUPDPOFMDBNCJPEFUBTBTEFáVKPFOMBTDPSSJFOUFTEFHBTPEFMÎRVJEP 

C6 V6X Yo2−6X YKn62−6X YAm6 



&TUBFDVBDJÓOEJàFSFEFMBFDVBDJÓO 

EFEVDJEBQBSBMBEFTUJMBDJÓO ZBRVFOJ7OJ-TPODPOT UBOUFT -BTWBSJBDJPOFTEF7TFQVFEFOSFMBDJPOBSDPOMBUBTBEFáVKPDPOTUBOUFEFMHBTEFBSSBTUSF P QPSUBEPS ( 

K2

<  &− n6



JHVBMRVFMBFDVBDJÓO  "MDPNCJOBSMBTFDVBDJPOFT  B  SFTVMUB  Y



B

%FTQVÊTEFTBDBSMBEFSJWBEB TVTUJUVJSFOMBFDVBDJÓO  ZIBDFSTJNQMJàDBDJPOFTBMHFCSBJDBT MMFHBNPTB 

−Yo2

Vsal, yA,sal

KYn6  `n′ V6X&−n6n6−n6>

C

Lent, xA

ent

yent

ysal

xsal xent

Vent, yA

ent

Lsal, xAsal

'*(63" $¦-$6-0%&"#403#&%03" &426&."%&-"$0-6./" # $¦-$6-0%&'3"$$*0/&4.0-"3&4*/5&3'"$*"-&41&/%*&/5&4−, 9, :

www.FreeLibros.me

  "OÃMJTJT)56/56EFBCTPSCFEPSFTZTFQBSBEPSFTEFBSSBTUSF



"MJOUFHSBSFTUBFDVBDJÓOSFTVMUB n6!hVa

]



]2

Yo2− %

n6!Zci

K Yn6  `n′ V6X &−n6n6−n6>



4VTUJUVJNPTFOMBFDVBDJÓO  ZRVFEB n6!hVa

K `nV6X

 n6!Zci





&MUÊSNJOP7 LZB"D FTMBBMUVSBEFVOBVOJEBEEFUSBOTGFSFODJBEFGBTFHBTFPTB )( EFàOJEBFOMB FDVBDJÓO B  4FQVFEFEFUFSNJOBSMBWBSJBDJÓOEF)(DPOMBFDVBDJÓO  ZMBàHVSB WÃMJEBTQBSBBC TPSCFEPSFTZEFTUJMBEPSFT&MUÊSNJOPRVFWBSÎBNÃTFOMBFDVBDJÓO  FTFMáVKPEFNBTB QFTP  EFMMÎRVJEP 8-)(EFQFOEFEF8-FOQSPQPSDJÓOBTVQPUFODJB−B−&OVOBTPMBTFDDJÓOEF VOBCTPSCFEPS VODBNCJPEFFOFMáVKPEFMMÎRVJEPTFSÎBCBTUBOUFHSBOEF&TPDBVTBSÃ DVBOEP NVDIP VODBNCJPEFFO)(-BDBOUJEBELZBFTJOEFQFOEJFOUFEFMBDPODFOUSBDJÓO QPSRVFFM FGFDUPEFMBDPODFOUSBDJÓOZBTFJODMVZÓFOL Z FOMBFDVBDJÓO  $PNPMBWBSJBDJÓOEF)(FOMB TFDDJÓOEFMBDPMVNOBFTSFMBUJWBNFOUFQFRVFÒB DPOTJEFSBSFNPTRVF)(FTDPOTUBOUF&OUPODFT  MBFDVBDJÓO  TFDPOWJFSUFFO n6!Zci



]2=< n6!hVa

&−n6abYn6 &−n6n6−n6> 



RVFTFTVFMFFTDSJCJSFOMBGPSNB ]2=1BSBOPPMWJEBSMBT DBNCJBSFNPTMBTVOJEBEFTEF MBTQSFTJPOFTQSBUN DN)HBUN DN)HQQBUNDN)H -PT WBMPSFT EF , TF DBMDVMBO DPO MB FDVBDJÓO E  1PS FKFNQMP  QBSB FM EJÓYJEP EF DBSCPOP

www.FreeLibros.me

  1FSNFBDJÓOEFHBTFT

@b!8D' 2



egE8D' $ibh ''-(')% × &%−&%$%#%%'*) 2 ;e$6 eeE8D' $ibh  ;e $6 (%#)(')% × &%−&%$%#%%'*)

ZMPNJTNPQBSBFMPYÎHFOPZFMOJUSÓHFOP1BSBVTBSFTUPTUÊSNJOPTFOVOQSPDFEJNJFOUP EFUBOUFPT EFCFNPTDPNFO[BSDPOVOWBMPSEF'Q"y$ÓNPQSPQPOFSVOWBMPSSB[POBCMF EF'Q" 4JQSPQPOFNPTVOWBMPSEFZQ JQBSBDVBMRVJFSBEFMPTDPNQPOFOUFT QPESFNPTDBMDVMBS ZS JDPOMBFDVBDJÓOEFPQFSBDJÓOQBSBFMDPNQPOFOUF MB D

BSSFHMBEBDPNPTJHVF ng!^ 2 −

u n & − u e!^

nZci!^ &−u

Z QPESFNPT EFUFSNJOBS OVFTUSB QSPQPTJDJÓO EF 'Q"  PSEFOBOEP MB FDVBDJÓO C  DPNPTJHVF Fp/AiZciVi^kV 2 PE^ $ibh ne!^Reg ng!^ − ee ne!^ 

1PSFKFNQMP QSPQPOESFNPTBSCJUSBSJBNFOUFRVFZQ $0&OUPODFT FMQSJNFSWBMPS UFOUBUJWP EF 'Q"   $PO FTUB QSPQPTJDJÓO  ,N $0    ,N 0   Z ,N /-BFDVBDJÓO G TFUSBOTGPSNBFO nZci!^ 2%#+(- /FDFTJUBNPTVOWBMPSNBZPSEF'Q" PVOBQSPQVFTUBNFOPS & @b^−&θ

QBSBZQ J

-PTTJHVJFOUFTWBMPSFTTFHFOFSBSPODPOVOBIPKBEFDÃMDVMP FTUJNBOEPFMTJHVJFOUFWBMPS EFZQ $0 4JTFRVJFSF TFQVFEFVTBS4PMWFSDPO&YDFM  ne!8D' %#*% %#)* %#)** %#)*). %#)*)+

;e$6 %#%%'+-. %#%%)(*, %#%%)&,) %#%%)&,%#%%)&-.

mg!^ %#+(&#%%+ %#...)'%#...*+( %#....+-

&OUPODFT "'Q 'Q" < 'FOU > 'Q" <    >    DN %FBDVFSEPDPOMBFDVBDJÓO D

,N $0 ,N 0Z,N / -BT GSBDDJPOFT NPMBSFT EFM SFUFOUBEP  PCUFOJEBT DPO MB FDVBDJÓO F

 TPO ZS $0   ZS 0 ZS /-BTGSBDDJPOFTNPMBSFTEFMQFSNFBEP EFBDVFSEPDPO MBFDVBDJÓO D

TPOZQ 0 ZQ 0ZZQ / 1BSBBTFHVSBSTFRVFVTUFEQVFEFSFTPMWFSQSPCMFNBTEFQFSNFBDJÓOEFWBSJPTDPNQPOFO UFT  DPOàHVSF TV QSPQJB IPKB EF DÃMDVMP Z SFTVFMWB FTUF FKFNQMP  P UBNCJÊO FM QSPCMFNB ((FBOLPQMJT  SFTVFMWFFMTJTUFNBEFQFSNFBEPSQBSBWBSJPTDPNQPOFOUFTDPO VONÊUPEPEJGFSFOUF QFSPMPTSFTVMUBEPTTPOJEÊOUJDPT WFBFMQSPCMFNB(  5FOHBFODVFOUBRVFFMQFSNFBEPOPFTNVZQVSP"VORVFFMOJUSÓHFOPUJFOFMBNFOPS QFSNFBCJMJEBE FOFMQFSNFBEPUPEBWÎBRVFEBNÃTOJUSÓHFOPRVFEJÓYJEPEFDBSCPOP&TP TFEFCFBMBHSBODBOUJEBEEFOJUSÓHFOPFOMBBMJNFOUBDJÓO RVFQSPEVDFVOBGVFS[BNPUSJ[ HSBOEF RVF GVFS[B BM OJUSÓHFOP B BUSBWFTBS MB NFNCSBOB &M SFUFOUBEP FT CBTUBOUF NÃT QVSPRVFMBBMJNFOUBDJÓO1BSBPCUFOFSVOBDPSSJFOUFEFOJUSÓHFOPUPEBWÎBNÃTQVSBDPO

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMPTQSPDFTPTEFTFQBSBDJÓODPONFNCSBOB

FTUBBMJNFOUBDJÓO QPEFNPTBVNFOUBSFMDPSUFZMBQSFTJÓOEFMSFUFOUBEP4JOFNCBSHP VO NÊUPEPNFKPSTFSÎBVTBSVOBNFNCSBOBDPONBZPSTFMFDUJWJEBE  ¶4.04*4*/7&34"

-BÓTNPTJTJOWFSTB 30 EFSFWFSTFPTNPTJT FTVOQSPDFTPRVFTFVTBDPOGSFDVFODJBQBSBQVSJàDBSZ EFTBMBSBHVB&MBHVBMÎRVJEBTFJOUSPEVDFBQSFTJÓOZBUSBWJFTBVOBNFNCSBOBOPQPSPTB FOEJSFD DJÓODPOUSBSJBBMBEFMBÓTNPTJT MBÓTNPTJTTFEFàOJSÃNÃTBEFMBOUF -BNBZPSQBSUFEFMBTTBMFTZ EFMBTNPMÊDVMBTTJODBSHBTPOSFUFOJEBTQPSMBNFNCSBOB"TÎ FMQFSNFBEPFTVOBHVBNVDIPNÃT QVSBZFMSFUFOUBEPTFWVFMWFCBTUBOUFNÃTDPODFOUSBEP-BTNFNCSBOBTEFVTPGSFDVFOUFTFNVFT USBOFOMBàHVSBZTPO VOBGPSNVMBDJÓOEFBDFUBUPZUSJBDFUBUPEFDFMVMPTB  QPMJBNJEBT BSPNÃUJDBT BSBNJEBT Z QPMJBNJEBTBSPNÃUJDBTEFFOMBDFDSV[BEP &ZLBNQ  &OMBÓTNPTJT JOWFSTBTFVTBONÓEVMPTEFàCSBIVFDBZEFNFNCSBOBFOFTQJSBM àHVSB $PNPMPTUVCPTEFM HBEPTSFTJTUFOHSBOEFTQSFTJPOFTEFDPNQSFTJÓO FOMPTTJTUFNBTEFàCSBIVFDBTFBDPTUVNCSBUFOFS MBBMUBQSFTJÓOFOFMMBEPEFMBFOWPMWFOUF GVFSBEFMBTàCSBT  &O VO TJTUFNB EF ÓTNPTJT JOWFSTB  TF SFRVJFSF  FO FM DBTP OPSNBM  VO USBUBNJFOUP QSFWJP QBSB FMJNJOBSUPEBTMBTQBSUÎDVMBTRVFQVFEBOPCTUSVJSMBNFNCSBOB4JIBZJPOFTPTPMVUPTFOTPMVDJÓO RVF UFOHBOQPDBTPMVCJMJEBE FOFMEJTFÒPEFCFIBCFSVODÃMDVMPEFTPMVCJMJEBEQBSBEFUFSNJOBSTJWBOB QSFDJQJUBSTPCSFMBNFNCSBOBDVBOEPTFDPODFOUSFFMSFUFOUBEP4JFTQSPCBCMFRVFIBZBQSFDJQJUBDJÓO  FTPTJPOFTPTPMVUPTEFCFOFMJNJOBSTFPDPOWFSUJSTFFONÃTTPMVCMFTQBSBFWJUBSRVFQSFDJQJUFO6OFT RVFNBEFVOTJTUFNBTFODJMMPEFÓTNPTJTJOWFSTB EPOEFBQBSFDFFMFRVJQPBVYJMJBSNÃTJNQPSUBOUF TFWFFOMBàHVSB&OMBQSÃDUJDB MPTTJTUFNBTFOHSBOFTDBMBQVFEFOUFOFSDJFOUPTEFNÓEVMPTEF NFNCSBOBDPOFDUBEPTUBOUPFOTFSJFDPNPFOQBSBMFMP àHVSB$&O#BLFSFUBM 

&ZLBNQ 

)PZ4JSLBS  Z/PCMFZ4UFSO  TFFODVFOUSBONÃTEFUBMMFTTPCSFMPTFRVJQPT 16.4.1

Análisis de la ósmosis y la ósmosis inversa

-BGVFS[BJNQVMTPSBEFáVKPFOMBÓTNPTJTJOWFSTBFTMBEJGFSFODJBFOUSFMBDBÎEBEFQSFTJÓOBUSBWÊT EFMBNFNCSBOB ZMBEJGFSFODJBEFQSFTJPOFTPTNÓUJDBTBUSBWÊTEFMBNFNCSBOB  Q− &OUPODFT  FMáVKPWPMVNÊUSJDPEFMTPMWFOUFFT 

?hdak 2

;hdak @ 2 hdak Δe − Δx!A$b ' Y†V  6 ibh

B C

ZFMáVKPEFNBTBEFMTPMWFOUFFT 

?′hdak 2?hdak šhdak 2

;hdak šhdak @ š 2 hdak hdak Δe − Δx!\$b ' Y†V  6 ibh

GZVXi^kdh eVgVigViVb^Zcid GZX^gXjaVX^‹cdeX^dcVa

D E F

GZiZciVYd VYZhZX]d VabVX‚c YZV\jV ejgV

; iVcfjZ

[^aigd

WdbWVYZ VaiVegZh^‹c

B‹YjadYZ ‹hbdh^h>ck#

eZgbZVYd

'*(63" &426&."%&6/4*45&."%&¶4.04*4*/7&34"

www.FreeLibros.me

  ¶TNPTJTJOWFSTB



&OFTUBTFDVBDJPOFT ,TPMWFTMBQFSNFBCJMJEBEEFMTPMWFOUF RVFOPSNBMNFOUFFTBHVB BUSBWÊTEFMB NFNCSBOB DVZPFTQFTPSFGFDUJWPEFQJFMFTUNTZ TPMWFTMBEFOTJEBEEFNBTBEFMTPMWFOUF-BDBÎEB EFQSFTJÓOBUSBWÊTEFMBNFNCSBOBFT QQS−QQ-BEJGFSFODJBEFQSFTJPOFTPTNÓUJDBTBUSBWÊT EFMBNFNCSBOBFT  WFBMBEFTDSJQDJÓONÃTBEFMBOUF &MáVKPEFNBTBEFTPMVUPBUSBWÊTEFMB NFNCSBOB + " TFQVFEFFTDSJCJSFOMBGPSNBTJHVJFOUF 

?′6 2

@ ′6 Δm!\$b'Y†V  ibh



EPOEF, "FTMBQFSNFBCJMJEBEEFMTPMVUPZ YFTMBEJGFSFODJBEFGSBDDJPOFTEFQFTPEFMTPMVUPB USBWÊTEFMBNFNCSBOB1BSBVOBNFNCSBOBDPOSFUFODJÓOQFSGFDUBEFMTPMVUP , " 1BSBFTUVEJBSMBÓTNPTJTJOWFSTB QSJNFSPEFCFNPTFTUVEJBSMBÓTNPTJT%VSBOUFÊTUB FMTPMWFO UFBUSBWJFTBVOBNFNCSBOBTFNJQFSNFBCMF VOBRVFQFSNJUFFMQBTPEFMTPMWFOUF QFSPOPEFTPMVUPT PJPOFT EFTEFMBSFHJÓONÃTDPODFOUSBEBBMBNFOPTDPODFOUSBEB1PSFKFNQMP TJFOVOMBEPEFVOB NFNCSBOBTFNJQFSNFBCMFTFUJFOFBHVBQVSBZFOFMPUSPMBEPTFUJFOFVOBTPMVDJÓOEFB[ÙDBS FM BHVBFOUSBSÃBMBTPMVDJÓOEFB[ÙDBSZMBEJMVJSÃ"TÎ FOMBàHVSBFMáVKPPTNÓUJDPFTEFEFSFDIB BHVBQVSB IBDJBMBJ[RVJFSEB TPMVDJÓOEFB[ÙDBS &TUBEJSFDDJÓOOBUVSBMEFáVKPEFTPMWFOUFFTMB EJSFDDJÓORVFDBVTFMBJHVBMBDJÓOEFMPTQPUFODJBMFTRVÎNJDPT1PESFNPTEFUFOFSFMáVKP PJOWFSUJS MP BVNFOUBOEPMBQSFTJÓOEFMBTPMVDJÓOEFB[ÙDBS NFEJBOUFFMQJTUÓORVFTFWFFOFMMBEPJ[RVJFSEP -BQSFTJÓOPTNÓUJDB  FTMBQSFTJÓOBEJDJPOBMRVFTFSFRVJFSF FOFMMBEPDPODFOUSBEP QBSBEFUFOFS FMáVKPPTNÓUJDP TVQPOJFOEPRVFFMMBEPEFMQFSNFBEPDPOUJFOFBHVBQVSB TJOTPMVUP -BQSFTJÓOPTNÓUJDBFTVOBQSPQJFEBEUFSNPEJOÃNJDBEFMBTPMVDJÓO"TÎ  FTVOBWBSJBCMFEFFT UBEPRVFEFQFOEFEFMBUFNQFSBUVSB QSFTJÓOZDPODFOUSBDJÓO QFSPOP EFMBNFNCSBOB TJFNQSFZRVF MBNFNCSBOBTFBTFNJQFSNFBCMF&OFMFRVJMJCSJPPTNÓUJDPTFSFRVJFSFRVFMPTQPUFODJBMFTRVÎNJDPT EFMTPMWFOUFFOMPTEPTMBEPTEFMBNFNCSBOBTFBOJHVBMFT0CTFSWFRVFMPTTPMVUPTOPFTUÃOFOFRVJMJ CSJP QPSRVFOPQVFEFOBUSBWFTBSMBNFNCSBOB"VORVFMBQSFTJÓOPTNÓUJDBTFQVFEFNFEJSFOGPSNB EJSFDUB MPNÃTGSFDVFOUFFTDBMDVMBSMBBQBSUJSEFPUSBTNFEJDJPOFT QPSFKFNQMP 3FJE  1BSBVO MÎRVJEPJODPNQSFTJCMF MBQSFTJÓOPTNÓUJDBTFDBMDVMBDPONFEJDJPOFTEFQSFTJÓOEFWBQPS

xkhdakZciZ 2GI ,c



KEhdakZciZ  KEhdajX^‹c



"RVÎ WTPMWFOUFFTFMWPMVNFONPMBSQBSDJBMEFMTPMWFOUF0USPNÊUPEPGSFDVFOUFFTSFMBDJPOBSMBQSF TJÓOPTNÓUJDBDPOMBEFQSFTJÓOEFMQVOUPEFDPOHFMBDJÓO 3FJE  1BSBTJTUFNBTEJMVJEPT MB QSFTJÓOPTNÓUJDBTVFMFTFSVOBGVODJÓOMJOFBMEFMBDPODFOUSBDJÓO π 2VS m;gVX#bdaVgdπ 2V′m;gVX#ZceZhd 

B C

EPOEFVS PB TFEFUFSNJOBHSBàDBOEPMPTEBUPTDPOVOBSFDUB"NFEJEBRVFMBTPMVDJÓOTFUPSOBNÃT DPODFOUSBEB MBQSFTJÓOPTNÓUJDBBVNFOUBDPONÃTSBQJEF[RVFMBJOEJDBEBQPSMBSFMBDJÓOMJOFBM e^hi‹c

HdajX^‹c

6\jVejgV BZbWgVcV hZb^eZgbZVWaZ

'*(63" "1"3"501"3"13&4*¶/04.¶5*$"

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMPTQSPDFTPTEFTFQBSBDJÓODPONFNCSBOB

1BSBBMHVOPTTJTUFNBTEJMVJEPT MBDPOTUBOUFMJOFBMTFQVFEFDBMDVMBSDPOMBFDVBDJÓOEFWBOU)PGG VS 35



D

:BRVFFOMBFDVBDJÓOEFWBOU)PGGTFTVQPOFRVFFTWÃMJEBMBMFZEF3BPVMU FTUFSFTVMUBEPTFSÃ JODPSSFDUPTJMBTPMVDJÓOTFBTPDJBPTFEJTPDJB BVORVFMBFDVBDJÓOFNQÎSJDB B QVFEBTFHVJS TJFOEPFYBDUB %FTBGPSUVOBEBNFOUF FMáVKPPTNÓUJDPOBUVSBMUJFOFMBEJSFDDJÓODPOUSBSJBBMBRVFTFEFTFBQBSB QSPEVDJSBHVBQVSB&OMBÓTNPTJTJOWFSTBTFFNQVKBBMTPMWFOUFQBSBRVFTBMHBEFMBTPMVDJÓODPODFO USBEBZFOUSFBMBTPMVDJÓOEJMVJEB1PSFTPTFOFDFTJUBFOFSHÎBQBSBDPODFOUSBSFMSFUFOUBEP$PNPMB ÓTNPTJTJOWFSTBJOWJFSUFMBEJSFDDJÓOOBUVSBMEFáVKP FOGPSNBJOIFSFOUFFTVOQSPDFTPEFEFTFRVJMJ CSJP&MBVNFOUPEFQSFTJÓOPTNÓUJDBBNFEJEBRVFTFDPODFOUSBNÃTFMSFUFOUBEPUBNCJÊOJNQPOF VOMÎNJUFOBUVSBMBMBSFDVQFSBDJÓOEFMTPMWFOUFQVSPNFEJBOUFMBÓTNPTJTJOWFSTB4JVOPUSBUBEF SFDVQFSBSEFNBTJBEPTPMWFOUF FMSFUFOUBEPTFWVFMWFNVZDPODFOUSBEP MBEJGFSFODJBEFQSFTJPOFT PTNÓUJDBTFWVFMWFFYUSFNBEBNFOUFHSBOEFZMBDBÎEBEFQSFTJÓOOFDFTBSJBFOMBFDVBDJÓO   QBSBVOBUBTBEFáVKPSB[POBCMFTFWVFMWFEFNBTJBEPHSBOEFQBSBUFOFSVOBPQFSBDJÓOQSÃDUJDB &MQSPDFEJNJFOUPEFBOÃMJTJTFYQMJDBEPFOMBTFDDJÓOBOUFSJPS QBSBMBQFSNFBDJÓOEFHBTFT GPS NBMBCBTFQBSBBOBMJ[BSMBÓTNPTJTJOWFSTB%FTBGPSUVOBEBNFOUFFTUFBOÃMJTJTFTNÃTDPNQMJDBEP QPS MBQSFTJÓOPTNÓUJDB RVFFTUÃJODMVJEBFOMBFDVBDJÓO  Z QPSRVFMBTWFMPDJEBEFTEF USBOTGFSFODJBEFNBTBTPONVDIPNFOPSFTFOMPTTJTUFNBTMÎRVJEPT$PNPMBTWFMPDJEBEFTEFUSBOT GFSFODJBEFNBTBTPOSFMBUJWBNFOUFCBKBT MBGSBDDJÓOFOQFTPEFTPMVUPFOMBQBSFEEFMBNFNCSBOB  YX TFSÃNBZPSRVFMBGSBDDJÓOFOQFTPEFMTPMVUPFOFMJOUFSJPSEFMSFUFOUBEP YS&TUBBDVNVMBDJÓO EFTPMVUPFOMBTVQFSàDJFEFMBNFNCSBOBTFEFCFBMNPWJNJFOUPEFMTPMWFOUFBUSBWÊTEFMBNFNCSB OB RVFBSSBTUSBBMTPMVUPIBDJBMBQBSFEEFFMMB:BRVFFMTPMVUPOPBUSBWJFTBMBNFNCSBOBTFNJQFS NFBCMF TVDPODFOUSBDJÓOBVNFOUBSÃFOMBQBSFEZEFCFEJGVOEJSTFIBDJBBUSÃT EFMBQBSFEIBDJBFM JOUFSJPSEFMBTPMVDJÓO&TUFGFOÓNFOPFTMBQPMBSJ[BDJÓOEFDPODFOUSBDJÓORVFTFJMVTUSBFOMBàHVSB -BQPMBSJ[BDJÓOEFMBDPODFOUSBDJÓOUJFOFVOHSBOFGFDUPTPCSFMBTFQBSBDJÓOPCUFOJEBFOMB ÓTNPTJTJOWFSTBZMBVMUSBàMUSBDJÓO WFBMBTJHVJFOUFTFDDJÓO $PNPMBQPMBSJ[BDJÓOEFDPODFOUSB DJÓOIBDFRVFYXYS MBQSFTJÓOPTNÓUJDBBVNFOUBFOFMMBEPEFMSFUFOUBEPZ EFBDVFSEPDPOMB FDVBDJÓO 

 FM áVKP EJTNJOVZF -B QPMBSJ[BDJÓO EF DPODFOUSBDJÓO IBSÃ BVNFOUBS Y FO MBFDVBDJÓO  ZFMáVKPEFMTPMVUPQVFEFBVNFOUBS MPRVFUBNCJÊOFTJOEFTFBCMF :BRVF+ TPMW' Q −YQ  MBFDVBDJÓO  TFQVFEFEFTBSSPMMBSVTBOEPMBFDVBDJÓO B

DPNPTJHVF ml 9^[jh^‹c^ckZghV ;aj_dYZXdckZXX^‹c

'*(63" 10-"3*;"$*¶/%& $0/$&/53"$*¶/"$6.6-"$*¶/%&-40-650 :%*'64*¶/*/7&34"%&-.*4.0

mg

δ

me

o o2% BZbWgVcV

www.FreeLibros.me

o2δ

  ¶TNPTJTJOWFSTB





?hdak 2; e′

&− me  @hdak P eg − ee  − xg ml− xe me R  2 ρhdak6 ibh

B

-PTWBMPSFTEFYTPOGSBDDJPOFTEFNBTBZMBQSFTJÓOPTNÓUJDBFOFMMBEPEFMSFUFOUBEPEFQFOEFEFMB DPODFOUSBDJÓOEFTPMVUPFOMBQBSFEEFMBNFNCSBOB1BSBTJNQMJàDBSFMBOÃMJTJT QSPWJTJPOBMNFOUF TVQPOESFNPTRVFMPTEBUPTEFMBQSFTJÓOPTNÓUJDBTPOMJOFBMFT ZTFBKVTUBOFOGPSNBTBUJTGBDUPSJBB MBFDVBDJÓO C &OUPODFT MBFDVBDJÓOEFáVKPTFUSBOTGPSNBFO 

?hdak 2

@ ;e′& me  2 hdak Peg ibh hdak 6

V ′ml

eg

meR 

C

1BSB SFMBDJPOBS MB DPODFOUSBDJÓO FO MB QBSFE DPO MB DPODFOUSBDJÓO EFM SFUFOUBEP  EFàOJSFNPT BM NÓEVMPEFQPMBSJ[BDJÓOEFDPODFOUSBDJÓO . FOGVODJÓOEFMBGSBDDJÓOFOQFTP .YXYS





&OCSFWFTFFYQMJDBSÃOMPTNÊUPEPTQBSBNFEJSPDBMDVMBS."MTVTUJUVJSMBEFàOJDJÓOEF.FOMB FDVBDJÓO C

TFPCUJFOF 

?hdak 2

;e′& me  @ 2 hdak Peg š′hdak 6 ibh

ee

V ′Bmg

meR 

D

5BNCJÊOTFQVFEFEFTBSSPMMBSMBFDVBDJÓO 

EFMáVKPEFTPMVUP QBSBFTDSJCJSMBFOUÊSNJOPTEFM NÓEVMPEFQPMBSJ[BDJÓOEFDPODFOUSBDJÓO 

?′6 2

@6 @6 ;′eme Bm g − m e  2 m l − m e2 6 ibh ibh



&OFTFODJB VTBSFNPTFMNJTNPQSPDFEJNJFOUPDPOFMRVFEFTQFKBNPTMBTDPODFOUSBDJPOFTFOMPT QFSNFBEPSFTEFHBT&TUPFT EFTQVÊTEFTVQPOFSRVF,"OPFTDFSP ZRVFFTJOEFQFOEJFOUFEFMB WFMPDJEBEEFUSBOTGFSFODJBEFTPMWFOUF ZRVF,TPMWFTJOEFQFOEJFOUFEFMBWFMPDJEBEEFUSBOTGFSFODJB EFMTPMVUP EFTQFKBSFNPT' QEFMBTFDVBDJPOFT D Z 

JHVBMBSFNPTMBTEPTFDVBDJPOFT ZEFTQFKBSFNPTMBDPODFOUSBDJÓORVFRVFSBNPT"MJHVBMBSMBTFDVBDJPOFTRVFEB 

š′hdak6@hdak $@6 6 Bmg − me  P eg − ee − Bmg − me V ′R 2 ibh &− me  mei bh



$POWJFOFEFàOJSMBTFMFDUJWJEBE EFMBNFNCSBOBDPNPTJHVF α 2@hdak $@hdajid 2@hdak $@6 





"IPSB QPEFNPT EFTQFKBS YS FO GVODJÓO EF YQ P WJDFWFSTB $PNP FT NÃT GÃDJM EFTQFKBS YS  BTÎ MP IBSFNPTBRVÎ 

mg 2

me Pme V  šhdak  &  šhdak eg  ee &R BP&  V  šhdak  &meR





&TUBFDVBDJÓOEFWFMPDJEBEEFUSBOTGFSFODJBSFQSFTFOUBMBWFMPDJEBEEFUSBOTGFSFODJBEFTPMWFOUFZ TPMVUPQPSMBNFNCSBOB FOVOJEBEFTEFGSBDDJÓOEFQFTP4J,"  TFSÃJOàOJUB YQTFSÃDFSP ZYSTFEFCFSÃEFUFSNJOBSDPOVOCBMBODFEFNBTB4JMBTFMFDUJWJEBEOPFTDPOTUBOUF  EFQFOEFSÃEF YX.YS&OUPODFTTFSÃDPOWFOJFOUF QBSBàOFTEFDÃMDVMP EFTQFKBSBYQFOGVODJÓOEFYS&TUBEFEVD DJÓOTFEFKBQBSBFMQSPCMFNB$

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMPTQSPDFTPTEFTFQBSBDJÓODPONFNCSBOB

-BFDVBDJÓO 

EFWFMPDJEBEEFUSBOTGFSFODJB TFEFCFSFTPMWFSFOGPSNBTJNVMUÃOFBDPO VOBFDVBDJÓOEFCBMBODFEFNBTB%FOVFWPTVQPOESFNPTRVFFMNÓEVMPEFMBNFNCSBOBFTUÃCJFO NF[DMBEP&MNÓEVMPFTJEÊOUJDPBMEFMBàHVSB" FYDFQUPRVFMPTUÊSNJOPTFOZTFTVTUJUVZFO QPSMBGSBDDJÓOFOQFTPFOFMMÎRVJEP-PTCBMBODFTEFNBTBFYUFSOPTQBSBFTUFNÓEVMPCJFONF[DMB EP FOVOJEBEFTEFQFTP TPO ′ !; Zci ′ mZci 2;e′me ;hVa ′ m hVa  ; Zci ′ 2;e′ ; hVa



B C

"MEFTQFKBSYQMMFHBNPTBMBFDVBDJÓOEFPQFSBDJÓO 

me 2−

&− u′ mhVa u′

mZci  u′



TJFOEP ' Q' FOUFTFMDPSUFFOVOJEBEFTEFNBTB-BFDVBDJÓO  FTBOÃMPHBBMBFDVBDJÓO  PCUFOJEBQBSBFMQFSNFBEPSEFHBTFTCJFONF[DMBEP &OFMNÓEVMPCJFONF[DMBEP YSFTDPOTUBOUF JHVBMBYTBM&OUPODFT MBFDVBDJÓO  FTWÃMJEB TJTFTVTUJUVZFBYSQPSYTBM4JOFNCBSHP DPNPOPSNBMNFOUFIBZQPMBSJ[BDJÓOEFDPODFOUSBDJÓO  YX.YTBMZTFEFCFEFUFSNJOBS.6OBWF[DPOPDJEB. TFQVFEFOSFTPMWFSTJNVMUÃOFBNFOUFMBT FDVBDJPOFT  Z 

BOBMÎUJDBNFOUF WFBFMFKFNQMP PHSBàDBOEPBNCBTFOVOTJTUFNB EFYQFOGVODJÓOEFYTBM-BFDVBDJÓO  FTVOBSFDUB JEÊOUJDBBMBMÎOFBEFPQFSBDJÓOPCUFOJEB QBSBMBQFSNFBDJÓOEFHBT-BDVSWBRVFSFQSFTFOUBBMBFDVBDJÓO  TFHSBàDBDBMDVMBOEPMPT WBMPSFTEFMBNJTNBNBOFSBRVFFOFMFKFNQMP0CTFSWFRVFFOVOBHSÃàDBEFYQDPOUSBYTBM FTUB DVSWBRVFEBSÃBCBKPEFMBMÎOFBYQYTBM &MQSPDFEJNJFOUPTFJMVTUSBSÃFOFMFKFNQMP àHVSB  EFTQVÊTEFIBCFSEFTDSJUPMPTNÊUPEPTQBSBEFUFSNJOBS. -PTEBUPTEFÓTNPTJTJOWFSTBQVFEFOQSFTFOUBSTFFOGPSNBEFMDPFàDJFOUFEFSFDIB[P3 

G2

m g − me me mhVa − me  2 2&− mg mhVa mhVa



4JTFDPOPDF3 MBFDVBDJÓO  FTMBEFWFMPDJEBEEFUSBOTGFSFODJBQBSBVOTJTUFNBEFÓTNPTJT JOWFSTBQFSGFDUBNFOUFNF[DMBEP4JTFDPOPDFOMPTWBMPSFTEFYFOU  Z3 TFQVFEFODBMDVMBSYQZYTBM SFTPMWJFOEPTJNVMUÃOFBNFOUFMBTFDVBDJPOFT  Z  $PNPFTUBTFDVBDJPOFTTPOMJOFBMFT FMQSPDFEJNJFOUPFTEJSFDUP&MDPFàDJFOUFEFSFDIB[PJOIFSFOUF RVFFTFMDPFàDJFOUFEFSFDIB[P DVBOEPOPIBZQPMBSJ[BDJÓOEFDPODFOUSBDJÓO .

UJFOFFMTÎNCPMP3P &+&.1-0 ¶TNPTJTJOWFSTBTJOQPMBSJ[BDJÓOEFDPODFOUSBDJÓO 4FFTUÃFOTBZBOEPVOBOVFWBNFNCSBOBDPNQVFTUBFOVOTJTUFNBEFNFNCSBOBQFSGFDUB NFOUFNF[DMBEP DPOVOBQSFTJÓOEFSFUFOUBEPEFBUNZVOBQSFTJÓOEFQFSNFBEPEF BUN$BMDVMFMBTGSBDDJPOFTFOQFTPBMBTBMJEBEFMBTDPSSJFOUFTEFQFSNFBEPZSFUFOUB EP)BZVODPFàDJFOUFNVZBMUPEFUSBOTGFSFODJBEFNBTBZ.&MDPFàDJFOUF BHVBTBM - LHBUN  TPMWLH- EFOTJEBEEFMBHVBQVSB  B   FOVOJEBEFTEFáVKPEFNBTB ZMBDPSSJFOUFRVFFOUSBUJFOFEFDMPSVSP EFTPEJP GSBDDJÓOFOQFTP C   FOVOJEBEFTEFáVKPEFNBTB ZMBDPSSJFOUFRVFFOUSBUJFOFEFDMPSVSP EFTPEJP GSBDDJÓOFOQFTP 4PMVDJÓO " %FGJOB$BMDVMFYQZYTBMQBSBMPTDBTPTB ZC 

www.FreeLibros.me

  ¶TNPTJTJOWFSTB



#Z$&YQMPSFZQMBOFF4FQVFEFOSFTPMWFSTJNVMUÃOFBNFOUFMBTFDVBDJPOFT  Z  QBSBDBMDVMBSYQZYTBM$PNPFMDBNCJPFOMBTDPOEJDJPOFTEFPQFSBDJÓOTÓMP BGFDUBMBFDVBDJÓO 

MBFDVBDJÓOEFWFMPDJEBEEFUSBOTGFSFODJBFTJHVBMQBSBMBT QBSUFTB ZC  % )ÃHBMP-BFDVBDJÓO 

EFWFMPDJEBEEFUSBOTGFSFODJBDPOVOJEBEFTEFQFTPFT mg 2



me Pme V  šhdak  &  šhdak eg  ee &R BP&  V  šhdak  &meR



SFQFUJEB



&MUÊSNJOPFTB FMDPFàDJFOUFMJOFBMQBSBFMFGFDUPEFMBDPODFOUSBDJÓOTPCSFMBQSFTJÓO PTNÓUJDB FOVOJEBEFTEFGSBDDJÓOEFQFTP&O1FSSZZ(SFFO ‰FEJDJÓO  1ÃH  BQBSFDFOMBTQSFTJPOFTPTNÓUJDBTQBSBTPMVDJPOFTBDVPTBTEFDMPSVSPEFTPEJP "ž$ZGSBDDJÓONPMBS MBQSFTJÓOPTNÓUJDBFTBUN&OUPODFT FOVOJEBEFT NPMBSFT BçBUNGSBDDJÓONPMBSBUNGSBDDJÓONPMBS



%FCFNPTQBTBSBçBB FOVOJEBEFTEFGSBDDJÓOFOQFTP B YPB BçNY EPOEFYFTMBGSBDDJÓONPMBS1BSBTPMVDJPOFTNVZEJMVJEBT



N 'SBDDNPMBSEFMTPMVUP  Y 'SBDDFOQFTPEFTPMVUP  1.BHVB  1.TPMVUP



:cidcXZh V ′ 2VS



-BFDVBDJÓO 

EFWFMPDJEBEEFUSBOTGFSFODJB TFQVFEFVTBSQBSBSFMBDJPOBSB YSDPOYQDPO.  - LHBUN

B BUN'SBDDFOQFTP  TPMW LH- QSBUNZQQBUN



b EB V\jV &-#%&+ 2VS 2*% 2&*#))+Vib$;gVXX#ZceZhd m *-#)* EB hdajid

mg 2

mepmeP%#(*&&*#))+%#.., &R %#(*&%#..,&% &#%P& P%#(*&&*#))+%#.., &RmeR

mg 2

mepme)#)%*(% )#&).*r & )#)%*(me

& &r

-BFDVBDJÓOFTDVBESÃUJDBFOYQTJOFNCBSHP DPNPYFOU MBTDPODFOUSBDJPOFTTPO CBKBTZTFQVFEFMJOFBMJ[BS6OQVOUPFTFMPSJHFO YS YQ"MTFMFDDJPOBSVOWBMPS QFRVFÒPEFYQRVFRVFEFFOMBSFHJÓOMJOFBM QPSFKFNQMP YQ

QPESFNPTEFàOJS VOBFDVBDJÓOMJOFBMBEFDVBEBEFWFMPDJEBEEFUSBOTGFSFODJB$POYQ TFPCUJFOF mgme 2%#%%)2

%#%%)p%#%%))#)%*( )#&).*r 2%#%&+(& )#)%*(%#%%)



-B QFOEJFOUF EF YS    YQ    B YS    YQ    FT YQ YS   −   − ZMBFDVBDJÓOMJOFBMJ[BEBFTYQYS



"IPSBSFTPMWFSFNPTTJNVMUÃOFBNFOUFMBFDVBDJÓOMJOFBMJ[BEBEFWFMPDJEBEEFUSBOTGF SFODJBZMBFDVBDJÓOEFPQFSBDJÓO MB 

PCTFSWBOEPRVFYSYTBMQBSBVOTFQBSB EPSQFSGFDUBNFOUFNF[DMBEP



1BSUFB $PNP ' Q' FOUZYFOU MBFDVBDJÓO  FTYQ  YTBM  

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMPTQSPDFTPTEFTFQBSBDJÓODPONFNCSBOB



&TUBFDVBDJÓOTFSFTVFMWFTJNVMUÃOFBNFOUFDPOMBFDVBDJÓOMJOFBMJ[BEBEFWFMPDJEBE EFUSBOTGFSFODJB-PTSFTVMUBEPTTPOYTBMZYQ



1BSUFC $PNP ZYFOU MBFDVBDJÓO  FT YQ−  YTBM 



&TUBFDVBDJÓOTFSFTVFMWFTJNVMUÃOFBNFOUFDPOMBFDVBDJÓOMJOFBMJ[BEBEFWFMPDJEBE EFUSBOTGFSFODJB MPTSFTVMUBEPTTPOYTBMZYQ & $PNQSVFCF-BTTPMVDJPOFTHSÃàDBT MBMJOFBMJ[BDJÓOGPSNBMZFMBKVTUFEFVOBSFDUBEF UFOEFODJB FOVOBIPKBEFDÃMDVMP MMFHBOFOFTFODJBBMPTNJTNPTSFTVMUBEPT ' (FOFSBMJDF &TUF FKFNQMP JMVTUSB DÓNP QSFEFDJS FM GVODJPOBNJFOUP EF VO TJTUFNB EF ÓTNPTJTJOWFSTBTJOQPMBSJ[BDJÓOEFDPODFOUSBDJÓO&OMVHBSEFMJOFBMJ[BSMBFDVBDJÓO EFWFMPDJEBEEFUSBOTGFSFODJB QPESÎBNPTIBCFSSFTVFMUPTJNVMUÃOFBNFOUFMBFDVBDJÓO DVBESÃUJDBEFWFMPDJEBEEFUSBOTGFSFODJBZMBFDVBDJÓOEFPQFSBDJÓOMJOFBM"MBTCB KBTDPODFOUSBDJPOFTRVFTFNBOFKBSPOFOFTUFFKFNQMP FMSFTVMUBEPTFSÃJEÊOUJDP FO FTFODJB$PNPMBQPMBSJ[BDJÓOEFDPODFOUSBDJÓOFTJNQPSUBOUFDPOGSFDVFODJB MBQSF EJDDJÓO DVBOEPMBUSBOTGFSFODJBEFNBTBOPFTFYUSFNBEBNFOUFSÃQJEB TFJOWFTUJHBFO FMFKFNQMP 16.4.2

Determinación experimental de las propiedades de las membranas

&TQPTJCMFVTBSWBMPSFTFYQFSJNFOUBMFTEFYQZYTBMQBSBEFUFSNJOBS "#1SJNFSPTFIBDFVOFYQF SJNFOUP DPO VOB DFMEB NVZ CJFO NF[DMBEB  CBKP DPOEJDJPOFT FO MBT RVF OP IBZB QPMBSJ[BDJÓO EF DPODFOUSBDJÓO%FTQFKBOEPMBTFMFDUJWJEBEEFMBFDVBDJÓO 

SFTVMUB 

2

& me Bmg me šhdakPeg

ee

me

Bmg

me V ′R





EPOEF CBKPMBTDPOEJDJPOFTEFMFYQFSJNFOUP .ZMPTEFNÃTUÊSNJOPTEFMMBEPEFSFDIPTFDPOP DFO&TUFNÊUPEPTFJMVTUSBFOFMFKFNQMP &+&.1-0 %FUFSNJOBDJÓOEFMBTQSPQJFEBEFTEFNFNCSBOBTQBSBÓTNPTJTJOWFSTB $POUJOVBNPTMBTQSVFCBTEFMBOVFWBNFNCSBOBDPNQVFTUBRVFTFVTÓFOFMFKFNQMP -PTEPTFYQFSJNFOUPTTFIJDJFSPODPOVOBQSFTJÓOEFBUNFOFMSFUFOUBEPZBUNFO FMQFSNFBEP-BUFNQFSBUVSBFTž$4FPCUVWJFSPOMPTEBUPTTJHVJFOUFT &YQFSJNFOUPB&MáVKPEFBHVBQVSBGVF- NEÎB  &YQFSJNFOUPC&OVOTJTUFNBQFSGFDUBNFOUFNF[DMBEPEFMBCPSBUPSJP DPOYFOUEF DMPSVSPEFTPEJP 'SBDDFOQFTP TFNJEJÓFMDPFàDJFOUFEFSFDIB[P3ZSFTVMUÓ-B PQFSBDJÓOGVFDPO &MTJTUFNBGVFNVZNF[DMBEPZTFQVFEFTVQPOFSRVFOPIVCP QPMBSJ[BDJÓOEFDPODFOUSBDJÓO .  $BMDVMFMPTQBSÃNFUSPTEFáVKPEFBHVBQVSBZMBTFMFDUJWJEBEBHVBTBM 4PMVDJÓO " %FGJOB$BMDVMF,TPMWUNTZ BHVBTBM #Z$&YQMPSFZQMBOFF&MFYQFSJNFOUPBOPTQFSNJUFDBMDVMBS,TPMWUNTDPOYSYQ DPO MBFDVBDJÓO D &MFYQFSJNFOUPCOPTQFSNJUFDBMDVMBSYQZYTBMDPOMBTFDVBDJPOFT  Z  &OUPODFT DPOMBFDVBDJÓO   DPOYSYTBMZ.

TFDBMDVMB MBTFMFDUJWJEBE BHVBTBM

www.FreeLibros.me

  ¶TNPTJTJOWFSTB



% )ÃHBMP&YQFSJNFOUPB$POYSYQ TFQVFEFEFTQFKBS,TPMWUNTEFMBFDVBDJÓO D  ? @hdak 2 V\jVejgV ibh eg − ee &%'.A $b' Y†V A @hdak 2 2,(#* &*#%− &#%Vib Vibb' Y†V  ibh

 

&YQFSJNFOUPC"MSFTPMWFSTJNVMUÃOFBNFOUFMBTFDVBDJPOFT  Z  PCUFOF NPT



me 2



&− GmZci  &− Gu′



ZDPOYQDPOPDJEP



mhVa 2





me &− G





4FTVTUJUVZFOMBTDBOUJEBEFTZSFTVMUB me 2

&− %#.-(%#%%'( 2%#%%%%**)* &− %#.-(%#(%

mhVa 2%#%%%%**)*$&− %#.-(2%#%%('+'



-BFDVBDJÓO  DPO.FT



V\jV"hVa



2

me Peg

& me mhVa me eVgVB2&  ee  mhVa meV′Ršhdak



EPOEFB BUN 'SBDDEFQFTP RVFTFEFUFSNJOÓFOFMFKFNQMPZMBEFOTJ EBEEFMTPMWFOUFFTLH-&OUPODFT MBTFMFDUJWJEBE TFQVFEFEFUFSNJOBSDPOMB FDVBDJÓO   aV\jV"hVa

2%#(*&

A `\Vib

& $PNQSVFCF-PTWBMPSFTOVNÊSJDPTFTUÃOEFOUSPEFJOUFSWBMPTSB[POBCMFT ' (FOFSBMJDF&TUFFKFNQMPJMVTUSBDÓNPEFUFSNJOBSWBMPSFTEFQBSÃNFUSPTDPOFYQFSJ NFOUPT-BTFMFDUJWJEBEEFUFSNJOBEBDPOFYQFSJNFOUPTTFVTÓFOFMFKFNQMPQBSB DBMDVMBS FM DPNQPSUBNJFOUP FTQFSBEP EF VO NÓEVMP EF NFNCSBOB  DVBOEP OP IBZ QPMBSJ[BDJÓOEFDPODFOUSBDJÓO  &M áVKP EF BHVB QVSB TF NJEF Z TF VTB DPO GSFDVFODJB QBSB DBMDVMBS FM WBMPS EF ,TPMWUNT&TVOPEFMPTNÊUPEPTQSFGFSJEPT QPSTFSNVZGÃDJMZSFQSPEVDJCMF5FOHB FODVFOUBRVFFMáVKPEJTNJOVZFFOGPSNBBQSFDJBCMFDVBOEPIBZQSFTFODJBEFTBM "TÎ OVODBTFEFCFOVTBSMPTWBMPSFTEFMáVKPEFBHVBQVSBDPNPFTUJNBDJÓOEJSFDUB EFMBDBQBDJEBEEFBMJNFOUBDJÓOEFMTJTUFNB  -PTEBUPTEFSFDIB[PTFVTBODPOGSFDVFODJBQBSBDBMDVMBSFMWBMPSEFMBTFMFDUJWJEBE  &TUBTFMFDUJWJEBEOPUJFOFFMNJTNPTJHOJàDBEPRVFMBTFMFDUJWJEBEFOMBQFS BHVBTBM NFBDJÓOEFHBTFT"RVÎ MBTFMFDUJWJEBETFEFàOFDPOMBFDVBDJÓO 

QFSPMBT

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMPTQSPDFTPTEFTFQBSBDJÓODPONFNCSBOB

QFSNFBCJMJEBEFTTFSFàFSFOBFDVBDJPOFTDPOEJTUJOUBTGVFS[BTJNQVMTPSBTZUJFOFO EJTUJOUBTVOJEBEFT"TÎ VOB NFOPSRVFOPRVJFSFEFDJSRVFTFUSBOTàFSBMBTBM FOGPSNBQSFGFSFOUFQPSMBNFNCSBOB 16.4.3

Determinación de la polarización de concentración

6OBWF[RVFTFDPOPDFOMPTWBMPSFTEF QVFEFOIBDFSTFFYQFSJNFOUPTDVBOEPTFFTQFSBRVFIBZB QPMBSJ[BDJÓOEFDPODFOUSBDJÓO.TFEFUFSNJOBEFTQFKÃOEPMBEFMBFDVBDJÓO   

B2

mePme Všhdak&  šhdakegee &R  mgP&  Všhdak&meR



5PEPTMPTUÊSNJOPTEFMMBEPEFSFDIPTFDPOPDFOZTFQVFEFDBMDVMBS.-BFTUJNBDJÓOEF.OPT QFSNJUJSÃFWJUBSMMFWBSBDBCPFYQFSJNFOUPTDPTUPTPTZUBSEBEPT&TUPTFJMVTUSBFOFMFKFNQMP &OMBàHVSBTFNPTUSÓVOFTRVFNBEFMBQPMBSJ[BDJÓOEFDPODFOUSBDJÓO&TUBàHVSBSF QSFTFOUBMBTJUVBDJÓONÃTTFODJMMB RVFFTEJGVTJÓODPOUSBSJBEFFTUBEPFTUBCMFZVOJEJNFOTJPOBMEFM TPMVUPBMJOUFSJPSEFMBDPSSJFOUFEFSFUFOUBEP DPOVOBNFNCSBOBRVFSFDIB[BQFSGFDUBNFOUF 3  &MCBMBODFEJGFSFODJBMEFNBTBQBSBFTUFDBTPTJNQMFFT QSPCMFNB$



?hdakm 9

Ym 2%  Yo



EPOEF%FTMBTPMVCJMJEBEFOMBTPMVDJÓOMÎRVJEB&TUBFDVBDJÓOFTUÃTVKFUBBDPOEJDJPOFTFOMBGSPO UFSBMBDPODFOUSBDJÓOFTJHVBMBMBDPODFOUSBDJÓOFOMBQBSFEDVBOEP[ 

YYXFO[

B

ZMBDPODFOUSBDJÓOFTJHVBMBMBDPODFOUSBDJÓOYSFOFMJOUFSJPS DVBOEP[FTNBZPSRVFFMFTQFTPSEF MBDBQBMJNÎUSPGF  &MWBMPSEF EFQFOEFEFMBTDPOEJDJPOFTEFPQFSBDJÓO DPNPHFPNFUSÎB WFMP DJEBEZ5 

YYSFO[  

C

4JTFEFàOFFMDPFàDJFOUFEFUSBOTGFSFODJBEFNBTBDPNP 

L% 



MBTPMVDJÓOFT 

B2

ml 2Zme?hdak $`  mg



&MDPFàDJFOUFEFUSBOTGFSFODJBEFNBTBEFQFOEFEFMBTDPOEJDJPOFTEFPQFSBDJÓOZUJFOFMBTNJTNBT VOJEBEFTRVF+TPMW &TUFEFTBSSPMMPFTÙUJMQBSBEFUFSNJOBSMPRVFBGFDUBMBQPMBSJ[BDJÓOEFDPODFOUSBDJÓO4JBVNFOUB FMáVKPEFTPMWFOUF+TPMW .BVNFOUB4JBVNFOUBFMDPFàDJFOUFLEFUSBOTGFSFODJBEFNBTB MBQPMB SJ[BDJÓOEFDPODFOUSBDJÓOEFDSFDF"MBVNFOUBSMBEJGVTJWJEBEBVNFOUBL"TÎ BMPQFSBSBNBZPS UFNQFSBUVSBEJTNJOVZF. BVORVFIBZMÎNJUFTPCWJPTQPSMBFTUBCJMJEBEUÊSNJDBEFMBNFNCSBOBZ MBFTUBCJMJEBEUÊSNJDBEFMBTQSPUFÎOBT1PSFKFNQMP MBNBZPSQBSUFEFMBTQSPUFÎOBTOPUJFOFOFTUB CJMJEBEUÊSNJDB"MEJTNJOVJSFMFTQFTPS EFMBDBQBMJNÎUSPGFDVBOEPBVNFOUBMBUVSCVMFODJBZTF PQFSBBUBTBTDPSUBOUFTFODBOBMFTFTUSFDIPTPUVCPTBOHPTUPT UBNCJÊOBVNFOUBSÃL

www.FreeLibros.me

  ¶TNPTJTJOWFSTB



&MVTPDVBOUJUBUJWPEFMBFDVBDJÓO  SFRVJFSFWBMPSFTEFMDPFàDJFOUFEFUSBOTGFSFODJBEF NBTB  RVF TF EFUFSNJOFO FYQFSJNFOUBMNFOUF P CJFO DPO VOB DPSSFMBDJÓO QBSB L RVF FO ÙMUJNP UÊSNJOPTFCBTBFOEBUPTFYQFSJNFOUBMFT 4JTFEJTQPOFEFEBUPTFYQFSJNFOUBMFTRVFQFSNJUBOFM DÃMDVMPEF.DPOMBFDVBDJÓO 

FOUPODFTTFQVFEFVTBSMBFDVBDJÓO  QBSBEFUFSNJOBS L )BZ EJTQPOJCMF VOB HSBO DBOUJEBE EF DPSSFMBDJPOFT QBSB USBOTGFSFODJB EF NBTB QBSB EJWFSTBT DPOEJDJPOFTEFHFPNFUSÎBZEFáVKP 8BOLBUZ,OBFCFM  $VBUSPEFFMMBT RVFTFVTBOFOMPT TFQBSBEPSFTEFNFNCSBOB TPOMBTDPSSFMBDJPOFTQBSBFMáVKPUVSCVMFOUPFOUVCPT QBSBáVKPMBNJOBS FOUVCPTZFOUSFQMBDBTQBSBMFMBTZQBSBUBORVFTCJFONF[DMBEPT #MBUUFUBM 8BOLBU  8BOLBUZ,OBFCFM  1BSBFMGMVKPUVSCVMFOUPFOUVCPT FMDPFàDJFOUFEFUSBOTGFSFODJBEFNBTB TFQVFEFDBMDVMBSDPO 

H]2

Y i` 2%#%'(GZ%#-(HX&$(![aj_dijgWjaZcid  9

B

EPOEF4IFTFMOÙNFSPEF4IFSXPPE-PTOÙNFSPTEF3FZOPMET 3F ZEF4DINJEU 4D TFEFàOFO DPNPTJHVF GZ2YijW š$μ!HX 2μ$š9 



C D

ZVCFTMBWFMPDJEBEQSPNFEJPFOFMUVCP&TTFHVSPRVFFMáVKPUPUBMNFOUFUVSCVMFOUPPDVSSBDVBOEP 3F ZTVFMFBQBSFDFSFOBQBSBUPTEFVMUSBàMUSBDJÓODPO3F 1BSBFMGMVKPMBNJOBSFOVOUVCPEFMPOHJUVE-ZSBEJP3 DPOWFMPDJEBEQSPNFEJPVC FMDPFà DJFOUFNFEJPEFUSBOTGFSFODJBEFNBTBFT 

`2&#'.*

jW9' GA

&$(



B

1BSBFMGMVKPMBNJOBSFOUSFQMBDBTQBSBMFMBTBMBEJTUBODJBEFI FMDPFàDJFOUFNFEJPEFUSBOTGFSFODJB EFNBTBFT 

`2&#&,,

jW9' ]A

&$(



C

1BSBNFNCSBOBTQMBOBTFOVOUBORVFUVSCVMFOUPCJFOBHJUBEP TFQVFEFFTUJNBSFMDPFàDJFOUFEF USBOTGFSFODJBEFNBTBDPO 

`YiVcfjZ 9

2%#%))((

' ωYiVcfjZ

k

%#,*

HX%#(( 

B

EPOEFLFTUÃFODNT  FTMBWFMPDJEBEEFMBHJUBEPSFOSBEJBOFTT EUBORVFFTFMEJÃNFUSPEFMUBORVF  FODN %FTMBEJGVTJWJEBE FODNTZMBWJTDPTJEBEDJOFNÃUJDBFT   -PTUBORVFTBHJUBEPTTPO VOBDPOàHVSBDJÓOBEFDVBEBFOFMMBCPSBUPSJP &+&.1-0 ¶TNPTJTJOWFSTBDPOQPMBSJ[BDJÓOEFDPODFOUSBDJÓO $POUJOVBSFNPTFOTBZBOEPMBOVFWBNFNCSBOBDPNQVFTUBEFMPTFKFNQMPTZ4F IJ[PVOFYQFSJNFOUPNÃTBž$ DPOVOBQSFTJÓOFOFMSFUFOUBEPEFBUNZQSFTJÓOFO QFSNFBEPEFBUN"EFNÃTEFMPTEBUPTJOEJDBEPTFOFMFKFNQMP TFPCUVWJFSPOMPT TJHVJFOUFTEBUPTOVFWPT

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMPTQSPDFTPTEFTFQBSBDJÓODPONFNCSBOB

&YQFSJNFOUPD4FIJDJFSPOEFUFSNJOBDJPOFTFOVOTJTUFNBEFUBORVFBHJUBEPEFDNEF EJÃNFUSPDPONBNQBSBT4FFTQFSBRVFTFBWÃMJEBMBFDVBDJÓO B QFSPEFCFBKVTUBSTF FMDPFàDJFOUF&MBHJUBEPSUSBCBKÓBSQN-BTPMVDJÓOFOMBFOUSBEBUVWP EFDMPSVSPEFTPEJP GSBDDJÓOFOQFTP-BTGSBDDJPOFTFOQFTPNFEJEBTGVFSPOYQ ZYTBM $POCBTFFOFTUPTFYQFSJNFOUPT EFUFSNJOFFMWBMPSEFMDPFàDJFOUFFOMBDPSSFMBDJÓOQBSB USBOTGFSFODJBEFNBTBFOUBORVFTBHJUBEPTUVSCVMFOUPT FDVBDJÓOB  4PMVDJÓO " #Z$%FGJOB FYQMPSFZQMBOFF1PESFNPTDBMDVMBSFMNÓEVMPEFQPMBSJ[BDJÓO.DPOMB FDVBDJÓO 

+TPMWDPOMBFDVBDJÓO D

FMWBMPSEFMDPFàDJFOUFEFUSBOTGFSFODJB EFNBTBDPOMBFDVBDJÓO  ZVOOVFWPDPFàDJFOUFQBSBMBDPSSFMBDJÓOFOMBFDVB DJÓO B  % )ÃHBMP&YQFSJNFOUPD$PNPTFNJEJFSPOYQZYTBMZTFDPOPDFO B QSZQQ TFTVTUJ UVZFOEJSFDUBNFOUFMPTWBMPSFTFOMBFDVBDJÓO   B2

B2

 

mePmeαV′šhdak−& αšhdakeg−ee &R mgP& αV′šhdak−&meR

%#%%&)*p%#%%&)*P%#(*&&*#))+%#..,−&R %#(*&%#..,&) &r 2&#'&%#%%+.-*p& P%#(*&&*#))+%#..,−&R%#%%&)*r

&OUPODFT TFDBMDVMBFMáVKPEFTPMWFOUFDPOMBFDVBDJÓO D

VTBOEP,TPMWUNT  RVFTFEFUFSNJOÓFOFMFKFNQMP ZDPNPYSYTBMQBSBVOUBORVFCJFONF[DMBEP  ?hdak 2



Zh^\jVaV!

@hdak Peg  eg  VBmg  meR Zh^\jVaV ibh

?hdak 2,(#*p&* & &*#))+P&#'&-%#%%+.-* %#%%&)*Rr2&%'%#..A $b' Y†V



0CTFSWFRVFFTUBDBOUJEBEFTVOQPDPNFOPSRVFFMáVKPEFBHVBQVSB QPSRVFMBEJGF SFODJBEFQSFTJPOFTPTNÓUJDBTSFEVDFMBGVFS[BJNQVMTPSB



"MEFTQFKBSLEFMBFDVBDJÓO  SFTVMUB



`2?hdak$acB2.)-#*+$ac&#'&-2)-%.#.A $b' Y†V2%#%%**+,Xb$h#



-B FDVBDJÓO B  TF QVFEF FTDSJCJS DPO VOB DPOTUBOUF EFTDPOPDJEB  FO MVHBS EF &TBDPOTUBOUFTFEFTQFKBZRVFEB



8dchiVciZ2



`YiVcfjZ 9

ωYiVcfjZ k

−%#,*

μ š9

−%#((



C

$PNPMBTPMVDJÓOFTCBTUBOUFEJMVJEB TFQVFEFOVTBSMBTQSPQJFEBEFTEFMBHVB š2%#..,\$Xb(!μ2&#%Xe2%#%&ed^hZ2%#%&\Xb$h ω2.%%geb



'xgVY^VcZh &b^c 2.)#'*gVY^VcZh$h gZkdajX^‹c +%h

-B EJGVTJWJEBE EFM /B$M FO BHVB B ž$ FT × − DNT 4IFSXPPE FU BM    QÃH   4F QVFEF FTUJNBS % B ž$ TVQPOJFOEP RVF MB EFQFOEFODJB SFTQFDUP B MB

www.FreeLibros.me

  ¶TNPTJTJOWFSTB



UFNQFSBUVSBFTMJOFBMZEFTQVÊTEFUFSNJOBSFMWBMPSFYQFSJNFOUBMEFMBDPOTUBOUF DPO MBFDVBDJÓO C  9CV8&'*°82&#&,×&%−*

'.-#&+ 2&#'%×&%−*Xb'$h '.&#&+

Xb &'Xb h &#'%×&%−*Xb'$h

%#%%**+, 8dchiVciZ2



%#%&%\Xb$h \ Xb' −* &#'%×&% %#.., h Xb(

%#..,

\ gVY &'Xb' .)#'* Xb( h %#%&%\Xb$h

−%#,*

×

−%#((

2%#%&*(

& $PNQSVFCF1BSBVOBCVFOBDPSSFMBDJÓOEFUSBOTGFSFODJBEFNBTB FTUPTFBDFSDBSB[P OBCMFNFOUFBMWBMPSQVCMJDBEPEF6TBSFNPTFMWBMPSNFEJEPEFMBDPOTUBOUF QBSBDBMDVMBSMBPQFSBDJÓOFOFMFKFNQMP ' (FOFSBMJDF&TUFFKFNQMPJMVTUSBDÓNPTFQVFEFOTFMFDDJPOBSMPTEBUPTFYQFSJNFOUBMFT ZIBDFSBKVTUFTàOPTFOMBTDPSSFMBDJPOFTEFUSBOTGFSFODJBEFNBTB BKVTUBOEPMBTDPOT UBOUFT &OFMFYQFSJNFOUPDTFOFDFTJUBSPOWBSJPTQBTPTQBSBMMFHBSBMDPFàDJFOUFEFUSBOTGFSFODJBEFNBTBL ­TUFFTFMDBTPJOWBSJBCMF QPSRVFLOPFTVOBWBSJBCMFRVFTFNJEBFOGPSNBEJSFDUB TJOPRVFEFQFO EFEFMBJOUFSQSFUBDJÓOEFEBUPTVTBOEPVONPEFMP6OBWF[PCUFOJEPL TÓMPDPOUBNPTDPOVOEBUP FYQFSJNFOUBMQBSBDPNQBSBSMPDPOMBDPSSFMBDJÓO FDVBDJÓO B /PDPODPSEBSPO6TUFETFTFO UJSÃUFOUBEPBVTBSMBDPSSFMBDJÓO DPONÃTEFVOEBUPFYQFSJNFOUBM4JOFNCBSHP MBTDPSSFMBDJPOFT EFUSBOTGFSFODJBEFNBTBOPTPONVZFYBDUBT4VFMFOJOEJDBSCJFOMBTUFOEFODJBT DPNPFMFGFDUPEF MPTOÙNFSPTEF3FZOPMETZEF4DINJEU

QFSPFMWBMPSBCTPMVUPDBMDVMBEPQVFEFEJGFSJSNVDIP4F QVFEFVTBSVOTPMPEBUPQBSBBKVTUBSMBDPOTUBOUFFOMBDPSSFMBDJÓO QBSBBQMJDBSMBBFTUFTJTUFNBFO QBSUJDVMBS4JIVCJFSBEJTQPOJCMFTNÃTEBUPT QPESÎBNPTDPNQSPCBSUPEBMBDPSSFMBDJÓO &+&.1-0 $  ÃMDVMPEFMBPQFSBDJÓOEFÓTNPTJTJOWFSTBDPOQPMBSJ[BDJÓO EFDPODFOUSBDJÓO $BMDVMFMPTWBMPSFTEFYQ YTBMZ+TPMW TJFOMBNFNCSBOBRVFTFFTUVEJÓFOMPTFKFNQMPT BTFTFQBSÓVOBGSBDDJÓOEFQFTPEFEFDMPSVSPEFTPEJPFOBHVB FOVOUBORVF BHJUBEPRVFFTHFPNÊUSJDBNFOUFTJNJMBSBMEFMFKFNQMP FYDFQUPRVFUJFOFDNEF EJÃNFUSPZMBWFMPDJEBEEFMBHJUBEPSFT SQN-BQSFTJÓOFOFMSFUFOUBEPFTBUNZMB EFMQFSNFBEPFTBUN4FUSBCBKBBVODPSUF ZBž$ 4PMVDJÓO " #Z$%FGJOB FYQMPSFZQMBOFF4FSFRVJFSFDBMDVMBSQSJNFSPLDPOMBFDVBDJÓO B  VTBOEP MB DPOTUBOUF NPEJàDBEB &O FTUF QVOUP TF DPNQMJDB MB TPMVDJÓO 1BSB EFUFS NJOBS.DPOMBFDVBDJÓO  EFCFNPTDPOPDFS+TPMW RVFTFQVFEFDBMDVMBSDPOMB FDVBDJÓO D TJTFDPOPDJFSBYSYTBM YQZ.$PNPTFFTQFDJàDBFMDPSUF TF DBMDVMBSÎBOYTBMZYQSFTPMWJFOEPTJNVMUÃOFBNFOUFMBTFDVBDJPOFT  Z 

TJ TFDPOPDJFSB.&TUFDÎSDVMPTFQVFEFJOUFSSVNQJSVTBOEPVONÊUPEPEFUBOUFPT6OB GPSNBSFMBUJWBNFOUFDÓNPEBEFIBDFSMBQSVFCBZFSSPS EPOEFTFSFRVJFSFNBOJQVMBS MBTFDVBDJPOFT TFJMVTUSBFOMBTFDDJÓO)ÃHBMP

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMPTQSPDFTPTEFTFQBSBDJÓODPONFNCSBOB

% )ÃHBMP:BRVFMBTPMVDJÓOUPEBWÎBFTNVZEJMVJEB VTBSFNPTMBTQSPQJFEBEFTEFMBHVB ZMBEJGVTJWJEBEPCUFOJEBFOFMFYQFSJNFOUPD-BEJàDVMUBEEFFTUFDÃMDVMPFTRVFUP EBTMBTWBSJBCMFTOFDFTBSJBTTFSFRVJFSFOQBSBFMDÃMDVMPEFFMMBTNJTNBT-BDVSWBEF WFMPDJEBEEFUSBOTGFSFODJBEFQFOEFEF. ZTJTFHSBàDBDPNPYSFOGVODJÓOEFYQ TF EFCFSÃWPMWFSBUSB[BSQBSBDBEBWBMPSEF.6OBBMUFSOBUJWBFTBDPNPEBSMBFDVBDJÓO  DPNPTJHVF 

Bmg2me



PαšhdakV′−&me αšhdakeg−ee &R  αšhdakV′−&me &



"IPSB VOBHSÃàDBEFYQDPOUSB .YS  .YTBM TFSÃVOBTPMBDVSWB&ODPSSFTQPOEFO DJBBFTUBOVFWBHSÃàDB PSEFOBSFNPTMBFDVBDJÓO 

EFPQFSBDJÓO FOMBGPSNB



me 2−

&− u′ BmhVa  Bu′

mZci  u′





&OVOBHSÃàDBEFYQFOGVODJÓOEF .YTBM FTVOBSFDUBDPOQFOEJFOUF−Z FMDSVDFDPOYQ .YTBM FTYQYFOU 

  

)BCSÃRVFWPMWFSBHSBàDBSMBFDVBDJÓOEFPQFSBDJÓODBEBWF[RVFDBNCJF. -BJOUFSTFDDJÓODPO .YTBM FO YQ FT .YTBM .YFOU −  $POMBFDVBDJÓO  TFQVFEFOHFOFSBSMPTWBMPSFTQBSBGPSNBSVOBUBCMB BmhVa 2me dBm hVa 2



P%#(*&%#..,&*#))+−&Rme %#(*&%#..,&%−& & P%#(*&%#..,&*#))+−&Rme &

P)#)%*(me )#&).*Rme P)#)%*(me &R me % %#%%( %#%%* %#%&





BmhVa % %#%&'( %#%'%) %#%)%'

&TUFDÃMDVMPTFMMFWBBDBCPTÓMPFOFTUBTDPOEJDJPOFTEJMVJEBT QPSRVFMBBMJNFOUBDJÓO FTNVZEJMVJEB-BMÎOFBEFPQFSBDJÓO FDVBDJÓO 

UFOESÃ eZcY^ZciZ2−

&−%#) &#* !^ciZghZXX^‹cXdcme2%#%&$%#)%2%#'*# 2− %#)B B



-BJOUFSTFDDJÓODPO.YTBM YQ FT. − .



$PNPQSJNFSWBMPSUFOUBUJWPVTBSFNPT. VOQPDPNFOPSRVFFMWBMPSNFEJEP BOUFSJPS-PTSFTVMUBEPTTFWFOFOMBàHVSB



1FOEJFOUFEFMBMÎOFBEFPQFSBDJÓO−−ZFMDSVDFDPO.YTBM YQ FT 

  

4PMVDJÓODPO. EFMBàHVSB YQ .YTBM 1PSDPOTJHVJFOUF YTBM .YTBM . -BFDVBDJÓO D TFUSBOTGPSNBFO

www.FreeLibros.me

  ¶TNPTJTJOWFSTB

%#%'*



meBmhVa 2%2

mZci a a ;e$;Zci 

2%#%'*

%#%'% me %#%&* B2&#' B2&#%,() %#%&%

BmhVa 2%#%&+,

%#%%* me2%#%%(, %

me2%#%%)&

BmhVa 2 %#%&*'

%

%#%%*

%#%&*

%#%&

%#%'%

8jgkV YZKZa# IgVch[# %#%'*

BmhVa

'*(63" 40-6$*¶/4*.6-5¦/&"%&-"$637"%&7&-0$*%"%%& 53"/4'&3&/$*":-"-±/&"%&01&3"$*¶/ 1"3"&-&+&.1-0 ?hdak 2,(#*P&%− &− &*#))+%#%&+,− %#%%)&R2+),#&A $b'Y†V



$POMBFDVBDJÓO  TFPCUFOESÃFMWBMPSDBMDVMBEPEF. VOBWF[EFUFSNJOBEBL DPOMBFDVBDJÓO 

VTBOEPFMDPFàDJFOUFFODPOUSBEPFOFMFYQFSJNFOUPD6TBSF NPT%  Z EFMFYQFSJNFOUPD ω2&*%%geb `2

'xgVY^VcZh &b^c 2&*,#%-gVY^VcZh$h gZkdajX^‹c +%h

%#%&*(&#'%×&%−* '%

%#..,'%'&*,#%- %#%&%

%#,*

%#%&% %#...&#'%×&%−*

%#((



`2%#%&%+Xb$h2.&)%#-A$b'Y†V



"IPSBQPESFNPTDBMDVMBS.DPOMBFDVBDJÓO  ZWFSJàDBSOVFTUSPWBMPSUFOUBUJWP

   

BXVaX 2Zme+),#&$.&)%#-2&#%,() BXVaX  BiZciVi^kd#

4FOFDFTJUBVOWBMPSNFOPS1SPCBSFNPTMBTVTUJUVDJÓOEJSFDUBVTBOEPFMWBMPSDBMDVMB EP . /VFWBMÎOFBEFPQFSBDJÓOQFOEJFOUF−− *OUFSTFDDJÓODPO.YTBM  

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMPTQSPDFTPTEFTFQBSBDJÓODPONFNCSBOB



&OUPODFT EFMBàHVSB YQ .YTBMZYTBM



+TPMW EFMBFDVBDJÓO D

FT ?hdak 2,(#*P&%− &− &*#))+%#%&*'− %#%%(,R2+)-#(A $b'Y†V



:BRVFLOPDBNCJÓ MBFDVBDJÓO  SFTVMUBFO BXVaX 2Zme+)-#($.&)%#-2&#%,(*



&OFTFODJB FTUFWBMPSEF.DBMDFTJEÊOUJDPBMWBMPSUFOUBUJWP&OUPODFT VTBS.



-PTWBMPSFTDBMDVMBEPTTFSÃO +TPMW-NEÎB YQ 'SBDDFOQFTPZYTBM 'SBDDFOQFTP

& $PNQSVFCF-PTSFTVMUBEPTPCUFOJEPTDPJODJEFODPOOVFTUSBTFYQFDUBUJWBT&TVOBWF SJàDBDJÓO ÙUJM Z SÃQJEB  QFSP OP HBSBOUJ[B RVF OP IBZB FSSPSFT 5BNCJÊO TF QVFEFO WFSJàDBSMPTSFTVMUBEPTQBSBFMDBTPMÎNJUFFORVF. DPOMPTSFTVMUBEPTPCUFOJEPT FOFMFKFNQMPQBSBMBNJTNBDPODFOUSBDJÓOEFMBBMJNFOUBDJÓO NJTNBTQSFTJPOFT ZDPSUFRVFFOFTUFQSPCMFNB YTBMZYQ &OMBàHVSB DVBOEP . MBJOUFSTFDDJÓOEFMBMÎOFBEFPQFSBDJÓO OPTFNVFTUSBQBSB. DPOMBMÎOFB EFWFMPDJEBEEFUSBOTGFSFODJBFTUÃFOYTBMZYQ-BDPODPSEBODJBFT CBTUBOUFCVFOB ' (FOFSBMJDF-PTDÃMDVMPTEFMBPQFSBDJÓOGVFSPOQPSQSVFCBZFSSPS QPSRVFTFOF DFTJUBSPO MBT WBSJBCMFT EFTDPOPDJEBT QBSB DBMDVMBS PUSBT JODÓHOJUBT  RVF B TV WF[ TF OFDFTJUBSPOQBSBDBMDVMBSMBTQSJNFSBTJODÓHOJUBT&TUFDÎSDVMPTFSPNQFQSPQPOJFOEP VOBWBSJBCMF IBDJFOEPMPTDÃMDVMPTZEFTQVÊTWFSJàDBOEPFMWBMPSQSPQVFTUP$POFM NÊUPEPHSÃàDP BMWPMWFSBUSB[BSMBTPMVDJÓOQBSBVOTJTUFNBCJFONF[DMBEPTFTJNQMJ àDBSPOMPTUBOUFPT-BDPOWFSHFODJBGVFSÃQJEB&OTJTUFNBTNÃTDPODFOUSBEPTPDPO BHJUBDJÓONFOPTWJHPSPTBZWBMPSFTEF.Z NVDIPNBZPSFT RVFQVFEFOTFSGVODJP OFTOPMJOFBMFTEFMBGSBDDJÓOFOQFTP

MBDPOWFSHFODJBQVFEFTFSNÃTMFOUB  &MDÃMDVMPTFQVFEFIBDFSUBNCJÊOFOVOBIPKBEFDÃMDVMPVTBOEP4PMWFSQBSBMMFHBSB VOBTPMVDJÓOTJNVMUÃOFBEFMBTFDVBDJPOFT&OUPODFT MBTPMVDJÓOHSÃàDBFTVOBDPN QSPCBDJÓONVZDÓNPEB QPSRVF.TFDPOPDFDPOMBTPMVDJÓOFOMBIPKBEFDÃMDVMP  )VCPNFOPTQPMBSJ[BDJÓOEFDPODFOUSBDJÓOFOFMTJTUFNBNBZPSRVFFOFMFYQFSJ NFOUPD QPSRVFFMDPFàDJFOUFEFUSBOTGFSFODJBEFNBTBGVFBQSFDJBCMFNFOUFNBZPS  DPNQBSBEPDPO &MNBZPSOÙNFSPEF3FZOPMET NBZPSEJÃNFUSPZ NBZPS DBVTÓFMNBZPSWBMPSEFL  -BÓTNPTJTJOWFSTBTFVTBOPSNBMNFOUFQBSBQSPEVDJSBHVBVMUSBQVSBQBSBMBTJOEVT USJBTFMFDUSÓOJDBZGBSNBDÊVUJDB&OFTBTBQMJDBDJPOFT 3PTFBDFSDBNVDIPNÃTB ZYFOUFTNFOPS&TUPTTJTUFNBTUJFOFOQPDBQPMBSJ[BDJÓOEFDPODFOUSBDJÓO .  Z QSPEVDFOVOQFSNFBEPNVZQVSP  &OUPEPTFTUPTDÃMDVMPTTFTVQPOFRVFMBNFNCSBOBOPFTUÃEBÒBEBZOPUJFOFBHV KFSPT"ÙOVOBQJDBEVSBEJNJOVUBQVFEFDBVTBSVOHSBOBVNFOUPFOYQ&MMÎRVJEP QBTBSÃQPSVOBHVKFSPFOáVKPDPOWFDUJWP DPOVOBDPODFOUSBDJÓOEFTBMYX&TUFáVKP TFSÃ CBTUBOUF HSBOEF  EFCJEP B MB HSBO DBÎEB EF QSFTJÓO "EFNÃT  UBNCJÊO QVFEF IBCFSNPMÊDVMBTHSBOEFTOPEFTFBEBTRVFQBTFOQPSMPTBHVKFSPTFOMBNFNCSBOB&M GVODJPOBNJFOUPEFMPTTJTUFNBTEFÓTNPTJTJOWFSTBEFCFWJHJMBSTFFOGPSNBDPOUJOVB ZMBTNFNCSBOBTEBÒBEBTTFEFCFOPCUVSBSPDBNCJBS

www.FreeLibros.me

  6MUSBGJMUSBDJÓO



 -BEVSBDJÓOEFMBNFNCSBOBEFQFOEFSÃEFTVNBUFSJBMZEFMBTDPOEJDJPOFTEFPQF SBDJÓO&OMPTHBTUPTEFPQFSBDJÓOTFEFCFOJODMVJSMPTDPTUPTEFSFQPTJDJÓOEFMBT NFNCSBOBT  4JVODBTPMÎNJUFOPDPODVFSEBDPOVODÃMDVMPJOEFQFOEJFOUF EFCFIBCFSVOFSSPS FOFMDÃMDVMPPSJHJOBM FOFMNÊUPEPQBSBPCUFOFSFMDBTPMÎNJUFPFOFMDÃMDVMPJOEF QFOEJFOUF4JFMDBTPMÎNJUFDPODVFSEBDPOVODÃMDVMPJOEFQFOEJFOUF DPNPTVDFEF FOFTUFQSPCMFNBQBSB.

OPIFNPTEFNPTUSBEPRVFTFBDPSSFDUPFMDÃMDVMP QBSBDVBOEP. "MBVNFOUBSMBDBOUJEBEEFDBTPTMÎNJUFRVFDPODVFSEBODPOMPT DÃMDVMPTJOEFQFOEJFOUFT BVNFOUBOVFTUSBDPOàBO[BFOMBTPMVDJÓOHFOFSBM  &OFMFOVODJBEPEFMQSPCMFNBTFJOEJDÓRVFMPTUBORVFTTPOHFPNÊUSJDBNFOUFTJ NJMBSFT4JOPMPTPO QSPCBCMFNFOUFMBDPOTUBOUF FOMBDPSSFMBDJÓOEFUSBOTGFSFO DJBEFNBTB FDVBDJÓO B

TFSÃEJGFSFOUFFOMPTEPTUBORVFT-BTJNJMBSJEBE HFPNÊUSJDBFTMPRVFQFSNJUFFTDBMBSMPTFRVJQPT 16.4.4

Ósmosis inversa con soluciones concentradas

6OBTJUVBDJÓONÃTDPNQMJDBEBFTMBRVFTFQSFTFOUBDVBOEPYSZFODPOTFDVFODJBYX TPODPODFO USBEBTZMBQSFTJÓOPTNÓUJDBEFQFOEFEFYQFOVOBGPSNBOPMJOFBM4FQVFEFEFEVDJSVOBFDVBDJÓO BWBO[BEBEFWFMPDJEBEEFUSBOTGFSFODJBTJMBQSFTJÓOPTNÓUJDBEFMQFSNFBEPFTMJOFBMFOYQ FTEFDJS  BYQ:BRVFFMQFSNFBEPFTCBTUBOUFEJMVJEP FTUBFDVBDJÓOFTWÃMJEBDPOGSFDVFODJB BVODVBOEP Q OPTFBVOBGVODJÓOMJOFBMEFYFOYFOUZYTBM4FQBSUFEFMBFDVBDJÓO B ZTFTVTUJUVZFOFOFMMB YX.YSZ Q YQ B YQ4FEFTQFKB' QEFMBFDVBDJÓOSFTVMUBOUFZEFMBàHVSB 

TFJHVBMBOZ TFPSEFOBOMPTUÊSNJOPT 

šhdakAmePeg ee xBmg Va meR2& meBmg me 

B

4VQPOESFNPTRVFMBQSFTJÓOPTNÓUJDB .YS TFDPOTJHVFFOGPSNBUBCVMBSPEFFDVBDJÓO4FEFTB SSPMMBFOUÊSNJOPTEFYQZTFBHSVQBOMPTUÊSNJOPT 

šhdakAV a &me' PšAeg ee š AxBmg & Bmgme Bmg 2% 

C

4JFTDPHFNPTVOWBMPSEF.YSQPESFNPTEFUFSNJOBS .YQ ZDBMDVMBSYQ%FTQVÊTTFQPESÃHFOFSBS MBDVSWB35 JODMVZFOEPMBQSFTJÓOPTNÓUJDBOPMJOFBMZMBQPMBSJ[BDJÓOEFDPODFOUSBDJÓO4JFMNÓ EVMPEFNFNCSBOBFTUÃQFSGFDUBNFOUFNF[DMBEP MBFDVBDJÓOEFPQFSBDJÓOFTMBFDVBDJÓO   &OUPODFTMBTPMVDJÓOTJHVFDPNPFOFMFKFNQMP  6-53"'*-53"$*¶/

-B VMUSBàMUSBDJÓO FT PUSP NÊUPEP EF TFQBSBDJÓO DPO NFNCSBOB VUJMJ[BEP QBSB QVSJàDBS MÎRVJEPT 4FBQMJDBQBSBSFDVQFSBSQSPUFÎOBTFOQSPDFTPTEFMBTJOEVTUSJBTBMJNFOUJDJBZGBSNBDÊVUJDB&TÙUJM QBSBTFQBSBSFNVMTJPOFTiQFSNBOFOUFTu QPSRVFMBTHPUJUBTEFBDFJUFOPBUSBWJFTBOMBNFNCSBOB 5BNCJÊOTFVTBQBSBFMJNJOBSQBSUÎDVMBTDPMPJEBMFTàOBTZQBSBSFDVQFSBSDPMPSBOUFTEFMBHVBSFTJ EVBM&ONVDIBTBQMJDBDJPOFT DPNPFMQSPDFTBNJFOUPEFMTVFSPMÃDUFP MBVMUSBàMUSBDJÓOZMBÓTNPTJT JOWFSTBTFVTBOFOTFSJF-BTQSPUFÎOBTWBMJPTBTTFSFDVQFSBODPOVMUSBàMUSBDJÓOZFMQFSNFBEPEF FTFTJTUFNBTFNBOEBBMTJTUFNBEFÓTNPTJTJOWFSTB-PTB[ÙDBSFTZTBMFTSFTJEVBMFTTFDPODFOUSBO FOFMTJTUFNBEFÓTNPTJTJOWFSTBRVFFMJNJOBFMBHVB&OUPODFT FMQFSNFBEPDPODFOUSBEPTFQVFEF GFSNFOUBSQBSBQSPEVDJSFUBOPM ÃDJEPMÃDUJDPVPUSPTQSPEVDUPT &MFRVJQPQBSBMPTTJTUFNBTEFVMUSBGJMUSBDJÓOTFQBSFDFDPOGSFDVFODJBBMEFMPTTJTUFNBT EFÓTNPTJTJOWFSTB QFSPUSBCBKBBQSFTJPOFTNFOPSFT4JOFNCBSHP FTUBTJNJMBSJEBEOPMMFHBIBTUB

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMPTQSPDFTPTEFTFQBSBDJÓODPONFNCSBOB

FMOJWFMNPMFDVMBS3FDVFSEFRVFMBTNFNCSBOBTQBSBÓTNPTJTJOWFSTBOPTPOQPSPTBTZTFTFQBSBO EFCJEPBVONFDBOJTNPEFTPMVDJÓOZEJGVTJÓO-BTNFNCSBOBTQBSBVMUSBàMUSBDJÓOTPOQPSPTBTZ TFTFQBSBOQPSUBNBÒP-BTNPMÊDVMBTHSBOEFTTFTFQBSBOFOMPTQPSPTEFMBQFMÎDVMBEFMHBEBEF MBNFNCSBOB QPSMPRVFRVFEBOFOFMSFUFOUBEP-BTNPMÊDVMBTQFRVFÒBTDBCFOFOMPTQPSPTRVF BUSBWJFTBOIBDJBFMQFSNFBEP$PNPTVFMFIBCFSVOBEJTUSJCVDJÓOEFUBNBÒPTEFQPSP MBTNPMÊDV MBTEFOUSPEFMJOUFSWBMPEFUBNBÒPTEFQPSPQBSDJBMNFOUFQBTBOZQBSDJBMNFOUFTFSFUJFOFO&OVO DPODFQUPBMHPTJNQMJàDBEP MBVMUSBàMUSBDJÓOBOJWFMNPMFDVMBSFTVOBàMUSBDJÓODPOáVKPDSV[BEP %FCJEP BM NFDBOJTNP EF TFQBSBDJÓO  MBT NFNCSBOBT EF VMUSBàMUSBDJÓO UJFOFO áVKPT BQSFDJBCMF NFOUFNBZPSFTRVFMBTEFÓTNPTJTJOWFSTB"TÎ MBQPMBSJ[BDJÓOEFDPODFOUSBDJÓOTVFMFFNQFPSBSFO MBVMUSBàMUSBDJÓODPNQBSBEBDPOMBÓTNPTJTJOWFSTB QPSRVFIBZNVDIPNBZPSáVKPEFTPMWFOUFEFTEF FMJOUFSJPSEFMáVJEPRVFBUSBWJFTBMBQBSFE&TUBQPMBSJ[BDJÓOEFDPODFOUSBDJÓOQVFEFDBVTBSFOTV DJBNJFOUPEFMBNFNCSBOB RVFOPTÓMPEJTNJOVZFFMáVKP TJOPUBNCJÊOQVFEFSFEVDJSDPOSBQJEF[MB EVSBDJÓOEFMBNFNCSBOB-BTNFNCSBOBTIJESPGÎMJDBTUJFOEFOBFOTVDJBSTFDPONFOPTSBQJEF[ QFSP UJFOFONFOPSFTEVSBDJPOFTRVFMBTNFNCSBOBTIJESPGÓCJDBT RVFBEFNÃTTPONÃTFTUBCMFT-BFMFDDJÓO EFMBNFKPSNFNCSBOBEFQFOEF FOUPODFT EFMBTDPOEJDJPOFTEFPQFSBDJÓO-BTNFNCSBOBTEFBDFUBUP EFDFMVMPTB àHVSB GVFSPOMBTQSJNFSBTRVFTFVTBSPOZBÙOTFVTBODVBOEPFTNÃTJNQPSUBOUFFM CBKPHSBEPEFJOUFSBDDJÓODPOMBTQSPUFÎOBT RVFMBEVSBDJÓOSFMBUJWBNFOUFDPSUBEFMBNFNCSBOB-BT NFNCSBOBTQPMJNÊSJDBTTFVTBODVBOEPTFFODVFOUSBODPOEJDJPOFTNÃTCÃTJDBT-BNFNCSBOBQPMJNÊ SJDBNÃTDPNÙOFTMBEFQPMJTVMGPOB àHVSB -BTNFNCSBOBTTFGBCSJDBOBMBNFEJEB QBSBTFQBSBS NPMÊDVMBTFOEJTUJOUPTJOUFSWBMPTEFUBNBÒP RVFEFQFOEFOEFMBàOBMJEBEEFMBTFQBSBDJÓO àHVSB  -PTGBCSJDBOUFTTVFMFOJOEJDBSMBFYDMVTJÓOEFQFTPNPMFDVMBSOPNJOBM SFQSFTFOUBEBQPSYFOMB àHVSB QFSPÊTUBOPFTUBOÙUJMDPNPMBDVSWBDPNQMFUBEFSFUFODJÓO "MQSJODJQJP TFQVFEFBOBMJ[BSMBVMUSBàMUSBDJÓODPOMPTNJTNPTQSPDFTPTRVFTFVTBOFOMBÓT NPTJTJOWFSTB"TÎ TPOWÃMJEBTMBTFDVBDJPOFT  Z  4JOFNCBSHP FOMBVMUSBàMUSBDJÓO MBT NPMÊDVMBTRVFTFSFUJFOFOTPONVZHSBOEFT DPONVDIBGSFDVFODJBZMBQSFTJÓOPTNÓUJDBRVFSFTVMUB FTNVZCBKB1BSBMBNBZPSQBSUFEFMBTBQMJDBDJPOFTEFVMUSBàMUSBDJÓO TFQVFEFJHOPSBSMBEJGFSFODJB

'*(63" 3&5&/$*¶/%&40-650 &/.&.#3"/"4 ".*$0/%*"'-0 1035&3   3&*.13&40$0/ "6503*;"$*¶/%& 1"4$)8&*5;&3 &%

)"/%#00, 0'4&1"3"5*0/ 5&$)/*26&4'03 $)&.*$"-&/(*/&&34  ‰&%*$*¶/ 

¥  .$(3"8)*--

Retención

Diámetro molecular aproximado

Exclusión de peso molecular nominal de la membrana

Peso molecular

www.FreeLibros.me

  6MUSBGJMUSBDJÓO



EFQSFTJPOFTPTNÓUJDBTZTFTJNQMJàDBMBFDVBDJÓOEFáVKPEFTPMWFOUF&MáVKPWPMVNÊUSJDPFT 

?hdak 2

@hdak eg − ee ibh





&OVOJEBEFTEFNBTB FMáVKPEFTPMWFOUFFT 

? hdak ′ 2?hdak š hdak 2

; e′ &− me @hdak š  e − ee  2 6 ibh hdak g



FOEPOEF' QFTMBWFMPDJEBEEFUSBOTGFSFODJBEFNBTBEFMQFSNFBEP QPSFKFNQMP FOLHT

YQFTMB GSBDDJÓOEFQFTPEFTPMVUPFOFMQFSNFBEPZ TPMWFTMBEFOTJEBEEFMTPMWFOUFQVSP$PNPWFSFNPT  FMOPUFOFSFODVFOUBMBEJGFSFODJBEFQSFTJPOFTPTNÓUJDBTFTVOBTJNQMJàDBDJÓONÃTJNQPSUBOUFEF MPRVFQBSFDFBMQSJODJQJP 1BSBMBTNFNCSBOBTEFUJQPDFEB[P TJVOQPSPOPFYDMVZFBMTPMVUP ÊTUFMMFHBSÃBMBQBSFEDPO VOBGSBDDJÓOEFQFTPYX.YSZQBTBSÃQPSFMQPSP&OFTUBTNFNCSBOBT TFQVFEFJOUFSQSFUBSBMSF DIB[PJOIFSFOUF3P . DPNPMBGSBDDJÓOEFáVKPRVFQBTBQPSMPTQPSPTRVFFYDMVZFOBMTPMVUP &OUPODFT −3PFTMBGSBDDJÓOEFáVKPRVFQBTBQPSMPTQPSPTRVFOPTFQBSBOTPMVUP -BGSBDDJÓOEFQFTPEFMQFSNFBEP YQ FTFOUPODFT 

me 2& Gdml 2& GdBmg 



%FFTUBFDVBDJÓOUBNCJÊOTFQVFEFEFTQFKBSMBGSBDDJÓOEFQFTPEFMSFUFOUBEP 

mg 2me $P& GdBR 



-BTFDVBDJPOFT  P  TPOMBTFDVBDJPOFTEFWFMPDJEBEEFUSBOTGFSFODJBQBSBMBVMUSBàMUSB DJÓO4POCBTUBOUFTFODJMMBT QPSRVFFMSFDIB[PJOIFSFOUF3PTFCBTBFOEBUPTFYQFSJNFOUBMFT 4JTF DPOPDJFSBFYQFSJNFOUBMNFOUF3PQBSBMBTDPOEJDJPOFTEFJOUFSÊTFOÓTNPTJTJOWFSTB TFQPESÎBVTBSFM NJTNPQSPDFEJNJFOUPFOFTUBÓTNPTJTJOWFSTB&TUFSFTVMUBEPFTNÃTTFODJMMPRVFFMQSPDFEJNJFOUP EFTDSJUPBOUFT QFSPSFRVJFSFEBUPTRVFDPOGSFDVFODJBOPTFDPOTJHVFOGÃDJMNFOUF 5FOHBFODVFOUB RVFMBTFDVBDJPOFTEFWFMPDJEBEEFUSBOTGFSFODJBQBSBMBVMUSBàMUSBDJÓOTÓMPEFQFOEFOEFMSFDIB[PEFM TPMVUPZEF.1BSBVONÓEVMPEFNFNCSBOBQFSGFDUBNFOUFNF[DMBEP TVQPOESFNPTRVFYSYTBM &OUPODFT  TF QVFEFO SFTPMWFS TJNVMUÃOFBNFOUF MB FDVBDJÓO   P 

 FTDSJUBT FO UÊSNJOPT EFYTBM KVOUPDPOMPTCBMBODFTEFNBTB FDVBDJPOFT 

PMBFDVBDJÓOEFPQFSBDJÓO  &TUB TPMVDJÓOTJNVMUÃOFBUBNCJÊOTFQVFEFPCUFOFSUSB[BOEPMBDVSWBEFWFMPDJEBEEFUSBOTGFSFODJBZMBEF PQFSBDJÓOFOVOTJTUFNBEFDPPSEFOBEBTEFYQFOGVODJÓOEFYS TBM WFBFMQSPCMFNB$ -BTFDVB DJPOFT  Z  P  UBNCJÊOTFQVFEFOSFTPMWFSFOGPSNBBOBMÎUJDBPOVNÊSJDB WFBFM QSPCMFNB$  -PTSFTVMUBEPTFYQFSJNFOUBMFTDPOCBKBTDPODFOUSBDJPOFTFOMBBMJNFOUBDJÓOPCBKPDPOEJDJPOFT FOMBTRVF.FTDFSDBOBBDPODVFSEBOCJFODPOMBTQSFEJDDJPOFTUFÓSJDBT4JOFNCBSHP DVBOEP MBDPODFOUSBDJÓOFOMBQBSFEFTBMUB DPOGSFDVFODJBZBOPTFQVFEFDPOUSPMBSFMáVKPEFTPMWFOUF+TPMW BKVTUBOEPMBEJGFSFODJBEFMBQSFTJÓO&OUPODFT ZBOPFTWÃMJEBMBFDVBDJÓO  "MHÙOPUSPGFOÓ NFOPQVFEFFTUBSDPOUSPMBOEPFMáVKP$POVOFYBNFODVJEBEPTPEFMBTVQFSàDJFEFMBNFNCSBOB EFTQVÊTEFFTUPTFYQFSJNFOUPTTFWFRVFVOBDBQBEFHFMDVCSFBMBTVQFSàDJFEFMBNFNCSBOB&TUB DBQBEFHFMBMUFSBMBSFMBDJÓOFOUSFáVKPZDBÎEBEFQSFTJÓOZDPOUSPMBMBUBTBEFáVKPEFMTPMWFOUF &MFGFDUPEFMBGPSNBDJÓOEFHFMFOMBQBSFEQVFEFFTUVEJBSTFVTBOEPMBFDVBDJÓOEFEJGVTJÓO 3FHSFTFNPTBMBàHVSB4VQVTJNPT FOGPSNBJNQMÎDJUB RVFMBDPODFOUSBDJÓOFOMBQBSFEFTVOB WBSJBCMFRVFQPEÎBBVNFOUBSTJOMÎNJUF&OMPTTJTUFNBTDPOHFMFT VOBWF[RVFMBDPODFOUSBDJÓOFOMB QBSFEFTJHVBMBYH MBDPODFOUSBDJÓOFOFMHFM QFSNBOFDFDPOTUBOUFFOYXYH"NFEJEBRVFTFTJHVF

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMPTQSPDFTPTEFTFQBSBDJÓODPONFNCSBOB

BDVNVMBOEPTPMVUPFOMBQBSFE MBDPODFOUSBDJÓOFOFMHFMOPDBNCJB QFSPFMFTQFTPSEFMBDBQBEF HFMBVNFOUB BTÎ YXTFWVFMWFVOBDPOTUBOUF EFUFSNJOBEBQPSFMDPNQPSUBNJFOUPHFMBOUFEFMTPMVUP &TUPTFJMVTUSBFOMBàHVSB&MWBMPSEFYHQVFEFWBSJBSEFTEFNFOPTEFFOQFTPFOMPTQPMJ TBDÃSJEPTZIBTUBFOWPMVNFOQBSBTVTQFOTJPOFTEFMÃUFYQPMJNÊSJDP #MBUUFUBM   1BSBBOBMJ[BSMPTTJTUFNBTHFMBOUFTTFQVFEFVTBSEFOVFWPMBFDVBDJÓO  DVBOEP3 6OBWF[RVFTFGPSNBVOHFM TVFMFTFSCBTUBOUFJOBNPWJCMFZFTSB[POBCMFTVQPOFSRVFMBSFUFODJÓO FT 4JTFSFEFàOFFMTJTUFNBEFDPPSEFOBEBTDPNPFOMBàHVSB MBTDPOEJDJPOFTFOMB GSPOUFSBTPOJHVBMFTRVFFOMBTFDVBDJPOFT  -BTPMVDJÓOUJFOFMBNJTNBGPSNBRVFFOMBFDVB DJÓO  4JOFNCBSHP DPNPYXZYSFTUÃOàKBT FMáVKPEFMTPMWFOUFFTMBWBSJBCMF4JEFTQFKBNPT FMáVKPEFTPMWFOUFFMSFTVMUBEPFT 

?hdak2

9 δ

,c

m\ m 2`,c \  mg mg



-BDPOTFDVFODJBEFFTUBFDVBDJÓOFTRVFVOBWF[RVFTFGPSNÓFMHFM FMáVKPEFTPMWFOUFRVFEB EFUFSNJOBEPQPSMBWFMPDJEBEEFEJGVTJÓOJOWFSTBEFMTPMVUP:ZBOPTFQVFEFDPOUSPMBSFMáVKPEFM TPMWFOUF y2VÊTVDFEFTJBVNFOUBNPTMBDBÎEBEFQSFTJÓOBUSBWÊTEFMBNFNCSBOBDVBOEPFOVOTJTUFNB IBZHFM &MáVKPEFTPMWFOUFBVNFOUBSÃFOGPSNBUFNQPSBM QFSPNÃTTPMVUPMMFHBBMBNFNCSBOBEF CJEPBáVKPRVFBUSBWJFTBMBNFNCSBOB RVFQVFEFFMJNJOBSTFQPSEJGVTJÓOJOWFSTB&MTPMVUPBEJDJP OBMTFEFQPTJUBFOMBDBQBEFHFM MPRVFBVNFOUBFMFTQFTPSEFFTBDBQB&TUPBVNFOUBMBSFTJTUFODJB BMáVKPZTFSFEVDFFMáVKPBUSBWÊTEFMBNFNCSBOB IBTUBRVFTFPCUJFOFEFOVFWPFMáVKPEFTPMWFO UFFOFTUBEPFTUBCMF EFàOJEPQPSMBFDVBDJÓO  5FOHBFODVFOUBRVFFTUFFGFDUP FOHFOFSBM  OPFTSFWFSTJCMF-BSFEVDDJÓOEFMBQSFTJÓOIBSÃRVFMBUBTBEFáVKPTFBNFOPSRVFMBJOEJDBEBQPS MBFDVBDJÓO 

QPSRVFQFSNBOFDFMBDBQBHSVFTBEFHFMTPCSFMBNFNCSBOB&TUBDBQBEFHFM TFQVFEFFMJNJOBSDPOGSFDVFODJBQBSBOEPFMTJTUFNBZIBDJFOEPSFUSPMBWBEP IBDFSQBTBSTPMWFOUF QVSPBVOBQSFTJÓONBZPSEFTEFFMMBEPEFMQFSNFBEP PQPSMBWBEPNFDÃOJDPEFMBTVQFSàDJFEFMB NFNCSBOB%FTBGPSUVOBEBNFOUF MBNFNCSBOBTFQVFEFFOTVDJBSEFTQVÊTEFGPSNBSTFFOFMMBVO HFMZQVFEFTFSNVZEJGÎDJMSFHSFTBSMBIBTUBTVDBQBDJEBEPSJHJOBMEFáVKP$VBOEPIBZDPOEJDJPOFT EFGPSNBDJÓOEFHFM TFSFDPNJFOEBVTBSNFNCSBOBTSFTJTUFOUFTBMFOTVDJBNJFOUP "MEJTNJOVJSFMFTQFTPS EFMBDBQBMJNÎUSPGF DPODBOBMFTEFMHBEPTPUVSCVMFODJB BVNFOUBSÃFM DPFàDJFOUFEFUSBOTGFSFODJBEFNBTBL ZFODPOTFDVFODJBFMáVKP)BTUBDJFSUPHSBEP FMJOHFOJFSP QVFEFBVNFOUBS%BVNFOUBOEPMBUFNQFSBUVSB&MFGFDUPEFFTBTWBSJBCMFTTPCSFFMDPFàDJFOUFEF USBOTGFSFODJBEFNBTBTFQVFEFFYQMPSBSDPOMBDPSSFMBDJÓOEFMBTFDVBDJPOFT  B  4JFM FOTVDJBNJFOUPFTHSBWFEFTQVÊTEFMBGPSNBDJÓOEFHFM QPESÃTFSOFDFTBSJPUSBCBKBSEFNPEPRVF ml2m\

i\ ib

'*(63" 10-"3*;"$*¶/%&$0/$&/53"$*¶/$0/ 6/"$"1"%&(&-&/-"1"3&%

me

www.FreeLibros.me

m

o D o2%

o2D

  6MUSBGJMUSBDJÓO



OVODBTFGPSNFYX.YSYHTJFNQSF&TPTFIBDFUSBCBKBOEPFODPOEJDJPOFTRVFSFEV[DBOB. BMUPTWBMPSFTEFL ZNBOUFOJFOEPCBKBYS CBKBTDPODFOUSBDJPOFTEFBMJNFOUBDJÓOZCBKPTDPSUFT  $VBOEPVOHFMOPTFGPSNB FMáVKPEFTPMWFOUFFOMBVMUSBàMUSBDJÓOTFDPOUSPMBDPOMBTFDVBDJPOFT 

FMNÓEVMPEFQPMBSJ[BDJÓOEFDPODFOUSBDJÓOTFQVFEFDBMDVMBSDPOMBFDVBDJÓO  ZMB TPMVDJÓOFTEJSFDUB -BNBZPSQBSUFEFMBTBMJNFOUBDJPOFTRVFTFQSPDFTBODPOVMUSBàMUSBDJÓODPOUJFOFOWBSJPTZ EJGFSFOUFTTPMVUPTy$ÓNPBOBMJ[BSFTUBTTFQBSBDJPOFT -BUFOUBDJÓONÃTBCSVNBEPSBFTFTUVEJBS  FOGPSNBJOEJWJEVBM DBEBTPMVUPZTVQPOFSWÃMJEBMBTVQFSQPTJDJÓO&TUPFT TVQPOFNPTRVFDBEB TPMVUPFOMBNF[DMBTFDPNQPSUBSÃEFMBNJTNBGPSNBFORVFMPIBDFJOEJWJEVBMNFOUF%FTQVÊTEF UPEP FTPGVFMPRVFIJDJNPTFOQFSNFBDJÓOEFHBTFTZFOÓTNPTJTJOWFSTB&OUPODFT QPESÎBNPT BOUJDJQBS RVF MBT NPMÊDVMBT HSBOEFT RVFEBSÃO SFUFOJEBT Z MBT NPMÊDVMBT QFRVFÒBT BUSBWFTBSÃO MB NFNCSBOB&MDPNQPSUBNJFOUPRVFTFPCTFSWBBNFOVEPFTMBOPGPSNBDJÓOEFHFM4JOFNCBSHP  TJTFGPSNB FMHFMDBTJTJFNQSFTFSÃIFSNÊUJDP NFOPTQPSPTP RVFMBNFNCSBOBZMBDBQBEFHFM DBQUVSBSÃMBTNPMÊDVMBTQFRVFÒBT&OUPODFT MPTDPNQPSUBNJFOUPTEFTFQBSBDJÓODPOZTJOHFMTFSÃO NVZEJGFSFOUFT4JFMPCKFUJWPEFMBPQFSBDJÓOEFVMUSBàMUSBDJÓOFTTFQBSBSMBTNPMÊDVMBTHSBOEFT ZQFRVFÒBT EFCFNPTUSBCBKBSCBKPDPOEJDJPOFTFOMBTRVFOPTFGPSNBHFM-BGPSNBDJÓOEFHFMFTZ FMFOTVDJBNJFOUPIBOFWJUBEPRVFFOMBVMUSBàMUSBDJÓOTFBQSPWFDIFUPEPTVQPUFODJBM QPSRVFDPO GSFDVFODJBMJNJUBOMBTFQBSBDJÓOZFMáVKP -BTNFNCSBOBTEFÓTNPTJTJOWFSTBUBNCJÊODBVTBSÃOHFMBDJÓOZFOTVDJBNJFOUP TJTFUSBCBKBO DPOBMJNFOUBDJPOFTRVFQVFEBOGPSNBSHFMFT1BSBFWJUBSMP TFBDPTUVNCSBVTBSVOTJTUFNBEFVM USBàMUSBDJÓOBOUFTEFMTJTUFNBEFÓTNPTJTJOWFSTB&OUPODFTFMTJTUFNBEFVMUSBàMUSBDJÓOFMJNJOBSÃ MBTQBSUÎDVMBTZMBTNPMÊDVMBTHSBOEFTRVFQVFEBOFOTVDJBSMBNFNCSBOBEFÓTNPTJTJOWFSTB&TUF QSPDFEJNJFOUPFTFMRVFTFIBDFFOFMQSPDFTBNJFOUPEFTVFSPEFMFDIF EPOEFFMTJTUFNBEFVMUSBàM USBDJÓOSFUJFOFMBTQSPUFÎOBTZFMTJTUFNBEFÓTNPTJTJOWFSTBSFUJFOFMPTB[ÙDBSFTZMBTTBMFT &+&.1-0 6MUSBGJMUSBDJÓODPOGPSNBDJÓOEFHFM &TUBNPTVMUSBàMUSBOEPQBSUÎDVMBTEFMÃUFYZTFTBCFRVFGPSNBOHFMDVBOEPYXYH &MTJTUFNBCJFONF[DMBEPTFPQFSBDPOVOBQSFTJÓOEFCBSFOFMQFSNFBEPZEFCBS FOFMSFUFOUBEP)JDJNPTVOBTFSJFEFFYQFSJNFOUPTDPOEJGFSFOUFTWBMPSFTEFMBDPODFOUSB DJÓOEFFOUSBEBDPOVODPSUFEF-BGSBDDJÓOFOQFTPEFMQFSNFBEPFTDFSPFOUPEPTMPT FYQFSJNFOUPT4FFODPOUSÓRVFIBZHFMBDJÓODVBOEPYFOUZFMáVKPNFEJEPFT  - NEÎB $BMDVMBSFMáVKPEFTPMWFOUFTJMBGSBDDJÓOFOQFTPYFOU FOMBFOUSBEB 4PMVDJÓO " %FGJOB$BMDVMF+TPMWDVBOEPYFOU   QQCBSZQSCBS # Z $ &YQMPSF Z QMBOFF 6TBSFNPT VO CBMBODF EF NBTB QBSB EFUFSNJOBS YS  YTBM QBSB  YFOUZMBFDVBDJÓO  QBSBDBMDVMBSLVTBOEPFMáVKPNFEJEPDPOFTUBGSBD DJÓOEFQFTPFOMBFOUSBEB&OUPODFT QBSBYFOU DBMDVMBSFNPTYSYTBM QPSRVF DPODPOàBO[B YQFTDFSP QPESFNPTTVQPOFSRVFTJHVFTJFOEPDFSPDVBOEPYFOU  6TBSFNPTMBFDVBDJÓO  QBSBDBMDVMBS+TPMWBFTUBNBZPSGSBDDJÓOFOQFTP % )ÃHBMP$POEJDJPOFTFYQFSJNFOUBMFT Ra 2&$(!; hVa a 2;aZci ;ae !;ahVa 2'$(;aZci ;aZci ( m 2 m ;ahVa Zci ' Zci 2&#*%#&)++2%#''%#

8dc me 2%!; hVa a mhVa 2; Zci a mZci d mhVa 2 8jVcYdm Zci 2%#&)++!mhVa

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMPTQSPDFTPTEFTFQBSBDJÓODPONFNCSBOB

0SEFOBNPTMBFDVBDJÓO   `2 

?hdak )*%%A$Y†V  b' A 2 lnm\$mg lc%#*$%#''% 2*)-&#'* b'Y†V



"IPSBSFTPMWFSFNPTMBFDVBDJÓO  DPOYFOUZYTBMYFOU



&MSFTVMUBEPGJOBMFT ?hdak 2*)-&#'*l c%#*$%#(%2',..#.+

A b'Y†V

& $PNQSVFCF%FTEFFMQVOUPEFWJTUBDVBMJUBUJWP DBCFFTQFSBSNFOPSáVKP QPSRVFNÃT QBSUÎDVMBTEFMÃUFYRVFTPOBSSBTUSBEBTIBDJBMBQBSFEQPSMJUSPEFáVJEPRVFQFSNFB QPSMBNFNCSBOB"EFNÃTEFDPNQSPCBSMBTFDVBDJPOFTZMPTDÃMDVMPT MBDPNQSPCB DJÓOFTEJGÎDJM ' (FOFSBMJDF)FNPTTVQVFTUPRVFLOPEFQFOEFEFMBDPODFOUSBDJÓO&TUPFTSB[POB CMFFOFMDBTPEFQBSUÎDVMBT  4JTFDPOPDJFSBVOBDPSSFMBDJÓOQBSBL QPESÎBNPTVTBSMBFDVBDJÓO  Z+TPMW  QBSBFTUJNBSYH  &MQSPDFEJNJFOUPHFOFSBMGVF B  6TBSVOBFDVBDJÓOEFEJTFÒPPSEFOBEBQBSBQPEFSFODPOUSBSVOQBSÃNFUSPEF EJTFÒP L VTBOEPDPOEJDJPOFTFYQFSJNFOUBMFT%FTQVÊT C 6TBSMBFDVBDJÓOEFEJTFÒPQBSBDBMDVMBSFMáVKPFOMBTDPOEJDJPOFTEFEJTFÒP &TUFQSPDFEJNJFOUPHFOFSBMFTNVZDPNÙOFOUPEPUJQPEFQSPCMFNBTEFTFQBSBDJÓO  &TGVOEBNFOUBMEFUFSNJOBSTJTFGPSNBVOBDBQBEFHFM `"EWFSUFODJB &YJTUFO SFTVMUBEPT FYQFSJNFOUBMFT Z FDVBDJPOFT QBSB VMUSBàMUSBDJÓO Z QBSB ÓTNPTJT JOWFSTBFONVDIBTZEJTUJOUBTVOJEBEFT%FCJEPBFTUP FTDPNÙODPNFUFSVOFSSPSEFVOJEBEFTTJOP TFJOEJDBOMBTVOJEBEFTFODBEBFDVBDJÓO&TTFODJMMPUBNCJÊODPNFUFSVOFSSPSFOMBEFOTJEBEEFMB TPMVDJÓORVFTFEFCFVTBSDVBOEPTFDPOWJFSUFMBDPODFOUSBDJÓO D FOH-PNPM- BY FOGSBDDJÓO EFQFTP-BDPOWFSTJÓODPSSFDUBEFH-BGSBDDJÓOFOQFTPFT 

m2 X!

\hdajid AhdajX^‹c

šhdajX^‹c!

\hdajX^‹c  AhdajX^‹c



%FTBGPSUVOBEBNFOUF MBEFOTJEBEEFMBTPMVDJÓO  TPMVDJÓO FTGVODJÓOEFMBDPODFOUSBDJÓO1BSBQFS NFBEPSFMBUJWBNFOUFQVSP 3DFSDBOBB

MBEFOTJEBEEFMBTPMVDJÓOEFQFSNFBEPFTBQSPYJNB EBNFOUFJHVBMBMBEFOTJEBEEFMTPMWFOUF$VBOEPMBTDPSSJFOUFTTPONÃTDPODFOUSBEBT DPNPFOMPT DBTPTEFMBBMJNFOUBDJÓOPEFMSFUFOUBEP EFCFDPOPDFSTFPFTUJNBSTFMBEFOTJEBE FOGVODJÓOEFMB DPODFOUSBDJÓO $VBOEPMBTDPODFOUSBDJPOFTTFFYQSFTBOFOH- DPOGSFDVFODJBTFIBDFOBQSPYJNBDJPOFTQBSBDBMDV MBSMPTáVKPT1PSFKFNQMP MBFDVBDJÓODPSSFDUBQBSBFMáVKPEFNBTBEFTPMWFOUFFT



g soluto 

g soluto

L solvente

L soluto  J A   J   J A  m 2 s   c p  L de solución 

m 2 s   solv  m2s  

B

1FSPDPOGSFDVFODJBTFVTBMBBQSPYJNBDJÓO 

+ "

g soluto m2s

J solv

L solvente m2s

× cp

g soluto en permeado  L de solución

C

1BSBDPFàDJFOUFTEFSFDIB[PSFMBUJWBNFOUFBMUPT FMQFSNFBEPFTCBTUBOUFQVSP +TPMW+"ZMBBQSPYJ NBDJÓOFTCBTUBOUFCVFOB&OPUSPTDBTPT QVFEFTFSRVFFTUBBQSPYJNBDJÓOOPTFBUBOFYBDUB

www.FreeLibros.me

  1FSWBQPSBDJÓO



-PTNÓEVMPTEFSFDIB[PZEFQPMBSJ[BDJÓOEFDPODFOUSBDJÓOTFEFàOFODPOGSFDVFODJB FOVOJEBEFT EFDPODFOUSBDJÓO 

GX 2& Xe $XhVa !BX 2Xl$XhVa 



$POFTUBTEFàOJDJPOFT FMáVKPEFNBTBEFTPMVUPFT ?a6 2BXXhVa & G°X?hdajX^‹c z BXXhVa & G°X?hdak 





EPOEF3PDFTFMSFDIB[PJOIFSFOUF NFEJEPDVBOEPOPIBZQPMBSJ[BDJÓOEFDPODFOUSBDJÓO .D  -BTFDVBDJPOFT  Z  TPOGPSNBTWÃMJEBTQBSBGPSNVMBSFMQSPCMFNB%FTBGPSUVOBEBNFO UF TFQVFEFTVQPOFSRVF3P3DPZRVF..D DVBOEPMBTFDVBDJPOFTFYBDUBTTPO 

G° 2 &−



me Xe $š hdajX^‹c!e  X 2&− ≈ &− e 2G °X  XhVa $š hdajX^‹c!hVa  mhVa XhVa

B2

ml mhVa

2

X Xl $š hdajX^‹c!e  ≈ l 2BX  XhVa $š hdajX^‹c!hVa   XhVa

B

C

4J TPMVDJÓO TBMZ TPMVDJÓO QTPONVZEJGFSFOUFT VOBDPOGVTJÓOEF3DPO3DZEF.DPO.DQVFEFDBVTBS VOFSSPSJNQPSUBOUF1BSBNBZPSFYBDUJUVE SFWJTFDÓNPTFEFàOFOUPEPTMPTUÊSNJOPT VTFMBTEFO TJEBEFT BEFDVBEBT EF TPMVDJÓO  EF QFSNFBEP Z SFUFOUBEP  QBSB QBTBSMBT B GSBDDJPOFT EF QFTP Z B DPOUJOVBDJÓOIBHBMPTDÃMDVMPTFOVOJEBEFTEFGSBDDJÓOEFQFTP  1&37"103"$*¶/

-BQFSWBQPSBDJÓOFTVOBUÊDOJDBEFTFQBSBDJÓODPONFNCSBOBRVFTFFTUÃEJGVOEJFOEPSÃQJEBNFOUF QPSRVFFTGSFDVFOUFRVFTFPCUFOHBOTFMFDUJWJEBEFTNVZBMUBTDPOáVKPTSB[POBCMFT&OMBQFSWBQP SBDJÓO VOMÎRVJEPDPOBMUBQSFTJÓOTFBMJNFOUBBVOMBEPEFMBNFNCSBOB6ODPNQPOFOUFQFSNFB MBNFNCSBOBFOGPSNBQSFGFSFODJBMZEFTQVÊTTFFWBQPSBFOFMMBEPQPTUFSJPSZTFSFUJSBVOWBQPS QSPEVDUP FMQFSNFBEP àHVSB -BQBMBCSBiQFSWBQPSBDJÓOuFTVOBDPOUSBDDJÓOEFQFSNFB DJÓOZFWBQPSBDJÓO&MSFUFOUBEP RVFOPBUSBWJFTBMBNFNCSBOB FTVOMÎRVJEPQSPEVDUPDPOBMUB QSFTJÓO&MQSPEVDUPEFTFBEPQVFEFTFSFMQFSNFBEPPFMSFUFOUBEP &OMBQFSWBQPSBDJÓO MBGVFS[BJNQVMTPSBEFMBTFQBSBDJÓO FOMBFDVBDJÓO 

FTMBEJGFSFODJB EFBDUJWJEBEFTBUSBWÊTEFMBNFNCSBOB-BFDVBDJÓOEFáVKPFT &ZLBNQ   

?^ 2"9^ X^

Y l cV^  Yo



FOMBRVFBJFTMBBDUJWJEBE%FTBGPSUVOBEBNFOUF OJFTUBFDVBDJÓOOJMB  UJFOFOHSBOBQMJDBDJÓO QSÃDUJDB$PNPFOHFOFSBMOPTFQVFEFSFTPMWFSVOBOÃMJTJTEFUBMMBEPFOTJUVBDJPOFTQSÃDUJDBT QPS FKFNQMP WFB/FFM 

VTBSFNPTVOBUFPSÎBNVZTJNQMJàDBEB RVFTFCBTBNVDIPFOEBUPTFYQF SJNFOUBMFTEFTFMFDUJWJEBE-PTQSPDFEJNJFOUPTEFNPEFMBEPRVFTFVTBSPOBOUFTQBSBQFSNFBDJÓO EFHBTOPTFBQMJDBOFOMBQFSWBQPSBDJÓO QPSRVFMPTáVKPTEFMPTEPTDPNQPOFOUFTJOUFSBDUÙBOFO GPSNBJNQPSUBOUF MBNFNCSBOBTFIJODIBZMBTQFSNFBCJMJEBEFTEFQFOEFONVDIPEFMBDPODFOUSB DJÓO4FQVFEFOFODPOUSBSNPEFMPTEFUBMMBEPTFOMPTMJCSPTEF%VUUBFUBM 

)PZ4JSLBS 

)VBOH 

.VMEFS  Z/PCMFZ4UFSO   :BRVFTFFGFDUÙBOBMNJTNPUJFNQPQFSNFBDJÓOTFMFDUJWBFONFNCSBOBZFWBQPSBDJÓO DPO MBQFSWBQPSBDJÓOTFTFQBSBZTFDPODFOUSB BMNJTNPUJFNQP"MFWBQPSBSTFFMMÎRVJEPFOFMMBEPEF TBMJEBEFMBNFNCSBOBUBNCJÊOBVNFOUBMBGVFS[BJNQVMTPSB4VQPOHBRVFMBGVFS[BJNQVMTPSBTF

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMPTQSPDFTPTEFTFQBSBDJÓODPONFNCSBOB

calentador

gases inertes

F9ent, x9ent, Tent bomba bomba de vacío

condensador permeado líquido

membrana

retentado Fent, xent, Tent

'*(63" &426&."4*.1-*'*$"%0%&1&37"103"$*¶/&/6/1"40 SFQSFTFOUBFOGPSNBBEFDVBEBQPSMBEJGFSFODJBEFQSFTJPOFTQBSDJBMFTBUSBWÊTEFMBNFNCSBOB-B QSFTJÓOQBSDJBMMPDBMFOFMMBEPEFMBFOUSBEB RVFTFJOEJDBDPOFOMBàHVSBFT e^!& 2m^!& KE^!& 



B

NJFOUSBTRVFMBQSFTJÓOQBSDJBMMPDBM FOFMMBEPEFMBTBMJEBTFJEFOUJàDBDPO ZFT e^!' 2n^!' eidi!' 

C

[jZgoV^bejahdgV^ 2$e^ 2m^!& KE^!& n^!' eidi!' 

D

 ZMBGVFS[BJNQVMTPSBMPDBMFT 

&OWJTUBEFRVFYJ  ZJ ZQUPU WBSÎBO MPTWBMPSFTMPDBMFTEFMBTQSFTJPOFTQBSDJBMFTZEFMBGVFS[BJN QVMTPSB EFQFOEFOEFMBTQBVUBTEFáVKPZMBDBÎEBEFQSFTJÓOFOFMNÓEVMPEFNFNCSBOB1VFEF BVNFOUBSTFMBGVFS[BJNQVMTPSBEJTNJOVZFOEPQUPU  ZBTFBIBDJFOEPFMWBDÎPDPNPJOEJDBMBàHVSB  PCJFO DPONFOPTGSFDVFODJB SFEVDJFOEPZJ VTBOEPVOHBTEFCBSSJEPFOFMMBEPEFMQFSNFB EP5BNCJÊO MBGVFS[BJNQVMTPSBTFQVFEFBVNFOUBSTJTFBVNFOUBMBQSFTJÓOQBSDJBMEFMDPNQPOFOUF JFOFMMBEPEFMBBMJNFOUBDJÓO&TPTVDFEFDPOBMJNFOUBDJPOFTNÃTDPODFOUSBEBT NBZPSYJ  ZNB ZPSFTUFNQFSBUVSBTFOMBFOUSBEB NBZPS17J  &MVTPEFNBZPSFTUFNQFSBUVSBTFOMBFOUSBEBQPESÃ SFRVFSJSNBZPSQSFTJÓOFOMBFOUSBEB QBSBFWJUBSMBFWBQPSBDJÓOEFMMÎRVJEPFOFTFMBEP-BNBZPS QSFTJÓOFOMBFOUSBEBOPIBDFBVNFOUBSNVDIPFMáVKPEFQFSNFBDJÓO /FFM  "VORVFFOHF OFSBMMBDPODFOUSBDJÓOEFMBFOUSBEBOPFTVOBWBSJBCMFCBKPFMDPOUSPMEFMEJTFÒBEPSFOVOTJTUFNBEF VOTPMPQBTP WFBMBàHVSB

FOTJTUFNBTIÎCSJEPTFTVOBWBSJBCMFEFEJTFÒP àHVSB  $PNP EF DPTUVNCSF FO MBT TFQBSBDJPOFT DPO NFNCSBOB  MB NFNCSBOB FT GVOEBNFOUBM QBSB UFOFSÊYJUP&OMBBDUVBMJEBETFVTBODPOGSFDVFODJBEPTDMBTFTEJGFSFOUFTEFNFNCSBOBFOMBQFSWB

www.FreeLibros.me

  1FSWBQPSBDJÓO



QPSBDJÓO1BSBFMJNJOBSUSB[BTEFTVTUBODJBTPSHÃOJDBTFOBHVB TFVTBVOBNFNCSBOBIJESPGÓCJDB  RVFTVFMFTFSEFIVMFEFTJMJDPOB1BSBFMJNJOBSUSB[BTEFBHVBFOTPMWFOUFTPSHÃOJDPT TFVTBVOB NFNCSBOBIJESPGÎMJDB DPNPQPSFKFNQMPEFBDFUBUPEFDFMVMPTB PVOBNFNCSBOBEFJOUFSDBNCJP JÓOJDP  EF ÃDJEP QPMJBDSÎMJDP  QPMJTVMGPOB  BMDPIPM QPMJWJOÎMJDP  VOB NFNCSBOB DPNQVFTUB Z [FPMJ UBDFSÃNJDB"NCBTDMBTFTEFNFNCSBOBTPOOPQPSPTBTZGVODJPOBONFEJBOUFVONFDBOJTNPEF TPMVDJÓOEJGVTJÓO-BTFMFDDJÓOEFVOBNFNCSBOBRVFEFQSFGFSFODJBQFSNFFFMDPNQPOFOUFNÃT EJMVJEP DPOGSFDVFODJBSFEVDJSÃFMÃSFBEFNFNCSBOBOFDFTBSJB &MVTPEFMBFWBQPSBDJÓOQBSBBVNFOUBSMBGVFS[BJNQVMTPSBQFSNJUFVTBSVOBNFNCSBOBNVZ TFMFDUJWB Z BM NJTNP UJFNQP DPOTFSWBS VO áVKP SB[POBCMF 4JO FNCBSHP  MB FWBQPSBDJÓO DPNQMJDB UBOUPFMFRVJQPDPNPFMBOÃMJTJT-BTQSFTJPOFTUÎQJDBTEFMQFSNFBEPTPOCBTUBOUFCBKBT EFB 1B  -FFQFS  %FCJEPBFTUBCBKBQSFTJÓO FMQFSNFBEPOFDFTJUBVOBHSBOÃSFBQBSBáVJS PCJFO MBDBÎEBEFQSFTJÓODBVTBEBQPSFMáVKPEFMQFSNFBEPTFSÃHSBOEF1PSUBOUP FOFTDBMBJOEVTUSJBMTF VTBONFNCSBOBTEFQMBDBZNBSDP FOFTQJSBMZEFàCSBTIVFDBTDPOBMJNFOUBDJÓOEFOUSPEFMBTàCSBT -BàHVSBNVFTUSBRVFTFSFRVJFSFOVOBCPNCBEFWBDÎPZVODPOEFOTBEPSQBSBSFDVQFSBSFM WBQPSEJMVJEPBCBKBQSFTJÓO"NFOPTRVFFMDPSUFTFBQFRVFÒP TFOFDFTJUBVOBGVFOUFBEJDJPOBMEF FOFSHÎB RVFTVNJOJTUSFFMDBMPSEFFWBQPSBDJÓO4JFMDPSUFFTQFRVFÒP MBFOFSHÎBEFMMÎRVJEPDBMJFOUF QVFEFTFSTVàDJFOUF1BSBDPSUFTNBZPSFT TFQVFEFDBMFOUBSVOBQBSUFEFMSFUFOUBEPQBSBSFDJSDVMBS MB&OFMMJCSPEF)VBOH  TFQSFTFOUBONÃTEFUBMMFTBDFSDBEFMFRVJQPZFMEJTFÒPEFMNJTNP "VORVFFOMBTVOJEBEFTEFQFSWBQPSBDJÓOMBTFMFDUJWJEBEQVFEFTFSCBTUBOUFBMUB QPSFKFNQMP  -FFQFS  QSFTFOUBWBMPSFTEFB 

MPTWBMPSFTOPTPOJOàOJUPT"TÎ TJFNQSFIBCSÃBMHP EFMBTVTUBODJBNFOPTQFSNFBCMFFOFMQFSNFBEPZBMHPEFMBTVTUBODJBNÃTQFSNFBCMFFOFMSFUFO UBEP4JMBDPODFOUSBDJÓOEFMBBMJNFOUBDJÓOZMBTFMFDUJWJEBETPOTVàDJFOUFNFOUFBMUBT FMTJTUFNB EFMBàHVSB DPOVOTPMPQBTP QVFEFQSPEVDJSVOQFSNFBEPPVOSFUFOUBEPRVFDVNQMBMBT FTQFDJàDBDJPOFTEFMQSPEVDUP4JOFNCBSHP MBPUSBDPSSJFOUFDPOUFOESÃVOBDBOUJEBEJNQPSUBOUFEF QSPEVDUPWBMJPTP&MTJTUFNBFOVOTPMPQBTPQVFEFQSPEVDJSBMUBQVSF[BPBMUBSFDVQFSBDJÓO QFSP OPMBTEPTBMNJTNPUJFNQP 4JTFEFTFBBMUBQVSF[BZBMUBSFDVQFSBDJÓOBMNJTNPUJFNQP PTJFMTJTUFNBEFVOQBTPOPQVFEF EBSVOQSPEVDUPDPOMBTFTQFDJàDBDJPOFTSFRVFSJEBT FTGSFDVFOUFVTBSVOTJTUFNBIÎCSJEPDPOSFDJS DVMBDJÓO )VBOH 4VLZ.BUTVSB 8BOLBU  -PTTJTUFNBTIÎCSJEPTVTBOEPTUJQPTEF TFQBSBDJÓOQBSBBMDBO[BSMBTFQBSBDJÓOSFRVFSJEB&MIÎCSJEPNÃTDPNÙOEFQFSWBQPSBDJÓOFTDPNCJ OBSMBDPOMBEFTUJMBDJÓO ZBTFBDPOEPTDPMVNOBT àHVSB" PVOBTPMBDPMVNOB àHVSB#  &OMBàHVSB" MBBMJNFOUBDJÓOBMBDPMVNOBEFEFTUJMBDJÓOGPSNBVOB[FÓUSPQPEFQVOUPEF FCVMMJDJÓONÎOJNP&TUBEFTUJMBDJÓOQSPEVDFFMDPNQPOFOUF" FTFODJBMNFOUFQVSP DPNPGPOEPT&M QSPEVDUPEFTUJMBEPEFMBDPMVNOB DFSDBOPBMBDPODFOUSBDJÓOB[FPUSÓQJDB TFNBOEBBMBVOJEBE EFQFSWBQPSBDJÓO4JFMDPNQPOFOUF"QFSNFBEFQSFGFSFODJBQPSMBNFNCSBOB FMQFSNFBEPFTUBSÃ NÃTDPODFOUSBEPFO"RVFFMEFTUJMBEP&OUPODFT FMQFSNFBEPTFSFDJSDVMBBMBDPMVNOBQBSBSFDV QFSBSFMQSPEVDUP"&MDPNQPOFOUF#TFSFUJFOFFOMBVOJEBEEFQFSWBQPSBDJÓOZTFDPODFOUSBFOFM SFUFOUBEP RVFFTMBBMJNFOUBDJÓOBMBDPMVNOBEFEFTUJMBDJÓO&MEFTUJMBEPEFMBDPMVNOBUBNCJÊO TFBDFSDBBMBDPODFOUSBDJÓOB[FPUSÓQJDBZFTQBSUFEFMBBMJNFOUBDJÓOBMBVOJEBEEFQFSWBQPSBDJÓO -PTGPOEPTQSPEVDJEPTFOMBDPMVNOBTPO FOFTFODJB #QVSP-BTEPTDPMVNOBTEFEFTUJMBDJÓO FOMBàHVSB"TFQBSFDFOBMBTDPMVNOBTEFMBàHVSB"$PNPMBVOJEBEEFQFSWBQPSBDJÓO TVTUJUVZFBMTFQBSBEPSMÎRVJEPMÎRVJEPFOMBàHVSB" FMTJTUFNBB[FPUSÓQJDPOPOFDFTJUBUFOFSVO B[FÓUSPQPIFUFSPHÊOFPZBTÎ MBàHVSB"FTEFBQMJDBDJÓONÃTHFOFSBM 4JMBTFMFDUJWJEBEFTMPTVàDJFOUFNFOUFBMUB FMSFUFOUBEPQVFEFMMFOBSMBTFTQFDJàDBDJPOFTEFQVSF [B&OUPODFTOPTFOFDFTJUBMBDPMVNOBEFEFTUJMBDJÓO MPDVBMSFTVMUBFOMPTPCWJPTBIPSSPTEFDPTUP EFDBQJUBMZEFPQFSBDJÓO&TUPTFJMVTUSBDPOEJBHSBNBEFáVKPTJNQMJàDBEP DPOVOBDPMVNOB QBSB

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMPTQSPDFTPTEFTFQBSBDJÓODPONFNCSBOB

Pervaporado

Retentado

Permeado

& Vacío

6#

Producto 1 (A puro)

Producto 2 (B puro)

Destilación

Destilación Pervaporado Etanol producto

Vacío

Calentador

Alimentación etanol-agua

'*(63" 4*45&." )±#3*%0%&1&37"103"$*¶/ "$01-"%0$0/%&45*-"$*¶/ " 4*45&."(&/&3"-$0/ %04$0-6./"4 # 4*45&." 4*.1-*'*$"%0%&6/"$0-6./"  1"3"%&4)*%3"5"$*¶/%& &5"/0-

Condensador

agua

7#

Destilación

SPNQFSFMB[FÓUSPQPFUBOPMBHVB àHVSB# 4FQVFEFVTBSDBMFOUBNJFOUPDPOWBQPSEJSFDUP FO MVHBSEFDPOVOWBQPSJ[BEPS -FFQFS  4FVTBVOBNFNCSBOBIJESPGÎMJDBRVFEFKBQBTBSBHVBFO GPSNBTFMFDUJWB&TUBàHVSBFT FOFTFODJB MBNJTNBRVFMBàHVSB# DPOFMTJTUFNBEFQFSWBQPSB DJÓOTVTUJUVZFOEPFMTFQBSBEPSOPFTQFDJàDBEP -PTTJTUFNBTIÎCSJEPTTFTVFMFOEJTFÒBSDPOVODPSUFCBKPQPSQBTP QBSBFWJUBSRVFFOFMTJTUFNB IBZBHSBOEFTDBÎEBTEFUFNQFSBUVSB&MDPSUFUPUBMQBSBUPEBMBVOJEBEQVFEFTFSDVBMRVJFSWBMPS RVFTFRVJFSB&OGPSNBUÎQJDB MBCPNCBEFWBDÎPDBVTBFMNBZPSDPTUPEFPQFSBDJÓO-BDBSHBTPCSF

www.FreeLibros.me

  1FSWBQPSBDJÓO



MBCPNCBEFWBDÎPTFQVFEFEJTNJOVJSSFGSJHFSBOEPMBFUBQBàOBMEFMDPOEFOTBEPSEFQFSNFBEP6O EJTFÒPBEFDVBEPEFMTJTUFNBEFJOUFSDBNCJPEFDBMPSQVFEFSFEVDJSFOGPSNBJNQPSUBOUFMPTDPTUPT EFFOFSHÎB 4JTFEJTQPOFEFEBUPTEFTFMFDUJWJEBEZEFáVKP TFQVFEFOEJTFÒBSMBTVOJEBEFTEFQFSWBQPSB DJÓOTJODPOPDFSMPTEFUBMMFTEFQPMBSJ[BDJÓOEFDPODFOUSBDJÓO EJGVTJÓOZMPTQBTPTEFFWBQPSBDJÓO 1BSBVOBTFQBSBDJÓOCJOBSJB TFEFàOFMBTFMFDUJWJEBE " #DPNP 

A6!72

n6$m6 n $& n6  2 6 m6$& m6 n7$m7

B C

FOMBRVFYZZTPOMBTGSBDDJPOFTEFQFTPFOFMMÎRVJEPZFMWBQPS SFTQFDUJWBNFOUF5BNCJÊOTF QVFEFOVTBSVOJEBEFTNPMBSFT QFSPDPOGSFDVFODJBMPTEBUPTTFJOGPSNBOFOGSBDDJÓOEFQFTP&TUB EFàOJDJÓOTFQBSFDFTVQFSàDJBMNFOUFBMBEFàOJDJÓOEFMBWPMBUJMJEBESFMBUJWBFOMBEFTUJMBDJÓO/B UVSBMNFOUF FOFTUFDBTPMBTFMFDUJWJEBEFTQBSBVOQSPDFTPEFWFMPDJEBEEFJOUFSDBNCJPZSFQSFTFOUB MBDVSWBEFWFMPDJEBEEFUSBOTGFSFODJB/PSFQSFTFOUBVOFRVJMJCSJP-PTEBUPTEFTFMFDUJWJEBETF TVFMFOPCUFOFSCBKPDPOEJDJPOFTFOMBTRVFFTEFTQSFDJBCMFMBQPMBSJ[BDJÓOEFDPODFOUSBDJÓO-BT TFMFDUJWJEBEFTEFUFSNJOBEBTFYQFSJNFOUBMNFOUFTPOGVODJPOFTDPNQMFKBTEFMBUFNQFSBUVSBZEFMB GSBDDJÓONPMBSFOFMMÎRVJEP QPSFKFNQMP WFBMBàHVSB  4JTFEJTQPOFEFEBUPTEFTFMFDUJWJEBE MPTQPEFNPTDPOWFSUJSBMGPSNBUPEFZFOGVODJÓOEFY  EFTQFKBOEPZ"FOMBFDVBDJÓO B 

;aj_dYZeZgbZVX^‹c \$b']

'%%% /(%o8 /)*o8 /+%o8 /,*o8

&%%%

;VXidgYZhZeVgVX^‹c

%

(%%

'%%

&%%

%

%

*% 8dciZc^YdYZZiVcdaZcZaa†fj^Yd ZceZhd

&%%

'*(63" &'&$504%&-" 5&.1&3"563":-"$0.104*$*¶/%&- -±26*%01"3".&.#3"/"%&"-$0)0- 10-*7*/±-*$0$0/&/1&40%&"(&/5& 1"3"&/-"$&4$36;"%04(3¦'*$" %&-'"$503%&1&3.&"$*¶/ )6"/(: 3)*. 

¥3&*.13&40$0/ "6503*;"$*¶/%&&-4&7*&3

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMPTQSPDFTPTEFTFQBSBDJÓODPONFNCSBOB

n62



A67m6  & A67 &m6

D

:BRVFMBTFMFDUJWJEBEEFQFOEFEFMBDPODFOUSBDJÓOEFMMÎRVJEP MBTFDVBDJPOFT B CZD UJFOFO WBMJEF[MPDBM %FOVFWPFYBNJOBSFNPTFMDBTPNÃTTFODJMMPNÓEVMPTEFNFNCSBOB CJFONF[DMBEPTFOMPT MBEPTEFMSFUFOUBEPZEFMQFSNFBEP&OFTUBTJUVBDJÓO MBFDVBDJÓO D FTWÃMJEBTJZTFTVTUJUVZF QPSZQZYQPSYTBM 

ne2

A67mhVa  & A67 &mhVa



FOFMMB ZQZYTBMTFSFàFSFOBMBTGSBDDJPOFTEFQFTPEFMDPNQPOFOUFNÃTQFSNFBCMFFOFMQFSNFBEP Z FOFMSFUFOUBEP SFTQFDUJWBNFOUF%FCFEFUFSNJOBSTFMBTFMFDUJWJEBE FOMBFDVBDJÓO 

BMB UFNQFSBUVSBEFPQFSBDJÓO5ZBMBGSBDDJÓOYTBMFOQFTPFOFMMÎRVJEP4JTFEJTQPOFEFEBUPTFOMBGPSNB EFMBàHVSB EFCFOTFSBMBUFNQFSBUVSBEFPQFSBDJÓO5EFMTJTUFNBEFQFSWBQPSBDJÓO &MCBMBODFHFOFSBMEFNBTBQBSBFMTJTUFNBEFVOTPMPQBTPEFMBàHVSBFT ;aZci 2;ae ;ahVa 



B

ZFMCBMBODFEFNBTBQBSBMBTVTUBODJBNÃTQFSNFBCMFFT ;aZci mZci 2;ae ne ;ahVa mhVa 



C

&TUBTFDVBDJPOFTTPOJEÊOUJDBTBMPTCBMBODFTFOMBQFSNFBDJÓOEFHBTFT FDVBDJPOFT B Z C

 DPOMBFYDFQDJÓORVFYIBTVTUJUVJEPBZ FOMBBMJNFOUBDJÓOZFMSFUFOUBEP&TUBTEPTFDVBDJPOFTTF QVFEFOSFTPMWFSTJNVMUÃOFBNFOUFSFTQFDUPBZQ-BFDVBDJÓOEFPQFSBDJÓORVFSFTVMUBFT

?a\$]#b#'

8a

#-

E

'%

#+

W

#)

&* &%

K #'

%

*

#'

#)

#+

#-

8

%

8 #'

#)

#+

#-

'*(63" 1&37"103"$*¶/%&.&;$-"4%&"(6"&5"/0-"-7"$±0 "53"7­4%&1&-±$6-"4 )0.0(­/&"4'"#3*$"%"4$0/10-±.&30)*%30'±-*$0$ $ $0/$&/53"$*¶/%&"(6" 1031&40&/&- -±26*%0 $ :&/&-1&3.&"%0 $ + '-6+0%&1&3.&"$*¶/1&-±$6-"%&10-*"$3*-0/*53*-0  . %&&41&403

5ž$ /&&- 

¥3&*.13&40$0/"6503*;"$*¶/%&&-4&7*&3

www.FreeLibros.me

  1FSWBQPSBDJÓO





ne2

& RamhVa Ra

mZci  Ra



FOEPOEFFMDPSUF ' Q' FOU&TUFSFTVMUBEPFT FOFTFODJB FMNJTNPRVFMBFDVBDJÓO  4J RVFSFNPTVTBSVOQSPDFEJNJFOUPHSÃàDP MBFDVBDJÓOEFPQFSBDJÓOSFQSFTFOUBSÃVOBMÎOFBSFDUBFO VOTJTUFNBEFDPPSEFOBEBTEFZQDPOUSBYTBM 4JTFFTQFDJàDBOYTBMZ5 MPRVFTJHOJàDBRVFTFDPOPDF "#

TFQPESÃOSFTPMWFSTJNVMUÃOFB NFOUFMBTFDVBDJPOFT  Z B C -BFDVBDJÓORVFSFTVMUBFTDVBESÃUJDBFOZQZMJOFBMFO  8BOLBU    1ÃHT   4F QVFEF EFTQFKBS ZQ DPO GBDJMJEBE %FTBGPSUVOBEBNFOUF  FTUF QSPDFEJNJFOUPFTNÃTDPNQMJDBEPZNFOPTÙUJMFOTJUVBDJPOFTSFBMFTEFMPRVFQBSFDFBQSJNFSB WJTUB$PNPFOHFOFSBMOPTFDPOPDFOYTBMOJ5 OPTFDPOPDFMBTFMFDUJWJEBEZFMDÃMDVMPTFDPNQMJDB 6TBSFNPTVOBTPMVDJÓOHSÃàDBTJNVMUÃOFBQBSBEFTBSSPMMBSVOQSPDFEJNJFOUPBMHPNÃTTFODJMMP RVF TFJMVTUSBSÃFOMPTFKFNQMPTZ &TOFDFTBSJPVOCBMBODFEFFOFSHÎBQBSBFTUJNBSMBUFNQFSBUVSBEFMTJTUFNBEFQFSWBQPSBDJÓO 4VQPOESFNPTRVFFTFTJTUFNBGVODJPOBFOFTUBEPFTUBCMFZRVFFTBEJBCÃUJDP&OUPODFT FMCBMBODF EFFOFSHÎBQBSBFMTJTUFNBRVFNVFTUSBMBàHVSBFT 

;aZci ]Zci 2;ae=e ;ahVa ]hVa 

B

%FàOJNPTBMQVOUPEFSFGFSFODJBDPNPFMDPNQPOFOUF"MÎRVJEPQVSPBMBUFNQFSBUVSB5SFG4VQP OJFOEPRVFFMDBMPSEFNF[DMBTFBEFTQSFDJBCMF MBTFOUBMQÎBTEFMBTDPSSJFOUFTMÎRVJEBTTPO 

]Zci 28EA!Zci IZci IgZ[!

]hVa 28EA!hVa IhVa IgZ[ 

C

ZMBFOUBMQÎBEFMWBQPSFT 

=e 28EK!eIe IgZ[ Lene!IgZ[ 

D

EPOEF QFTFMDBMPSMBUFOUFEFFWBQPSBDJÓOEFMQFSNFBEP EFUFSNJOBEPB5SFGZMBTDBQBDJEBEFTDBMP SÎàDBTFTUÃOUBNCJÊOQPSVOJEBEEFNBTB"MDPNCJOBSMBTFDVBDJPOFT  SFTVMUB 

a 8EA!hVa IhVa IgZ[  ;Zci a 8EA!Zci IZci IgZ[2;ae8EK!eIe IgZ[ ; ea Le ; hVa



:BRVFFMNÓEVMPEFNFNCSBOBFTUÃCJFONF[DMBEP FTSB[POBCMFTVQPOFSRVFFMTJTUFNBFTUÃFOFRVJ MJCSJPUÊSNJDP RVF5TBM5Q4JBSCJUSBSJBNFOUFIBDFNPTRVFMBUFNQFSBUVSBEFSFGFSFODJBTFBJHVBMB MBUFNQFSBUVSBEFTBMJEB 5SFG5TBM5Q MMFHBSFNPTBMBTGPSNBTTJNQMJàDBEBTEFMCBMBODFEFFOFSHÎB  



;aZci 8EA!Zci IZci IhVa 2; ea Le  Ra 2

8EA!Zci IZci IhVa   Le

IhVa 2IZci

RaLe  8EA!Zci

B

C

D

$POMBFDVBDJÓO C TFDBMDVMBFMDPSUFOFDFTBSJPQBSBPCUFOFSVOBUFNQFSBUVSBEFTBMJEBFTQFDJ àDBEB NJFOUSBTRVFMBFDVBDJÓO D QFSNJUFEFUFSNJOBSMBUFNQFSBUVSBEFTBMJEBQBSBDVBMRVJFS DPSUFFTQFDJàDBEP0CTFSWFRVFMBSFMBDJÓOFOUSFFMDPSUFZMBDBÎEBEFUFNQFSBUVSBFOMBDPSSJFOUFEF MÎRVJEPFTMJOFBM-BFDVBDJÓO D FTJOTUSVDUJWB:BRVFFMDBMPSMBUFOUFFTCBTUBOUFNBZPSRVF MBDBQBDJEBEDBMPSÎàDB MBUFNQFSBUVSBEFTBMJEBCBKBSÃQJEBNFOUFBNFEJEBRVFTFBVNFOUBFMDPSUF

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMPTQSPDFTPTEFTFQBSBDJÓODPONFNCSBOB

1BSBFWJUBSFTUBDBÎEBEFUFNQFSBUVSBFTDPNÙOVTBSVOTJTUFNBEFSFDJSDVMBDJÓODPOCBKPDPSUFQPS QBTP :BFTUBNPTMJTUPTQBSBEFTBSSPMMBSFMQSPDFEJNJFOUPEFTPMVDJÓOQBSBTJTUFNBTEFQFSWBQPSBDJÓO DPNQMFUBNFOUFNF[DMBEPT&TUFQSPDFEJNJFOUPFTEJSFDUPDVBOEPTFFTQFDJàDBOMBUFNQFSBUVSBEF TBMJEBPFMDPSUF4JTFFTQFDJàDBFMDPSUF DPOMBFDVBDJÓO D TFDBMDVMB5TBM1BSBUSB[BSMBDVSWB EFWFMPDJEBEEFUSBOTGFSFODJB TFTFMFDDJPOBOWBMPSFTBSCJUSBSJPTEFYTBM TFDBMDVMB "#DPOMPTEBUPT BEFDVBEPT  DPNP MBT àHVSBT  P  TF DBMDVMB ZQ DPO MB FDVBDJÓO   EF WFMPDJEBE EF USBOTGFSFODJBZTFHSBàDBFMQVOUPEFMBDVSWB4JTFEJTQPOFEFEBUPTFYQFSJNFOUBMFTEFZFOGVODJÓO EFYBMBUFNQFSBUVSBEFPQFSBDJÓO5 TFHSBàDBOEJSFDUBNFOUFDPNPZQDPOUSBYTBM-BTPMVDJÓOTJ NVMUÃOFBEFMBFDVBDJÓOEFTFMFDUJWJEBEZMPTCBMBODFTEFNBTBRVFEBFOFMQVOUPEFJOUFSTFDDJÓOEF MBDVSWBEFWFMPDJEBEEFUSBOTGFSFODJBZMBSFDUBEFPQFSBDJÓO FDVBDJÓO   WFBMBàHVSB FOFMFKFNQMP  &+&.1-0 1FSWBQPSBDJÓODÃMDVMPEFGBDUJCJMJEBE 4FEFTFBTFQBSBSBHVBZFUBOPMVTBOEPVOTJTUFNBEFQFSWBQPSBDJÓOEFVOTPMPQBTPZVTB VOBQFMÎDVMBEFBMDPIPMQPMJWJOÎMJDPEFNJDSBTEFFTQFTPS&MTJTUFNBEFQFSWBQPSBDJÓO  QFSGFDUBNFOUF NF[DMBEP  USBCBKBSÃ B ž$ DPO  LH EF BMJNFOUBDJÓOI &TUB BMJNFO UBDJÓODPOUJFOFFOQFTPEFBHVB4JFMQSPEVDUPSFUFOUBEPDPOUJFOFFOQFTPEF BHVB yTFSÃGBDUJCMFFTUFQSPDFTP 4PMVDJÓO " %FGJOB&OFTUFDBTP GBDUJCJMJEBERVJFSFEFDJSyFMQSPDFTPQVFEFIBDFSTFDPOMBBMJ NFOUBDJÓOBVOBUFNQFSBUVSBSB[POBCMF &OUPODFT QBSBEFUFSNJOBSMBGBDUJCJMJEBE  EFCFNPTEFUFSNJOBSMBUFNQFSBUVSBEFFOUSBEBRVFTFSFRVJFSF #Z$&YQMPSFZQMBOFF-BJOGPSNBDJÓOTPCSFWFMPDJEBEEFUSBOTGFSFODJBZMPTEBUPTEF áVKPQBSBFTUBQFMÎDVMBBQBSFDFOFO/FFM  ZTFWFOFOMBàHVSB-PTEBUPT ?′`\$]#b#'

ne′2%#.ne′2#.*

+

b. V# A†cZVhYZDe#

#-

,e

m hVa 2%#*+)

mhVa ′

?′2*#'

mZci ′

#+

mhVa s#*+

)

#) A−K

#'

%

#'

#)

#+

#-

'

%

#'

#)

#+

#-

mhVa

'*(63" 40-6$*¶/%&-&+&.1-0$637"%&7&-0$*%"%%&53"/4'&3&/$*" 1"3""(6"&5"/0-"53"7­4%& .%&"-$0)0-10-*7*/±-*$0"ž$ /&&-   $637"%&'-6+0%&/&&- 

¥3&*.13&40$0/"6503*;"$*¶/%&&-4&7*&3

www.FreeLibros.me

  1FSWBQPSBDJÓO

 



OFDFTBSJPTQBSBMPTCBMBODFTEFFOFSHÎBTFDPOTJHVFOFO1FSSZZ(SFFO 

QÃHJOBT Z &UBOPM$1 - &L+ LH, Z &L+LH&TUJNBEPTBž$ "HVB$1 - 8L+ LH, Z 8L+LH&TUJNBEPTBž$



$BMDVMBSFNPTFMDPSUFZMBUFNQFSBUVSBEFBMJNFOUBDJÓOOFDFTBSJBZEFTQVÊTFYBNJOB SFNPTMBGBDUJCJMJEBE % )ÃHBMP-PTEBUPTEF/FFM  TFHSBàDBOFOMBàHVSB-BMÎOFBEFPQFSBDJÓO RVFOPJOEJDB/FFM

FDVBDJÓO  QBTBQPSFMQVOUPZQYTBMYFOU RVFFTUÃFOMB MÎOFBZY-BMÎOFBEFPQFSBDJÓOEFCFDPSUBSBMBDVSWBEFWFMPDJEBEEFUSBOTGFSFODJB FOYTBM-BGSBDDJÓOFOQFTPEFQFSNFBEPTFQVFEFMFFSFOFTUFQVOUPZFTZQ EFBHVB GSBDDJÓOEFQFTP 



$PNPZBTFDPOPDFOUPEBTMBTGSBDDJPOFTEFQFTP MPNÃTGÃDJMFTSFTPMWFSTJNVMUÃOFB NFOUFMBTFDVBDJPOFT B Z C QBSBDBMDVMBSFMDPSUF   Ra 2

mZci mhVa  ne mhVa





1BSBFTUFQSPCMFNB   −  − 



1BSFDF RVF FTUF DPSUF FT NVZ BMUP 1BSB DPNQSPCBS MB GBDUJCJMJEBE QPEFNPT VTBS FM CBMBODFEFFOFSHÎBQBSBFTUJNBSMBUFNQFSBUVSBEFFOUSBEBSFRVFSJEB0SEFOBNPTMB FDVBDJÓO D DPNPTJHVF



IZci 2IhVa



RaLe  8EA!Zci



&MDBMPSMBUFOUFEFMQFSNFBEPTFFTUJNBDPNPTJHVF Le 2ne!L LL ne!: L:



Le 2%#.*LL %#%*L: 2''.%`?$`\ 





-BDBQBDJEBEDBMPSÎàDBEFMBBMJNFOUBDJÓOBž$TFDBMDVMBDPNPTJHVF 8EA!Zci 2nZci!l 8EA!LI2+% nZci!: 8EA!:I2+% 8EA!Zci 2%#+%8EA!L %#)%8EA!: 2(#+'`?$`\°8 

 



&OUPODFT EFMBFDVBDJÓO 

5FOU     ž$



&T PCWJP RVF FTUB UFNQFSBUVSB FT EFNBTJBEB &M QSPDFTP OP FT GBDUJCMF  QPSRVF MB NFNCSBOBTFEFHSBEBSÎBUÊSNJDBNFOUFZMBBMJNFOUBDJÓOOPTFSÎBMÎRVJEB4FVTBVO DPSUFEFNBTJBEPHSBOEF & $PNQSVFCF:BRVFMPTWBMPSFTUÎQJDPTEFMDPSUFTPO BQSPYJNBEBNFOUF PNFOPT  MBDPODMVTJÓORVFFMQSPDFTPOPFTGBDUJCMFFTSB[POBCMF ' (FOFSBMJDF&MFKFNQMPJMVTUSBRVFMBPQFSBDJÓOEFVOJEBEFTEFQFSWBQPSBDJÓODPO VOTPMPQBTPFTUÃDPOUSPMBEBQPSFMCBMBODFTJNQMJàDBEPEFFOFSHÎB FDVBDJÓO D  &OFTFODJB EFCFIBCFSMBFOFSHÎBTVàDJFOUFFOFMMÎRVJEPEFBMJNFOUBDJÓOQBSBFWB QPSBSMBGSBDDJÓORVFTFEFTFFFOFMMB-PTDPSUFTBMUPTSFRVJFSFOBMJNFOUBDJPOFTNVZ DBMJFOUFT QBSBTVNJOJTUSBSMBFOFSHÎBOFDFTBSJBFOMBFWBQPSBDJÓO

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMPTQSPDFTPTEFTFQBSBDJÓODPONFNCSBOB

&+&.1-0 1FSWBQPSBDJÓOEFTBSSPMMPEFVOEJTFÒPGBDUJCMF $PNPOPGVFGBDUJCMFMBPQFSBDJÓOFOFMFKFNQMP TFMFDDJPOBSVOBUFNQFSBUVSBEFBMJ NFOUBDJÓOBEFDVBEBZEFTBSSPMMBSVOQSPDFTPEFQFSWBQPSBDJÓOGBDUJCMFQBSBMBBMJNFOUBDJÓO EFFTFFKFNQMP4FEFTFBVOQFSNFBEPRVFUFOHBNÃTEFEFBHVB FOQFTP%FUFSNJOBS FMDPSUF MBTGSBDDJPOFTFOQFTPFOQFSNFBEPZSFUFOUBEPZFMÃSFBEFMBNFNCSBOB 4PMVDJÓO " %FGJOB6OBUFNQFSBUVSBBEFDVBEBEFBMJNFOUBDJÓOFTMBRVFFTUÃEFOUSPEFMPTMÎNJUFT BENJTJCMFTQPSMBNFNCSBOB MBBMJNFOUBDJÓOEFCFTFSMÎRVJEBBVOBQSFTJÓOSB[POBCMF )BZNVDIPTSFTVMUBEPTRVFTPODPSSFDUPT #Z$&YQMPSFZQMBOFF6OBBMJNFOUBDJÓOBQSFTJÓOTJHVFTJFOEPMÎRVJEBBž$$POVO DPSUFNFOPS FMQFSNFBEPUFOESÃNÃTEFEFBHVB4JFMDPSUFGVFSBDFSP MBMÎOFB EFPQFSBDJÓOTFSÎBWFSUJDBM%FBDVFSEPDPOMBàHVSB ZQFOFTUFDBTP1P ESFNPTVTBSZQQBSBFTUJNBS Q RVFTFOFDFTJUBQBSBDBMDVMBSFMDPSUF-BFYBDUJ UVEEFFTUBFTUJNBDJÓOTFQPESÃDPNQSPCBSEFTQVÊTEFUFSNJOBS % )ÃHBMP 1PEFNPT FTUJNBS FM DBMPS MBUFOUF EF FWBQPSBDJÓO EFM QSPEVDUP QFSNFBEP  ZQ ZFT Q 8  &L+LH&MWBMPSEF$1- FOUL+ LHž$  TFEFUFSNJOÓFOFMFKFNQMP&OUPODFT DPOMBFDVBDJÓO C

u′ 2

8EA!Zci IZci − IhVa 2(#+'&'%−+%$'((&2%#%.(!n λe ;e′ 2u′ ;Zci′ 2%#%.(&!%%%`\$]g2.(`\$]g



%FBDVFSEPDPOMBFDVBDJÓO 

MBQFOEJFOUFEFMBMÎOFBEFPQFSBDJÓOFT− −  −-BMÎOFBEFPQFSBDJÓOBQBSFDFFOMBàHVSB-BGSBDDJÓOFOQFTPEFM QFSNFBEPFT BQSPYJNBEBNFOUF QPSDPOTJHVJFOUF MBBQSPYJNBDJÓOGVFFYBDUB Z MBEFMSFUFOUBEPFTVOQPDPNBZPSRVF  &MáVKPQPSMBNFNCSBOBTFDBMDVMBDPOMBQBSUFEFáVKPEFMBàHVSB+ FTNÃTP NFOPTLH IN &OUPODFT FMÃSFBEFMBNFNCSBOBFT'Q + N & (FOFSBMJDF&OFTUBDPODFOUSBDJÓOFOFMMÎRVJEPSFUFOUBEP MBNFNCSBOBUJFOFBMUPáV KP&OFMWBMPSPSJHJOBMYTBMFOFMSFUFOUBEP RVFTFVTÓFOFMFKFNQMP FMáVKP FTNVDIPNFOPSZTFOFDFTJUBSÎBVOÃSFBEFNFNCSBOBCBTUBOUFNBZPS /BUVSBMNFOUF IBZNVDIPTEJTFÒPTGBDUJCMFTEJGFSFOUFT4JTFEFTFBVOBDPODFOUSBDJÓONBZPSEFM QFSNFBEP FTQSPCBCMFRVFMBNF[DMBBMJNFOUBEBEFFUBOPMBHVBEFMFKFNQMPTFDPODFOUSF QSJNFSPFOVOBDPMVNOBEFEFTUJMBDJÓOPSEJOBSJB BVOBDPODFOUSBDJÓONVDIPNÃTDFSDBOBBMBEFM B[FÓUSPQP WFBMBàHVSB# &OFMDBTPOPSNBM FMSFUFOUBEPTFSFDJDMBSÎBBMBDPMVNOBEFEFTUJ MBDJÓO1BSBSPNQFSFMB[FÓUSPQPFUBOPMBHVBBFTDBMBJOEVTUSJBMTFVTBOQFSWBQPSBDJÓO EFTUJMBDJÓO B[FPUSÓQJDB DBQÎUVMP ZBETPSDJÓO DBQÎUVMP   &'&$504%&-"1"65"%&'-6+0(&/&3"-

-PTTJTUFNBTDPNQMFUBNFOUFBHJUBEPTDPONFNCSBOBTPOSFMBUJWBNFOUFDPNVOFTFOMBTVOJEBEFTEF MBCPSBUPSJP QPSRVFTFQVFEFONJOJNJ[BSPFMJNJOBSMPTFGFDUPTEFMBQPMBSJ[BDJÓOEFDPODFOUSBDJÓO ZEFGPSNBDJÓOEFHFM&OMBTVOJEBEFTDPNFSDJBMFTTFTVFMFVTBSVOPEFMPTNÓEVMPTRVFNVFTUSBMB àHVSB QPSRVFTFQVFEFBDPNPEBSVOÃSFBHSBOEFEFNFNCSBOBFOVOWPMVNFOQFRVFÒP&T

www.FreeLibros.me

  &GFDUPTEFMBQBVUBEFGMVKPHFOFSBM



QPDPQSPCBCMFRVFMBTQBVUBTEFáVKPFOFMJOUFSJPSEFMáVJEP FOFTUBTVOJEBEFT TFBOQFSGFDUBNFOUF NF[DMBEBTFTNÃTQSPCBCMFRVFTFBQSPYJNFOBMáVKPDSV[BEP àHVSBB

BMáVKPDPODVSSFOUF àHVSB C  P B MB DPOUSBDPSSJFOUF àHVSB D  $PNP FTUBT QBVUBT HFOFSBMFT EF áVKP EBO DPNPSFTVMUBEPNFKPSTFQBSBDJÓORVFVONÓEVMPQFSGFDUBNFOUFNF[DMBEP OVFTUSPTSFTVMUBEPTBO UFSJPSFTTPOFTUJNBDJPOFTDPOTFSWBEPSBT&OFTUBTFDDJÓOBOBMJ[BSFNPTFKFNQMPTJEFBMFT FTUPFT TJO NF[DMBEPBYJBMZTJOQPMBSJ[BDJÓOEFDPODFOUSBDJÓO QBSBQFSNFBDJÓOEFHBTDPOFTUBTPUSBTQBVUBT EFáVKP QBSBEFUFSNJOBSMBNFKPSÎBFOMBTFQBSBDJÓO$PNPFOHFOFSBMMPTTJTUFNBTSFBMFTUJFOFO BMHPEFNF[DMBEPBYJBM MBTFQBSBDJÓORVFEBDPOGSFDVFODJBFOUSFMBDBMDVMBEBQBSBFMDBTPJEFBMZFM DBTPDPONF[DMBQFSGFDUB &+&.1-0 &GFDUPTEFMBQBVUBEFGMVKPTPCSFMBQFSNFBDJÓOEFHBTFT 4FQVFEFDPNQBSBSFMBVNFOUPEFTFQBSBDJÓOQBSBMBTEJWFSTBTQBVUBTEFáVKPDPOFMDBTP EFPYÎHFOPZOJUSÓHFOP(FBOLPQMJT  QSFTFOUBVOQSPCMFNBDPOVOBBMJNFOUBDJÓO DPOEFOJUSÓHFOP QSZQQDN)H 10UNT×−  0/  'FOU  DN/PSNTZDPSUF4FJNQMFNFOUBSPOMPTNPEFMPTRVFTFEFTDSJ CJSÃONÃTBEFMBOUFFOFTUBTFDDJÓO VTBOEPMBTIPKBTEFDÃMDVMPRVFNVFTUSBFMBQÊOEJDF EFMDBQÎUVMP-PTSFTVMUBEPTTFNVFTUSBOFOMBUBCMBFJMVTUSBORVFVOBQBVUBEFáVKP BDPOUSBDPSSJFOUFQSPEVDFNFKPSTFQBSBDJÓODPONFOPTÃSFBEFNFNCSBOB 6#

yp,sal

yent

yr,sal

7#

yp,sal

yr,sal

yent

8#

yp,sal

yent

yr,sal

'*(63" 1"65"4%&'-6+0&/4*45&."4%&1&3.&"$*¶/%&("4&4" '-6+0$36;"%0 $0/1&3.&"%0/0.&;$-"%0 # '-6+0$0/$633&/5& $ '-6+0"$0/53"$033*&/5&

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMPTQSPDFTPTEFTFQBSBDJÓODPONFNCSBOB

5"#-" 3&46-5"%041"3"'3"$$*0/&4.0-"3&4%& 09±(&/0$0/%*45*/5"41"65"4%&'-6+0 &/ 4*45&."4%&1&3.&"$*¶/%&("4&4 EVjiVYZ[aj_d

idiVabZciZbZoXaVYd XdcXjggZciZ [aj_dXgjoVYd [aj_dXgjoVYd ZQQSPNTVNZQ/ $FMMT   7BMVF'Q $FMMT   7BMVF'QUPUBM $FMMT   7BMVFZQQSPN $FMMT   7BMVF"SFBUPU $FMMT   7BMVFZS &OE4VC 16.A.2

Flujo concurrente

1BSBFMáVKPDPODVSSFOUFOPTFOFDFTJUBIBDFSQSVFCBZFSSPS ZFTNVZSÃQJEP&OMBIPKBEFDÃMDVMP TFDBQUVSBOMPTWBMPSFTSFRVFSJEPT5PEPTMPTDÃMDVMPTTFIBDFOFOFMQSPHSBNB7JTVBM#BTJD-BIPKB EFDÃMDVMPTFNVFTUSBDPOWBMPSFTQBSBMBTFQBSBDJÓOEFMPYÎHFOPZOJUSÓHFOPEFMFKFNQMP4F NVFTUSBOMPTSFTVMUBEPTEFMBTTJFUFQSJNFSBTFUBQBTEF/ZMPTSFTVMUBEPTàOBMFT0CTFSWFRVF MBQBMBCSBi'FOUuFTUÃFOMBDFMEB    8dcXjggZciZ ;Zci eZgb6

&%%%%%%nZci %#%%%%&-+-* eg C

^ ;g ne ng 6gZV ;e 7VabVhV nehVa 6gZVidi nghVa ;ghVa ;eidiVa

& ..-%%% %#+)()+'., %#'%-&'.((( '*'&&*(#%%' '%%% &#)**&.:"&& %#**%*,&'(. ((('-&-)&#+ %#&'(+%,&. -%%%%% '%%%%%

%#'%.i]ZiVidi &.% ee &%%

' ..+%%% %#+)',%* %#'%,'*'*('&.' )%%%

( ..)%%% %#+)&.)) %#'%+(-, '*)(()( +%%%

) ..'%%% %#+)&&%#'%**&* '**)+%-%%%

www.FreeLibros.me

%#'eZgb7 &. * ..%%%% %#+)%)&( %#'%)+)' '*+*.-. &%%%%

+ .--%%% %#+(.+)' %#'%(,, '*,,)-+ &'%%%

&#.+-*:"%+

, .-+%%% %#+(--+,*' %#'%'-.+) '*-.&%&#. &)%%%



$BQÎUVMP  *OUSPEVDDJÓOBMPTQSPDFTPTEFTFQBSBDJÓODPONFNCSBOB

&MTJHVJFOUFQSPHSBNB7JTVBM#BTJDDBMDVMBQFSNFBDJÓODPODVSSFOUF CBTÃOEPTFFOMPTOÙNFSPTRVF DPOUJFOFMBIPKBEFDÃMDVMP 4VC.BJO 

%JN/ J"T*OUFHFS %JNQS QQ B C D $PO" $PO# $K $KBOU 'U 'Q 'QUPUBM 'QBOU 'STBM QFSN" QFSN# 'S 'FOU  "SFB "SFBUPU ZU ZFOU ZS ZQ ZQBOU UIFUBUPU BMGB"T%PVCMF 4IFFUT i4IFFUMu 4FMFDU 3BOHF i#u i(4u $MFBS 'FOU$FMMT   7BMVF ZFOU$FMMT   7BMVF QS$FMMT   7BMVF QQ$FMMT   7BMVF UIFUBUPU$FMMT   7BMVF QFSN"$FMMT   7BMVF‹c#![dgbV8V

VXi^kVYd ¸ 9:6: HZe]VYZm 6"*%

VYhdgWZciZ

'

;gZjcYa^X] AVc\bj^g

[dgbV

,, V\jVYZe= gZ\jaVYd

bZi^aZcd'(

eZgaVYZ bV\cZi^iVn Va\^cVidYZ8V

a^cZVa

>‹c#![dgbV8V ' X^Xad]ZmVcd Vab^cV AVc\bj^g VXi^kVYV

¸ V\jVYZe= gZ\jaVYd

HdakZciZ

5"#-" $0/45"/5&4%&&26*-*#3*0 $0/5*/6"$*¶/

f

X \ @2 f 2%#%ba

′ 2*#-

′ 2@še &− εZ $εZ 2*#*

\bda ''X X\bda$A `\ & (,*X

b\ '*)!'*.X b\ f !X 2 \gZh^cVhZXV & (%#,.X \hdac

f2(#%&.X&$'#)'-

&$(#',,

ZXjVX^‹c

%#'b\=H6 bahdac#

s'*°

°8!1*#%\$&%%ba

°

+%° '%° e=2+#.



XdcY^X^dcZh

LVc`Vi&..%

Gji]kZc&.-*

&.-*

E^\[dgY&.,&

gZ[#

  4PSCFOUFTZFRVJMJCSJPEFTPSDJÓO 



$BQÎUVMP  *OUSPEVDDJÓOBMBBETPSDJÓO DSPNBUPHSBGÎBFJOUFSDBNCJPJÓOJDP

B TFBKVTUBCJFOBMPTEBUPTB5,ZTJMBDPOTUBOUFEFFRVJMJCSJPEFBETPSDJÓO," Q TFBQFHBBMBGPSNBEF"SSIFOJVT FDVBDJÓO  -PTEFNÃTWBMPSFTEF," QTPO," Q ,  ×− L1B −Z," Q , ×− L1B − WFBFMQSPCMFNB%  4PMVDJÓO " %FGJOB$BMDVMFMPTWBMPSFTEFQBSÃNFUSP," QRVFTFBKVTUFONFKPSBMBFDVBDJÓO B  QBSBMPTEBUPTEF,%FTQVÊTUSBDFMPTEBUPTEFJTPUFSNBZMBJTPUFSNBEF-BOH NVJSQBSBEFUFSNJOBSTJFTVOCVFOBKVTUF1PSÙMUJNP EFUFSNJOFTJMPTEBUPTEF," Q TBUJTGBDFOMBFDVBDJÓO  ZDBMDVMBS ) #Z$&YQMPSFZQMBOFF4FQVFEFPSEFOBSMBFDVBDJÓO B EFUBMNPEPRVFTFBVOB MÎOFBSFDUB4FNVMUJQMJDBOBNCPTMBEPTQPS  ," QQ" ZTFEJWJEFFOUSFR" e6 & 2 e f6 fb{m 6



&  fb{m@6

D



4JMBJTPUFSNBEF-BOHNVJSFTWÃMJEB VOBHSÃàDBEFQ"R"FOGVODJÓOEFQ"TFSÃMJOFBM 5BNCJÊOTFQVFEFIBDFSVOBKVTUFEJSFDUPOPMJOFBMBMPTEBUPTFOCSVUPFOMVHBSEFMB MJOFBMJ[BDJÓO



4FTBDBMPHBSJUNPOBUVSBMEFBNCPTMBEPTEFMBFDVBDJÓOEF"SSIFOJVT MB B



ac@6 2

= G

& I

ac@6!d 

C

4JTFTJHVFMBFDVBDJÓOEF"SSIFOJVT VOBHSÃàDBEF," QDPOUSB 5 TFSÃVOBSFDUB 5BNCJÊOTFQVFEFDPNQSPCBSTJRNÃYUJFOFVOBGPSNBEF"SSIFOJVT % )ÃHBMP-PTWBMPSFTEFQRB,TFWFOFOMBUBCMB-BHSÃàDBEFQRDPOUSBQ TFWFFOMBàHVSB"





0SEFOBEBBMPSJHFO RNÃY,"



&%%%−(+% 2%#'&(2&$f b{m!nf b{m 2)#+.bbda$\# 1FOEJFOUF (%%%−%

&



"TÎ  @62

&

fb{m

2

fb{m@6

%#'&( 2*#.&+×&%−)`EV−& (+%



ZMBJTPUFSNBEF-BOHNVJSB,FT



f2



-BHSÃàDBEFMBJTPUFSNBTFNVFTUSBFOMBàHVSB#-BDPODPSEBODJBFOUSFMBDVSWB EF-BOHNVJSZMPTEBUPTFTCBTUBOUFCVFOB -PTWBMPSFTQBSBMBHSÃàDBEF"SSIFOJVTTPO



)#+.*#.&+s&% )e6 & *#.&+s&% )e6

www.FreeLibros.me

  "OÃMJTJTEFMNPWJNJFOUPEFTPMVUPQBSBTJTUFNBTMJOFBMFT



5"#-" %"504%&&26*-*#3*01"3".&5"/0&/$"3#¶/"$5*7"%0$"-(0/1$# 3*55&3::"/( 7"-&/;6&-":.:&34   I2'.+@



I2(,(@

I2)-%@

e`EV

fbbda$\

e`EV

fbbda$\

e$f

e`EV

fbbda$\

',*#,--% &&(,#+'** ')&(#&)*% (,*,#+&&+ *'(.#.,'' +',)#&,,' ++-,#-*-.

'#%'.. )#%-'' *#%)&) *#(.-( *#*,+, *#+'&( *#+'&(

)-'#+'.% &&'(#-(+& &+'%#'*)* &...#)+(% ()),#(*%& ).'.#,&%) +&*+#.+,( +*-)#)(-*

&#&&*( &#-*&* '#'(%, '#*)(% (#&+,+ (#),.. (#+-%+ (#,+..

)('#,(* +%+#.-, ,'+#()) ,-+#'+' &%--#(&+ &)&+#+') &+,'#-&+ &,)+#*-'

+(,#,*.&'.+#'%(+ '(,-#+,&+ (,%.#()-+ *('.#+%(% +')+#*.-& ++-,#-*-.

%#(*+. %#,*-) &#'%)+ &#+%+& &#.&-) '#%,)* '#&)&*

I

&$ I

@6!e

ac@6!e

fb{m

acfb{m

'.+ (,( )-%

(#(,-:"( '#+-&:"( '#%-(:"(

'#%)*:"( *#.&+:") &#---:")

+#&.'

,#)((

-#*,*

+#&& )#+. (#-)

&#-&% &#*)* &#()*



&OMBàHVSB$TFNVFTUSBOMBTHSÃàDBTEFMO," QFOGVODJÓOEF5ZMORNÃYDPOUSB 5&TDMBSPRVFFOBNCBTHSÃàDBTMPTEBUPTTFBKVTUBOCJFODPOMÎOFBTSFDUBTZRVFMB SFMBDJÓOEF"SSIFOJVTRVFEBTBUJTGFDIBQBSB," QZQBSBRNÃY&OUPODFT EFBDVFSEPDPO MBFDVBDJÓO C QBSB," Q MBQFOEJFOUFFT− )3



1FOEJFOUF $=2 &-)%@&#.-,

XVa 2 (+*+XVa$\bda \bda@

& $PNQSVFCF-BàHVSB#FTVOBDPNQSPCBDJÓOEFMBKVTUFBMBTDPOTUBOUFTEF-BOH NVJS:BRVFMBDPODPSEBODJBFOUSFMBDVSWBZMPTEBUPTFTCBTUBOUFCVFOB TFDPOàSNB FMBOÃMJTJT-BCVFOBDPODPSEBODJBEFMBHSÃàDBEF"SSIFOJVTFTPUSBDPNQSPCBDJÓOEFM QSPDFEJNJFOUPEFBOÃMJTJT ' (FOFSBMJDF&MBKVTUFBMBSFDUB FOMBàHVSB$ FTNÃTFTUSFDIPRVFQBSBNVDIPT PUSPTTJTUFNBTEFBETPSDJÓO3FDVFSEFRVF BVORVFMBDBOUJEBEBETPSCJEBEJTNJOVZF FOHFOFSBMBNFEJEBRVFBVNFOUBMBUFNQFSBUVSB MBBETPSDJÓOOPTJFNQSFTFBQFHBB VOBSFMBDJÓOEF"SSIFOJVT0CTFSWFRVFFTUPEBWÎBNFOPTQSPCBCMFRVFMPTWBMPSFTEF RNÃYTFBQFHVFOBVOBFDVBDJÓOEF"SSIFOJVT BVORVFFTUFTJTUFNBTÎMPIBDF  "  /¦-*4*4%&-.07*.*&/50%&40-6501"3"4*45&."4-*/&"-&4 '6/%".&/504:"1-*$"$*0/&4"-"$30."50(3"'±"

-BTDPMVNOBTFNQBDBEBTTJNJMBSFTBMBEFMBàHVSBTPOMPTBQBSBUPTEFDPOUBDUPNÃTDPNVOFT RVFTFVTBOQBSBBETPSDJÓOZDSPNBUPHSBGÎB"VORVFIBZFYDFQDJPOFT TFTVFMFOPQFSBSWFSUJDBM NFOUF DPOFMáVKPQBSBMFMPBMFKFEFMBDPMVNOB-BBETPSDJÓO MBDSPNBUPHSBGÎBZFMJOUFSDBNCJP

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMBBETPSDJÓO DSPNBUPHSBGÎBFJOUFSDBNCJPJÓOJDP

6# &-%% &+%% &)%% &'%% &%%% š f -%% +%% )%% '%% %

%

&%%%

'%%%

(%%%

)%%%

*%%%

+%%%

,%%%

)%%%

*%%%

+%%%

,%%%

š )#%

7#

(#% bbda f \ '#%

&#%

%

%

&%%%

'%%%

(%%%

š`E6 & %#%%'

%#%%'*

I

%#%%(

%#%%(*

8# −+

&#.

−,

&#,

acfb{m ac@6 −-

&#*

−.

&#(

'*(63" (3¦'*$"4%&%"504%&&26*-*#3*01"3"&-&+&.1-0 " (3¦'*$"%&-±/&"3&$5" 1"3"-"*405&3."%&-"/(.6*3# *405&3." %&-"/(.6*3$ $0.130#"$*¶/%&-"&$6"$*¶/%&"33)&/*64

www.FreeLibros.me

  "OÃMJTJTEFMNPWJNJFOUPEFTPMVUPQBSBTJTUFNBTMJOFBMFT



JÓOJDPFOMBTDPMVNOBTFNQBDBEBTTPO FOGPSNBJOIFSFOUFQSPDFTPTEFFTUBEPOPFTUBCMF PCJFO QPSMPUFT$PNPFMTPMWFOUFFTFTUBDJPOBSJP TFTBUVSBSÃBMBDPODFOUSBDJÓOEFMBBMJNFOUBDJÓO TJÊTUB FOUSBBMBDPMVNOBFOGPSNBDPOUJOVB1PSDPOTJHVJFOUF UBNCJÊOEFCFIBCFSVOQBTPEFSFHFOFSB DJÓO RVFFMJNJOFMBNBZPSQBSUFPUPEPFMTPSCBUPEFMFNQBRVF-PTNÊUPEPTEFVTPDPNÙOFOMB SFHFOFSBDJÓOTPOQVSHBSDPOVOBDPSSJFOUFJOFSUF DBNCJBSMBUFNQFSBUVSB DBNCJBSMBQSFTJÓOPVTBS VOEFTBETPSCFOUF%FTQVÊTEFMQBTPEFSFHFOFSBDJÓOQPESÃIBCFSVOQBTPPQDJPOBMEFFOGSJBNJFOUP PEFTFDBEP%FTQVÊT DPNJFO[BFMTJHVJFOUFDJDMPDPOFMQBTPEFBMJNFOUBDJÓO&TPTQSPDFTPTTF BOBMJ[BSÃOFOMBTTFDDJPOFTB VTBOEPQSPDFEJNJFOUPTEFBOÃMJTJTDBEBWF[NÃTDPNQMFKPT &OFTUBTFDDJÓODPNFO[BSFNPTDPOMBUFPSÎBNÃTTJNQMF MBEFMNPWJNJFOUPEFTPMVUP QBSBMBTJTP UFSNBTMJOFBMFTBQMJDBEBBMBDSPNBUPHSBGÎBEFFMVDJÓO RVFFTFMQSPDFTPNÃTTJNQMFQPSBOBMJ[BS  &MBOÃMJTJTDPNQMFUPEFMPTQSPDFTPTEFTPSDJÓOSFRVJFSFTJNVMBDJÓOFODPNQVUBEPSB DPOVO QSPHSBNBCBTUBOUFDPNQMFKP QBSBSFTPMWFSMBTFDVBDJPOFTBMHFCSBJDBTZEJGFSFODJBMFTQBSDJBMFTBDP QMBEBT%FTBGPSUVOBEBNFOUF NVDIBTWFDFTMPTTJNVMBEPSFTOPJOEJDBOVODVBESPGÎTJDPEFQPSRVÊ TVDFEF MB TFQBSBDJÓO Z VOB WF[ PCUFOJEP VO SFTVMUBEP  MPT TJNVMBEPSFT OP EJDFO RVÊ IBDFS QBSB NFKPSBSMBTFQBSBDJÓO)BZVONÊUPEPSFMBUJWBNFOUFTJNQMF RVFTFCBTBFOBSHVNFOUPTGÎTJDPTZ RVFTFQVFEFSFTPMWFSDPOMÃQJ[ZQBQFM PDPOVOBIPKBEFDÃMDVMP

RVFEFNVFTUSBTFSNVZÙUJM  BVORVFOPTFBUPUBMNFOUFFYBDUP&MBOÃMJTJTEFNPWJNJFOUPEFTPMVUPFTVONÊUPEPRVFQFSNJUFB MPTJOHFOJFSPTVTBSSB[POBNJFOUPTZDPNQSFOTJÓOGÎTJDPT EFNPEPRVFQVFEBOUFOFSVOBJEFBEFMPT SFTVMUBEPTBQBSUJSEFFYQFSJNFOUPTPTJNVMBDJPOFT&MQBQFMEFMBOÃMJTJTEFNPWJNJFOUPEFTPMVUP FOMPTQSPDFTPTEFTPSDJÓOTFQBSFDFBMQBQFMEFMPTEJBHSBNBTEF.D$BCF5IJFMFFOMBEFTUJMBDJÓO  BCTPSDJÓOZFYUSBDDJÓO-BUFPSÎBEFMNPWJNJFOUPEFMTPMVUPTFVTBQBSBDPNQSFOEFSMBTTFQBSBDJP OFT ZQBSBMPDBMJ[BSQSPCMFNBT/PTFVTBQBSBMPTEJTFÒPTàOBMFT 17.2.1

Movimiento del soluto en una columna

&MTPMVUPPTPSCBUPFOFMJOUFSJPSEFMBTFDDJÓOFNQBDBEBEFVOBDPMVNOBQVFEFFTUBSFOVOPEFUSFT MVHBSFT1VFEFFTUBSFOFMFTQBDJPIVFDPJOUFSTUJDJBM FZFTUBSTFNPWJFOEPBMBWFMPDJEBEJOUFSTUJDJBM WJOUFS4JFMTPMVUPFTUÃFOMPTIVFDPTFOUSFQBSUÎDVMBT − F  QPTFBETPSCFFOFMTÓMJEPFTUBDJPOB SJP UFOESÃVOBWFMPDJEBEBYJBMOFUBJHVBMBDFSP&OPUSBTQBMBCSBT MBTNPMÊDVMBTEFMTPMVUPFTUÃO NPWJÊOEPTFBYJBMNFOUFBVOBBMUBWFMPDJEBE SFDVFSEFRVFWJOUFSFTNBZPSRVFWTVQFS PCJFOOPTF NVFWFO-BWFMPDJEBEQSPNFEJP VT EFMTPMVUP FT VT GSBDDJÓOEFMTPMVUPFOMBGBTFNÓWJM QPSFKFNQMP FOIVFDPTFOUSFQBSUÎDVMBT WJOUFS  

4FQVFEFDBMDVMBSFTUBGSBDDJÓO TJTFUJFOFFODVFOUBMBEJTUSJCVDJÓOEFVODBNCJPJODSFNFOUBM D FOMBDPODFOUSBDJÓOEFMTPMVUP QPSFKFNQMP FOLHNPMN ZTVDPSSFTQPOEJFOUFDBNCJP RFOMB DBOUJEBETPSCJEB QPSFKFNQMP FOLHNPMLHEFBETPSCFOUF  

'SBDDJÓOEFTPMVUPFO F $UEFO F    

-BDBOUJEBEFODBEBVCJDBDJÓOQVFEFEFUSNJOBSTFDBMDVMBOEPFMJOWFOUBSJPEFNBTB  

$UEFO F F 7PMTFHNFOUPEFDPMVNOB DBNCJPEF$POD  F ["D D    B

8iY#Zcadhedgdh2& EZEe@Y Kda#HZ\b#YZ8da#XVbW^dYZ8dcX# 2& EZEe@Y$o6X$X

C

EPOEF ,E FT MB GSBDDJÓO EF MPT QPSPT EPOEF QVFEFO DBCFS MBT NPMÊDVMBT &TUF UÊSNJOP TF WVFMWF JNQPSUBOUFFOMBDSPNBUPHSBGÎBQPSFYDMVTJÓOEFUBNBÒP RVFTFQBSBMBTNPMÊDVMBTDPOCBTFFOTV UBNBÒPZFOFMDBTPJEFBMOPUJFOFBETPSDJÓO  R 8V  

www.FreeLibros.me





$BQÎUVMP  *OUSPEVDDJÓOBMBBETPSDJÓO DSPNBUPHSBGÎBFJOUFSDBNCJPJÓOJDP

-BTFDVBDJPOFT B Z C FTUÃOFOLHNPMEFBETPSCBUP TJDFTUÃFOLHNPMN 8iY#hdgW^YV2&− εZ&− εeKda#Xda#Kda#HZ\b#YZXdajbcVXVbW^dYZ8iY#hdgW^YV





2&− εZ&− εeΔo6X šh

`\hdajid Δf!`\bda$`\VYh# b(



D

&MUÊSNJOP,EOPTFJODMVZFFOMBFDVBDJÓO D

QPSRVFTVQPOFNPTRVF RTFCBTBFOVOBNFEJDJÓO RVF FOGPSNBBVUPNÃUJDB ZBDPOUJFOFBDVBMRVJFSJNQFEJNFOUPFTUÊSJDP-BFDVBDJÓO D UBNCJÊO FTUBSÃFOLHNPMEFBETPSCBUP4JRZDUJFOFOEJTUJOUBTVOJEBEFTRVFMBTRVFTFVTBSPOFOFTUBEFEVDDJÓO  MPTCBMBODFTEFNBTBTFSÃOBMHPEJTUJOUPT DPNQBSFMBTFDVBDJPOFT B CZD DPOMB    "MJOTFSUBSMBFDVBDJÓO  FOMBFDVBDJÓO  SFTVMUB 

;gVXX^‹c2εZ Δo6XΔX$pΔo6XPεZ ΔX &− εZεe@Y ΔX &− εZ&− εeρh ΔfRr



%FTQVÊTEFIBCFSTVTUJUVJEPMBFDVBDJÓO  FOMB 

FMSFTVMUBEPTFQVFEFTJNQMJàDBSBMB TJHVJFOUFGPSNB WFBFMQSPCMFNBEFUBSFB$



jh2 &

k^ciZg  $f & EZ & EZ& Ee E e @Y  šh EZ EZ $X



 -BGPSNBFYBDUBEFMBFDVBDJÓO  EFQFOEFEFMBTVOJEBEFTRVFUFOHBOMPTEBUPTEFFRVJ MJCSJP1PSFKFNQMP TJRFTUÃFOLHEFTPMVUPLHEFTÓMJEPZYFTUÃFOLHEFTPMVUPLHEFáVJEP EF NPEPRVFMBFDVBDJÓOEFMBJTPUFSNBFTRG Y

EFCFFOUPODFTIBCFSVOUÊSNJOPEF ' LHáVJ EPN FOMBTFDVBDJPOFT B Z C Z YSFFNQMB[BB DFOFTBTFDVBDJPOFT&OUPODFT MB FDVBDJÓO  TFUSBOTGPSNBFO 

k^ciZg

jh2

šh š[

@Y

&

f m



B

4JUBOUPRDPNPDFTUÃOFOHNPMN TFPCUJFOFMBFDVBDJÓOQBSBVTFMJNJOBOEP TEFMBFDVBDJÓO    1BSBTJTUFNBTHBTFPTPT FMFRVJMJCSJPTFTVFMFFYQSFTBSFOGVODJÓOEFMBQSFTJÓOQBSDJBM 1" QPS FKFNQMP FDVBDJPOFT B Z C

&OUPODFT MBWFMPDJEBEEFMTPMVUP QBSBHBTFT FT 

jh2 &

& EZ Ee@Y EZ

k^ciZg  $f eIdI & EZ& Ee šh EZ $e6 š[

C

EPOEFrmGFTMBEFOTJEBENPMBS1BSBVOHBTJEFBM rmGQUPU35ZQUPUrmG35"TÎ QBSBMPTHBTFT JEFBMFT 

jh2 &

& EZ Ee@Y EZ

k^ciZg  $f & EZ& Ee šh GI EZ $e6

D

 -BTFDVBDJPOFT  Z  QFSNJUFODBMDVMBSMBWFMPDJEBEQSPNFEJPEFMTPMVUP TJDBMDV MBNPT R D

 R Y P R Q" 4JTVQPOFNPTRVFMBUSBOTGFSFODJBEFNBTBFTNVZSÃQJEB EF

www.FreeLibros.me

  "OÃMJTJTEFMNPWJNJFOUPEFTPMVUPQBSBTJTUFNBTMJOFBMFT



NPEPRVFFMTÓMJEPZFMáVJEPFTUÃOMPDBMNFOUF FODBEBWBMPSEF[ FOFRVJMJCSJP MBWFMPDJEBEEFM TPMVUPEFQFOEFTÓMPEFMDPNQPSUBNJFOUPFOFMFRVJMJCSJP R D

 R Y P R Q" ZEFMBTQSP QJFEBEFTEFMBDPMVNOBOPEFMBTWFMPDJEBEFTEFUSBOTGFSFODJBEFNBTB-BUSBOTGFSFODJBEFNBTB UFOESÃVOBJNQPSUBODJBDSÎUJDBQBSBEFUFSNJOBSMBGPSNBFORVFFMTPMVUPTFTFQBSBEFMQSPNFEJP WFBMBTTFDDJPOFTB &OMBTTFDDJPOFT ZJOTFSUBSFNPTMBJTPUFSNBBEFDVBEB FOMBTFDVBDJPOFT  Z   17.2.2

Teoría del movimiento del soluto para isotermas lineales

-BUFPSÎBFTNÃTTJNQMFDVBOEPTFVTBMBJTPUFSNBMJOFBM FDVBDJÓO C P C $PNPDBTJ UPEPTMPTEBUPTEFFRVJMJCSJPTFWVFMWFOMJOFBMFTBDPODFOUSBDJPOFTPQSFTJPOFTQBSDJBMFTTVàDJFOUF NFOUFCBKBT FYJTUFOBQMJDBDJPOFTSFBMFTEFMBTJTPUFSNBTMJOFBMFT  $VBOEPFTWÃMJEBMBFDVBDJÓO C

 R D,J ZMBFDVBDJÓO  TFUSBOTGPSNBFO 

jh!^2 &

k^ciZg  & EZ & EZ& Ee Ee@Y!^ šh@^a EZ EZ

B

QBSBUPEPBETPSCBUPJ/PUFRVFOJOHVOPEFMPTUÊSNJOPTEFQFOEFEFMBDPODFOUSBDJÓOEFMBETPSCBUP J"TÎ BCBKBTDPODFOUSBDJPOFT EPOEFMBJTPUFSNBMJOFBMFTWÃMJEB MBWFMPDJEBEEFMTPMVUPTFWVFMWF DPOTUBOUF-BWFMPDJEBEVT JEFMTPMVUPEFQFOEFEFMBUFNQFSBUVSB QPSRVF,J EFQFOEFEFMBUFNQF SBUVSB QPSFKFNQMP EFBDVFSEPDPOMBFDVBDJÓO 

4JTFUJFOFOWBSJPTTPMVUPTEJGFSFOUFTDPO EJTUJOUPTWBMPSFTEFDPOTUBOUFEFFRVJMJCSJP FMTPMVUPBETPSCJEPNÃTEÊCJMNFOUF FMWBMPSNÎOJNP EF,J TFNVFWFDPONÃYJNBSBQJEF[ZFMTPMVUPBETPSCJEPNÃTGVFSUFNFOUF FMEFNÃYJNPWBMPS EF,J TFNVFWFDPONÃYJNBMFOUJUVE$PNPTFNVFWFOBEJTUJOUBTWFMPDJEBEFTTFQVFEFOTFQBSBS 5BNCJÊOTFVTBDPOGSFDVFODJBVOBGPSNBEFFTUBFDVBDJÓOQBSBQPSPTJEBEÙOJDB WFBFMQSPCMFNB $ EPOEFBQBSFDFMBFDVBDJÓO C

  1BSB WJTVBMJ[BS FM QBOPSBNB DPNFO[BSFNPT DPO VOB DPMVNOB FNQBDBEB RVF BM QSJODJQJP TF FODVFOUSBMJNQJB D" &OFMNPNFOUPUDPNFO[BNPTBBHSFHBSVOBBMJNFOUBDJÓODPODPODFO USBDJÓOD" 'BVOBWFMPDJEBEJOUFSTUJDJBMDPOPDJEB4FQVFEFVTBSMBFDVBDJÓO B QBSBDBMDVMBS MBWFMPDJEBEEFMTPMVUP VT " FOFMFKFNQMPTFJMVTUSBFMQSPDFEJNJFOUPEFDÃMDVMP &OMBàHVSB "TFUSB[BFMEJBHSBNBEFNPWJNJFOUPEFTPMVUPPEJBHSBNBDBSBDUFSÎTUJDPQBSBFTUFQSPDFTP&M TPMVUPDPNJFO[BFO[ FOFMNPNFOUPUZTVCFBMBWFMPDJEBEVT " RVFFTMBQFOEJFOUFEFMBMÎOFB DBSBDUFSÎTUJDBRVFNVFTUSBMBàHVSB&TQSPCBCMFRVFTFGBDJMJUFNÃTFMQSPDFEJNJFOUPEFTQVÊTEF IBCFSFTUVEJBEPFMFKFNQMP-BTDPODFOUSBDJPOFTFOMBDPMVNOBTFNVFTUSBOFODVBUSPNPNFO UPTFOMBTàHVSBT# $ %Z&&MTPMVUPTVCFDPNPVOBPOEBBWFMPDJEBEDPOTUBOUFVT "4JMB BETPSDJÓOFTGVFSUF MBPOEBTFNVFWFEFTQBDJP NJFOUSBTRVFTJFTEÊCJM TFNVFWFDPOSBQJEF[.ÃT BEFMBOUF FOMBàHVSB TFNPTUSBSÃOPOEBTQBSBTJTUFNBTOPMJOFBMFT  1BSBDVBOEPMPTTJTUFNBTFTUÃOFOGSBDDJPOFTFOQFTP R"," YY" PR"L" ZZ" RFOLHEF TPMVUPLHEFTÓMJEPUPUBMZYZZFOLHEFTPMVUPLHEFáVJEP

MBFDVBDJÓO B TFDPOWJFSUFFO 

jh!^2 &

k^ciZg  & EZ š & EZ a & Ee h @6!m Ee@Y!^ š[ EZ EZ

1BSBHBTFTJEFBMFT DPO R Q"," Q MBFDVBDJÓO D TFUSBOTGPSNBFO

www.FreeLibros.me

D



$BQÎUVMP  *OUSPEVDDJÓOBMBBETPSDJÓO DSPNBUPHSBGÎBFJOUFSDBNCJPJÓOJDP

A

86!hVa 2%

6

7

86!hVa 2%

8

86!hVa 2%

9

86!hVa 286;

: 862%

jh

Y^hiVcX^V Vm^Va o!b

862%

862 86!;

862 86!;

862 86!; 862%

i%

i&

i'

i^Zbed!b^cjidh

i(

;

;

;

;

5i%

5i&

5i'

5i(3ih

'*(63" .07*.*&/50%&-"0/%"1"3"6/$".#*0&/&4$"-¶/%&-"$0/$&/53"$*¶/%& "-*.&/5"$*¶/" %*"(3"."%&-.07*.*&/50%&-40-6501"3"6/"*405&3."-*/&"-# $ %:& 40/$0/$&/53"$*0/&4&/-"$0-6./"$6"/%055 5 5:5 3&41&$5*7".&/5&$0.055*&.10 %&&4$"1& 5&4$-64 " 50%"-"$0-6./":-"4"-*%"&45¦/"$" ' 

k^ciZg

jh!^2 &

e@ Y!^



E

a šhGI@6!e

$POJTPUFSNBTMJOFBMFTFMEFOPNJOBEPSFOMBTFDVBDJPOFT B B E FTJOEFQFOEJFOUFEF MBDPODFOUSBDJÓO"TÎ QBSBàOFTEFNBOJQVMBDJÓOBMHFCSBJDBDPOWJFOFFTDSJCJSFTBTFDVBDJPOFTFO MBGPSNB 

VTJ$JWJOUFS EPOEF$JFTVOBDPOTUBOUF

F

"VORVFTPONVZDÓNPEBT MBTJTPUFSNBTMJOFBMFTUJFOFOQPDBTBQMJDBDJPOFTFOMPTQSPDFTPTJOEVT USJBMFT1BSBEJTNJOVJSFMEJÃNFUSPEFMBTDPMVNOBTZBTÎSFEVDJSMPTDPTUPT MBNBZPSQBSUFEFMBT TFQBSBDJPOFTJOEVTUSJBMFTTFIBDFODPOBMUBTDPODFOUSBDJPOFTPTFBDFSDBONVDIPBMMÎNJUFEFTPMVCJ MJEBE$PNPFTQSPCBCMFRVFFOUPODFTMBTJTPUFSNBTOPTFBOMJOFBMFTZFMVTPEFJTPUFSNBTMJOFBMFT QVFEFDBVTBSHSBOEFTFSSPSFT TFOFDFTJUBVTBSMBTUFPSÎBTOPMJOFBMFTEFMBTFDDJÓO QBSBTJTUF NBTDPODFOUSBEPT 17.2.3

Aplicación de la teoría lineal del movimiento del soluto a ciclos de purga y a la cromatografía de elución

&MDJDMPEFSFHFOFSBDJÓONÃTTJNQMFFTVODJDMPEFQVSHBRVFVTFVOHBTJOFSUFQPSUBEPS PEFBSSBTUSF  QBSBTJTUFNBTHBTFPTPT PCJFOVOTPMWFOUFJOFSUFQBSBTJTUFNBTMÎRVJEPT&TUFDJDMPTFQVFEFPQFSBS FOáVKPDPODVSSFOUF àHVSB" PBDPOUSBDPSSJFOUF àHVSB# $VBOEPFMHBTPFMMÎRVJEP EFQVSHBFOUSBBMBDPMVNOB CBKBMBQSFTJÓOQBSDJBMPMBDPODFOUSBDJÓOEFMBETPSCBUP QPSRVFTFFTUÃ EJMVZFOEP&TPIBDFRVFTFEFTBETPSCBFMBETPSCBUP WFBMBàHVSB

EFKBOEPRVFTFQVFEBMBWBS EFMBDPMVNOB&MHBTPFMTPMWFOUFEFBSSBTUSFJEFBMUJFOFMBTTJHVJFOUFTQSPQJFEBEFTGÃDJMEFTFQBSBS

www.FreeLibros.me

  "OÃMJTJTEFMNPWJNJFOUPEFTPMVUPQBSBTJTUFNBTMJOFBMFT



Solvente o gas de arrastre

Adsorbatos

Concentración (m) (× 10−3)

Alimentación

Solvente o gas de arrastre

Alimentación

Adsorbatos

2ª columna

modelo isocrático

Volumen del efluente (mL)

'*(63" 4*45&."4%&163("" '-6+0 $0/$633&/5& $0.0&/-"$30."50(3"'±" %&&-6$*¶/# "$0/53"$033*&/5& $ $0/$&/53"$*0/&4%&4"-*%"1"3" -"$30."50(3"'±"%&&-6$*¶/%& ¦$*%0"41¦35*$0 "41

"-"/*/" "-"  :'&/*-"-"/*/" 1)& &/6/"3&4*/"%& */5&3$".#*0%&$"5*0/&4 "(0450&5"-   3&*.13&40$0/"6503*;"$*¶/%&*/% &/($)&.3&4&"3$)  

¥ ".&3*$"/$)&.*$"-40$*&5:

EFMBETPSCBUP GÃDJMEFTBDBSEFMMFDIP OPUÓYJDP OPJOáBNBCMF GÃDJMNFOUFEJTQPOJCMFZQPDPDPTUPTP 1BSBTJTUFNBTDPOQVSHBHBTFPTB FMOJUSÓHFOPZFMIJESÓHFOPTFBDFSDBOBMJEFBMEFHBTEFBSSBTUSF $PNPFMBETPSCBUPFTUÃEJMVJEP OPFTDPNÙOVTBSDJDMPTEFQVSHBFOQSPDFTPTJOEVTUSJBMFTEFBETPS DJÓOBHSBOFTDBMB  -PTDJDMPTEFQVSHBTFTVFMFOVTBSFOMBDSPNBUPHSBGÎBEFFMVDJÓO FOFTQFDJBMFORVÎNJDBBOBMÎUJ DB-BDSPNBUPHSBGÎBEFFMVDJÓODPOTJTUFFOBMJNFOUBSVOWPMVNFOFOMBDPMVNOBFNQBDBEB TFHVJEP EFVOHBTJOFSUF TPMWFOUFPEFBSSBTUSF FOáVKPDPODVSSFOUF àHVSB"  4JFMTPMWFOUFPFMHBT QPSUBEPSUBNCJÊOTFBETPSCF FMQSPDFTPTFQVFEFUSBOTGPSNBSFODSPNBUPHSBGÎBEFHSBEJFOUF PEF EFTQMB[BNJFOUP RVFTFEFTDSJCJSÃEFTQVÊT -BDPMVNOBTFQVFEFFNQBDBSDPODVBMRVJFSBEFMPT BETPSCFOUFTPFNQBRVFTEFDSPNBUPHSBGÎBNFODJPOBEPT4JMPTTPMVUPTUJFOFOEJTUJOUBTJTPUFSNBT EFFRVJMJCSJP TFNPWFSÃOFOMBDPMVNOBBEJTUJOUBTWFMPDJEBEFTZTFTFQBSBSÃO àHVSB$ -B DSPNBUPHSBGÎB  UBOUP EF HBTFT DPNP EF MÎRVJEPT TF USBCBKB DPO GSFDVFODJB DPO FTUF NPEP EF FMV DJÓO QBSBEFUFSNJOBSMBTDPNQPTJDJPOFTEFNVFTUSBTEFTDPOPDJEBT-PTTJTUFNBTEFDSPNBUPHSBGÎB

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMBBETPSDJÓO DSPNBUPHSBGÎBFJOUFSDBNCJPJÓOJDP

EFFMVDJÓOFOHSBOFTDBMBTFFTUÃOQPQVMBSJ[BOEP FOFTQFDJBMFOMBTJOEVTUSJBTGBSNBDÊVUJDBTZEF SFBDUJWPTRVÎNJDPTàOPT#POOFSKFBZ5FSSBT 

-BEJTDI  Z3BUIPSFZ7FMBZVEIBO   EFTDSJCFODPOEFUBMMFMBTDPOTJEFSBDJPOFTEFEJTFÒPQBSBTJTUFNBTEFCJPDSPNBUPHSBGÎBFOHSBOFTDB MB-BEJMVDJÓOJOIFSFOUFFOMBTPQFSBDJPOFTEFQVSHBUJFOEFBIBDFSRVFFTPTQSPDFTPTTFBODPTUPTPT FOMBTTFQBSBDJPOFTBHSBOFTDBMB QFSPDVBOEPMBTBMJNFOUBDJPOFTTPODPNQMJDBEBT QVFEFTFSRVF OPIBZBPUSPNÊUPEPBMUFSOBUJWPEFTFQBSBDJÓO &+&.1-0 "OÃMJTJTMJOFBMEFMNPWJNJFOUPEFMTPMVUP FODSPNBUPHSBGÎBEFFMVDJÓO 6OBDPMVNOBEFNFUSPFTUÃFNQBDBEBDPOBMÙNJOBBDUJWBEB"MQSJODJQJP DPOUJFOFDJ DMPIFYBOPQVSP TPMWFOUF&OFMNPNFOUPU FOUSBVOQVMTPEFBMJNFOUBDJÓORVFDPO UJFOFHNPM-EFBOUSBDFOPZHNPM-EFOBGUBMFOPEJTVFMUPTFODJDMPIFYBOP &MQVMTPEVSBNJOVUPT DPOVOBWFMPDJEBETVQFSàDJBMEFDNNJOQBSBMPTQBTPTEF BMJNFOUBDJÓOZEFTPMWFOUF"QMJDBSMBUFPSÎBEFMNPWJNJFOUPEFMTPMVUPQBSBDBMDVMBSMBT DPODFOUSBDJPOFTBMBTBMJEB %BUPT%FOTJEBEBQBSFOUF FMáVJEPFTBJSF LHN  Q  F  G DJDMP IFYBOP LH- ,"-LHEFBETPSCFOUFZ, /-LHEFBETPSCFOUF TJFOEP "BOUSBDFOPZ/OBGUBMFOP,EQBSBBOUSBDFOPZOBGUBMFOP 4PMVDJÓO " %FGJOB&MBQBSBUPTFNVFTUSBFOMBàHVSBB%FTFBNPTDBMDVMBSDVBOEPTBMFOEFMB DPMVNOBMPTQVMTPTEFBOUSBDFOPZOBGUBMFOP # &YQMPSF4FQVFEFBQMJDBSMBFDVBDJÓO  QBSBEFUFSNJOBSWBMPSFTOVNÊSJDPTEF VT "Z6T /-BTMÎOFBTUSB[BEBTFOVOEJBHSBNBEFNPWJNJFOUPEFTPMVUPDPOFTBTNFEJ EBT QBSUJFOEPEFMJOJDJP UNJO ZUFSNJOBOEPFOFMàOBM UNJO EFMQVMTPEF BMJNFOUBDJÓO EFTDSJCFOFMNPWJNJFOUPEFMQSPNFEJPEFMBTNPMÊDVMBTEFBOUSBDFOPZ OBGUBMFOP$PNP, /," VT /VT "ZFMOBGUBMFOPEFCFTBMJSQSJNFSPEFMBDPMVNOB $ 1MBOFF$BMDVMBSVT /ZVT "5SB[BSFMEJBHSBNBEFNPWJNJFOUPEFTPMVUPQBSBVOQVMTP EFBMJNFOUBDJÓOEFNJOVUPT % )ÃHBMP-BWFMPDJEBEJOUFSTUJDJBMTFDBMDVMBDPOMBFDVBDJÓO C

k^ciZg 2khjeZg $EZ 2%#'b$b^c$%#(.2%#*&(b$b^c#



-BEFOTJEBEFTUSVDUVSBMTFDBMDVMBPSEFOBOEPMBFDVBDJÓO D

šh 2šW $P& EZ& ¾EeR2+)'#+`\$b($%#+&%#).2'&*%`\$b(



"IPSB MBTWFMPDJEBEFTEFMTPMVUPTFDBMDVMBODPOMBFDVBDJÓO   jh!62 &



%#+& %#*&&#% %#(.

0CTFSWFRVFIVCPRVFQBTBS, "EF-LHBNLH&OUPODFT jh!6 2



%#*&(b$b^c %#+&%#). '&*%`\$b(''A$`\ b( &%%%A %#(.

%#*&( 2%#%&(*b$b^c & %#,.- (+#'*&

9Z^\jVabdYd!jh!C 2

%#*&( 2%#%&-'b$b^c &#,.- '+#(+-

www.FreeLibros.me

  "OÃMJTJTEFMNPWJNJFOUPEFTPMVUPQBSBTJTUFNBTMJOFBMFT





&TUBTWFMPDJEBEFTEFMTPMVUPTPOMBTQFOEJFOUFTQBSBDBEBTPMVUP FOFMEJBHSBNBEF NPWJNJFOUP EFM TPMVUP àHVSB "  -BT MÎOFBT QBSB DBEB TPMVUP QVFEFO USB[BSTF EFTEFFMJOJDJPBMàOBMEFMQVMTPEFBMJNFOUBDJÓO-PTQVMTPTVPOEBTEFTPMVUPRVFSF TVMUBOTBMFOEFMBDPMVNOBB[-N DPNPNVFTUSBMBàHVSB#&MOBGUBMFOP TBMFEFBNJOVUPTZFMBOUSBDFOPTBMFEFBNJOVUPT-PTQJDPTEF OBGUBMFOPZBOUSBDFOPFTUÃOBTVTDPODFOUSBDJPOFTFOMBBMJNFOUBDJÓO Z HNPM- SFTQFDUJWBNFOUF & $PNQSVFCF -B FOUSBEB EF OBGUBMFOP DVBOEP U   TBMESÃ DVBOEP U  -VT /   N NNJO NJOVUPT%FJHVBMNPEP MBFOUSBEBEFBOUSBDFOPDVBOEPU TBMESÃDVBOEPUNJOVUPT$PNPMPTEPTQJDPTEVSBONJOVUPT FMOBGUBMFOP UFSNJOBEFTBMJSBMPTNJOVUPTZFMBOUSBDFOPBMPTNJOVUPT-PTDFOUSPTEF

pendiente = uN

pendiente = uA

tiempo, minutos

Conc. a la salida, gmol/L

'*(63" 3&46-5"%041"3"&-&+&.1-0 %&$30."530(3"'±"%&&-6$*¶/ " %*"(3"."%&.07*.*&/50%&-40-650 # 1&3'*-&4%&$0/$&/53"$*¶/"-"4"-*%"

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMBBETPSDJÓO DSPNBUPHSBGÎBFJOUFSDBNCJPJÓOJDP

MPTQJDPTDPNJFO[BOFOUBMJNNJOVUPTZFTUÃOFOZNJOVUPT&TPTSFTVM UBEPTDPODVFSEBODPOMBHSÃàDBEFMBàHVSB" ' (FOFSBMJDF $PNP FO MB UFPSÎB TJNQMF EFM NPWJNJFOUP EFM TPMVUP OP TF DPOTJEFSBO MPTGFOÓNFOPTEFEJGVTJÓO TFDBMDVMBRVFMPTQJDPTEFTBMJEBTPOPOEBTSFDUBOHVMBSFT àHVSB #  $VBOEP TF JODMVZFO MB USBOTGFSFODJB EF NBTB Z MB EJTQFSTJÓO BYJBM  MBTDVSWBTTFFYUJFOEFONÃTDPNPNVFTUSBMBàHVSB$-BUFPSÎBEFMNPWJNJFOUP EFM TPMVUP JOEJDB FO GPSNB DPSSFDUB FM DPNQPSUBNJFOUP EF VOB NPMÊDVMB QSPNFEJP "TÎ FMUJFNQPQBSBRVFTBMHBFMDFOUSPEFMPTQJDPTTFDBMDVMBFOGPSNBDPSSFDUB0CTFS WFRVFFMUÊSNJOPQSJODJQBMFOFMEFOPNJOBEPS QBSBBNCPTTPMVUPT FTFMEFBETPSDJÓO &TFTFSÃFMDBTPDVBOEPIBZBVOBBETPSDJÓOSFMBUJWBNFOUFGVFSUF 

#BTNBEKJBO  JOEJDBRVFVOBWFMPDJEBEMJOFBMUÎQJDBQBSBFMQBTPEFBMJNFOUBDJÓO  QBSBBETPSDJÓOFOTJTUFNBTMÎRVJEPT FTNT FRVJWBMFOUFBDNNJO&MQBTPEF QVSHBQVFEFTFSVOBTWFDFTNÃTSÃQJEP"TÎ MBTUBTBTEFáVKPFOFTUFQSPCMFNBTPO SB[POBCMFT

 )BZVOBBOBMPHÎBRVFQVFEFTFSÙUJMQBSBDPNQSFOEFSFTUFBOÃMJTJTEFMNPWJNJFOUPEFMTPMVUP -PTQSPCMFNBTTFQBSFDFOBMPTQSPCMFNBTBMHFCSBJDPTDVBOEPEPTUSFOFTDPNJFO[BOBTBMJSEFVOB FTUBDJÓOBMNJTNPUJFNQP QFSPDPOEJTUJOUBTWFMPDJEBEFT V"ZV#FODSPNBUPHSBGÎB 1PESÃVTUFE DBMDVMBSDVÃOEPMMFHBDBEBUSFOBVOBTFHVOEBFTUBDJÓO BVOBEJTUBODJB- ZDVÃOEPFMFYUSFNPEF MBDPMBEFDBEBUSFO BOÃMPHPBMUJFNQPEFBMJNFOUBDJÓO U' TBMFEFMBTFHVOEBFTUBDJÓO  &OMBQSÃDUJDBSFBMFTNVDIPNÃTGÃDJMDBMDVMBSMPTUJFNQPTEFTBMJEBDPNPTFJOEJDBFOFMQBTP& EFMFKFNQMP FOWF[EFUSB[BSFMEJBHSBNBEFNPWJNJFOUPEFMTPMVUPDPOVOBFTDBMBFYBDUB&TP TFQVFEFIBDFSDPOGBDJMJEBEFOVOBIPKBEFDÃMDVMP BVOQBSBQSPDFTPTNVDIPNÃTDPNQMJDBEPT4JO FNCBSHP TJFNQSFEFCFIBDFSTFVOFTRVFNBEFMEJBHSBNBEFNPWJNJFOUPEFMTPMVUP QPSRVFHVÎB FOMPTDÃMDVMPTZFTVOBDPNQSPCBDJÓOWJTVBMEFFMMPT  &OMPTTJTUFNBTSFBMFT MPTSFTVMUBEPTDBMDVMBEPTDPOMBUFPSÎBEFMNPWJNJFOUPEFMTPMVUPTFFY UJFOEFODPOTJEFSBCMFNFOUF EFCJEPBEJTQFSTJÓOBYJBM SFTJTUFODJBTBMBUSBOTGFSFODJBEFNBTBTZBM NF[DMBEPFOMPTWPMÙNFOFTNVFSUPTEFMBDPMVNOB WÃMWVMBTZUVCPT"TÎ MPTDÃMDVMPTQBSBFMTJTUFNB TJNQMFEFDSPNBUPHSBGÎBEFFMVDJÓORVFNVFTUSBMBàHVSB#TFFYUJFOEFOZMPTEPTQJDPTEFTPMV UPTFQPESÎBOUSBTMBQBS DPNPNVFTUSBMBàHVSB$&TFDÃMDVMPTFJMVTUSBSÃEFTQVÊTFOFMFKFNQMP 4JTFSFRVJFSFOHSBOEFTQVSF[BTEFQSPEVDUPT BDBVTBEFFTUBEJGVTJÓOEF[POBTFSFRVJFSFVO QBTPEFBMJNFOUBDJÓONVZDPSUPZPFMVTPEFVOBDPMVNOBMBSHB QBSBBQBSUBSMPTQJDPT"EFNÃT  FMTJHVJFOUFQVMTPEFFOUSBEBEFCFEFNPSBSTFEVSBOUFNVDIPUJFNQP QPSRVFTJOP MBFYUFOTJÓOEF [POBDBVTBSÃEFNBTJBEPUSBTMBQFEFMQJDPMFOUPDPOFMQJDPSÃQJEPEFMTJHVJFOUFQVMTPEFBMJNFOUB DJÓO&MSFTVMUBEPOFUPFTRVFMBDSPNBUPHSBGÎBEFFMVDJÓOQVFEFTFSNVZDPTUPTBFOBQMJDBDJPOFTEF HSBOFTDBMB-PTTJTUFNBTEFNPWJNJFOUPTJNVMBEPEFMFDIP 4.# EFTJNVMBUFENPWJOHCFE TPO DPOGSFDVFODJB NFOPTDPTUPTPTZTFBOBMJ[BSÃOFOMBTFDDJÓO  4FIBOEFTBSSPMMBEPEJWFSTBTWBSJBDJPOFTEFMBDSPNBUPHSBGÎBEFFMVDJÓO&OMBQSPHSBNBDJÓOEF GMVKP TFBVNFOUBMBUBTBEFáVKPQBSBFMVJSDPONÃTSBQJEF[MPTDPNQPOFOUFTMFOUPT FOMBàHVSB$ &TUBUÊDOJDBOPDBNCJBFMWPMVNFOEFMFMVZFOUFOFDFTBSJP QFSPSFEVDFFMUJFNQPEFPQFSBDJÓO-B QSPHSBNBDJÓOEFUFNQFSBUVSBBVNFOUBMBUFNQFSBUVSBEFMBDPMVNOBEVSBOUFMBFMVDJÓO-BNBZPS UFNQFSBUVSBIBDFEJTNJOVJSMBBETPSDJÓOEFMPTTPMVUPT QPSMPRVFTBMFONÃTQSPOUPZUBNCJÊONÃT DPODFOUSBEPT &M NÊUPEP SFMBDJPOBEP  EF HSBEJFOUF EF UFNQFSBUVSB  BVNFOUB MB UFNQFSBUVSB EFM áVJEPRVFFOUSBBVOBDPMVNOBBEJBCÃUJDB-PTDBNCJPTEFUFNQFSBUVSBTVFMFOUFOFSNÃTFGFDUPFO MPTTJTUFNBTHBTFPTPTRVFFOMPTMÎRVJEPT&OMPTTJTUFNBTMÎRVJEPTTFBDPTUVNCSBVTBSVOHSBEJFOUF EFTPMWFOUF DBNCJBOEPFMTPMWFOUFQBSBEJTNJOVJSMBTPSDJÓOEFMPTTPMVUPT-PTDBNCJPTDPNVOFT EFTPMWFOUFDPOTJTUFOFODBNCJBSTVGVFS[BJÓOJDB QPMBSJEBE Q) MBGSBDDJÓOEFMTPMWFOUFPSHÃOJDP

www.FreeLibros.me

  "OÃMJTJTEFMNPWJNJFOUPEFTPMVUPQBSBTJTUFNBTMJOFBMFT



ZMBBEJDJÓOEFVONBUFSJBMGVFSUFNFOUFTPSCJEP-PTHSBEJFOUFT RVFQVFEFOIBDFSTFFOGPSNBEF DBNCJPTDPOUJOVPTPFOGPSNBEFGVODJPOFTFTDBMÓO TFVTBODPOGSFDVFODJBFOMBTCJPTFQBSBDJPOFT -BEJTDI  4JTFIBDFVODBNCJPEFFTDBMÓOFOMBDPODFOUSBDJÓOEFVOBTVTUBODJBRVFTFBETPS CBNÃTRVFUPEPTMPTDPNQPOFOUFTEFMBBMJNFOUBDJÓO BMQSPDFTPTFMFDPOPDFDPNPDSPNBUPHSBGÎB EFEFTQMB[BNJFOUP  6OPEFMPTHSBOEFTQSPCMFNBTFOMBJOEVTUSJBFTMBQVSJàDBDJÓOEFTVTUBODJBTGVFSUFNFOUFBE TPSCJEBT DPNPQPSFKFNQMPMPTIJESPDBSCVSPTEFQFTPNPMFDVMBSNPEFSBEP EF$B$ EFDBEFOB MJOFBM 3VUIWFO  -PTTJTUFNBTEFQVSHBSFRVJFSFOEFNBTJBEPHBTPTPMWFOUFEFQVSHBQBSB FTBTFTQFDJFTGVFSUFNFOUFBETPSCJEBT5BNCJÊOFOMPTDJDMPTEFWBSJBDJÓOEFQSFTJÓO TFDDJÓO  TF SFRVJFSF EFNBTJBEP HBT EF QVSHB QBSB TBDBS MPT NBUFSJBMFT GVFSUFNFOUF BETPSCJEPT -PT DJDMPT UÊSNJDPT TFDDJÓO   QVFEFO DBVTBS EFNBTJBEB EFTDPNQPTJDJÓO UÊSNJDB  QPSRVF TF SFRVJFSFO UFNQFSBUVSBT NVZ BMUBT -PT DJDMPT EF EFTQMB[BNJFOUP RVF VTBO VO EFTBETPSCFOUF DPNP OQFO UBOP OIFYBOPZBNPOJBDP RVFRVFEBOBETPSCJEPTIBOEFNPTUSBEPTVFàDBDJBQBSBSFTPMWFSFTUF QSPCMFNBRVFEFPUSPNPEPTFSÎBJONBOFKBCMF 8BOLBU   %FTBGPSUVOBEBNFOUF MBOPNFO DMBUVSBFTDPOGVTB QPSRVFMPTDJDMPTEFEFTQMB[BNJFOUPQBSBMBBETPSDJÓOUJFOFOVOEFTBETPSCFOUF RVFTFQVFEFBETPSCFSDPONÃTPNFOPTGVFS[BRVFFMBETPSCBUP NJFOUSBTRVFFOMBDSPNBUPHSBGÎB EFEFTQMB[BNJFOUP FMEFTBETPSCFOUFFTFMDPNQVFTUPRVFTFBETPSCFNÃTGVFSUFNFOUF -PTDJDMPT TFSÃOCÃTJDBNFOUFMPTNJTNPTRVFFMDJDMPBDPOUSBDPSSJFOUFRVFNVFTUSBMBàHVSB#$PNPVOB BETPSDJÓOEFEFTQMB[BNJFOUPOFDFTJUBRVFTFSFDVQFSFFMEFTBETPSCFOUFRVFIBZFOFMQSPEVDUP DPO GSFDVFODJBQPSEFTUJMBDJÓO TPOQSPDFTPTSFMBUJWBNFOUFDPTUPTPTRVFTÓMPTFVTBODVBOEPGBMMBOMPT QSPDFTPTEFBETPSDJÓO&OMPTTJTUFNBTEFNPWJNJFOUPTJNVMBEPEFMFDIP 4.# TFVTBOMPTDJDMPTEF QVSHBZEFEFTQMB[BNJFOUP TFDDJÓO   "  /¦-*4*4%&.07*.*&/50%&40-6501"3"4*45&."4-*/&"-&4 "%403$*¶/5­3.*$":$0/7"3*"$*¶/%&13&4*¶/:.07*.*&/50 4*.6-"%0%&-&$)0

:BRVFMPTDJDMPTEFQVSHBVTBOHSBOEFTDBOUJEBEFTEFTPMWFOUFTFIBOEFTBSSPMMBEPPUSPTNÊUPEPT EFSFHFOFSBDJÓO&TPTNÊUPEPTZTVTBOÃMJTJTDPOMBUFPSÎBEFMNPWJNJFOUPEFMTPMWFOUF TPOFMUFNB EFFTUBTFDDJÓO 17.3.1

Adsorción con oscilación de temperatura

-B BETPSDJÓO DPO PTDJMBDJÓO EF UFNQFSBUVSB 54"  UFNQFSBUVSF TXJOH BETPSQUJPO  TF VTB DPO GSF DVFODJB DPO TJTUFNBT HBTFPTPT  FO FTQFDJBM QBSB SFDVQFSBS P FMJNJOBS USB[BT EF TVTUBODJBT RVF TF BETPSCFOGVFSUFNFOUF 3VUIWFO :BOH  4VTBQMJDBDJPOFTUÎQJDBTTPOMBFMJNJOBDJÓOEF DPOUBNJOBOUFT  DPNP MPT DPNQVFTUPT PSHÃOJDPT WPMÃUJMFT 70$  EF WPMBUJMF PSHBOJD DPNQPVOET  'VMLFS 3FZOPMETFUBM  ZFMTFDBEPEFHBTFT #BTNBEKJBO   &MDJDMPCÃTJDP VTBDPOUSBDPSSJFOUFEFMHBTSFHFOFSBOUFDBMJFOUFZTFWFFOMBàHVSB"4FQVFEFDPOTJEFSBS RVFFMDJDMPFTVOBPQFSBDJÓOEFQVSHBEPOEFFMHBTEFQVSHBFTUÃDBMJFOUF&MQBTPEFBMJNFOUBDJÓO QVFEFIBDFSTFZBTFBDPOáVKPBTDFOEFOUFPEFTDFOEFOUF4JFMHBTEFBMJNFOUBDJÓOáVZFFOGPSNB DPOUJOVB TFPQFSBOEPTPNÃTVOJEBEFTFOQBSBMFMP"VORVFFMHBTQVSPTVFMFTFSFMQSPEVDUPRVF TFRVJFSF FOBMHVOPTDBTPTFMBETPSCBUPDPODFOUSBEPFTFMQSPEVDUPWBMJPTP%FTQVÊTEFMQBTPEF SFHFOFSBDJÓO TF QVFEF JOUFSDBMBS VO FOGSJBNJFOUP PQDJPOBM 4F SFRVJFSF FM FOGSJBNJFOUP DVBOEP FMHBTEFBMJNFOUBDJÓOQVFEFSFBDDJPOBSDPOFMBETPSCFOUFDBMJFOUF-BJOTFSDJÓOEFMQBTPEFFO GSJBNJFOUPUJFOEFBPCUFOFSQSPEVDUPTNÃTQVSPT QFSPCBKBMBQSPEVDUJWJEBE LHEFBMJNFOUBDJÓO QSPDFTBEB  IPSB×LHEFBETPSCFOUF 

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMBBETPSDJÓO DSPNBUPHSBGÎBFJOUFSDBNCJPJÓOJDP

6#

Gas puro

Gas regenerante caliente

Gas caliente

Alimentación

Adsorbato concentrado

Gas puro frío

Paso de alimentación

Regeneración

Paso opcional de enfriamiento

7#

'*(63" "%403$*¶/$0/04$*-"$*¶/5­3.*$"" $*$-0"$0/53"'-6+01"3"4*45&."4 ("4&0404# 70-6.&/%*'&3&/$*"-%&$0/530-1"3"#"-"/$&4%&53"/4'&3&/$*"%&."4" $6"/%0-"5&.1&3"563"$".#*"65)64-"1"35&#&4.0%*'*$"$*¶/%&8"/,"5   $0/"6503*;"$*¶/¥ 1)*--*1$8"/,"5  -BCBTFQBSBFTUFNÊUPEPEFSFHFOFSBDJÓOFTMBHSBOSFEVDDJÓOEFMBDPOTUBOUFEFFRVJMJCSJP  RVFTFPCTFSWBFOMBNBZPSQBSUFEFMPTTJTUFNBTDVBOEPBVNFOUBMBUFNQFSBUVSB TFHÙOMBFDVB DJÓO  ZMBSFEVDDJÓOTJNVMUÃOFBEFMBQSFTJÓOQBSDJBMPMBDPODFOUSBDJÓO BMBÒBEJSFMHBTEF QVSHB&TUPTEPTFGFDUPTQVFEFODBVTBSMBFMJNJOBDJÓOEFMBETPSCBUPEFMBDPMVNOB$PNPQVFEFO

www.FreeLibros.me

  "OÃMJTJTEFMNPWJNJFOUPEFTPMVUPQBSBTJTUFNBTMJOFBMFT



QSFTFOUBSTFHSBOEFTBVNFOUPTFOMBDPODFOUSBDJÓOEFBETPSCBUP UBNCJÊOTFVTBOMPTTJTUFNBTDPO PTDJMBDJÓOEFUFNQFSBUVSBQBSBDPODFOUSBSDPSSJFOUFTHBTFPTBTEJMVJEBT$VBOEPOPTFSFRVJFSFFO GSJBSQBSBFWJUBSSFBDDJPOFTRVÎNJDBT TFIBOEFTBSSPMMBEPWBSJBTNPEJàDBDJPOFTEFFTUFDJDMPCÃTJDP /BUBSBKBOZ8BOLBU  &TBTNPEJàDBDJPOFTTFFYQMPSBSÃOFOMPTQSPCMFNBTEFUBSFB  6OBEFMBTHSBOEFTEFTWFOUBKBTEFMTJTUFNBEFBETPSDJÓODPOPTDJMBDJÓOEFUFNQFSBUVSBRVF NVFTUSBMBàHVSB" FTRVFTFQVFEFOOFDFTJUBSHSBOEFTDBOUJEBEFTEFHBTSFHFOFSBOUFQVSP  QBSBDBMFOUBSMBDPMVNOBEFBETPSDJÓOZFMBETPSCFOUF&TPTFEFCFBRVF BQSFTJPOFTOPSNBMFT  MBDBQBDJEBEDBMPSÎàDBWPMVNÊUSJDBEFMHBTFTCBTUBOUFCBKB FODPNQBSBDJÓODPOMBEFMBETPSCFO UFZEFMBFOWPMWFOUFNFUÃMJDBEFMBDPMVNOB&OUPODFT MBSFHFOFSBDJÓOQVFEFTFSSFMBUJWBNFOUF MFOUB DPTUPTBZOPMMFHBSBMBDPODFOUSBDJÓORVFTFRVJFSFEFMQSPEVDUPBETPSCBUP&TUBEFTWFOUBKB UJFOEFBUFOFSNFOPTJNQPSUBODJBDVBOEPFMHBTEFBMJNFOUBDJÓOFTCBTUBOUFEJMVJEPZMBBETPSDJÓO FTGVFSUF$PNPFMQBTPEFBMJNFOUBDJÓOTFSÃFOUPODFTNVZMBSHPZMBDBOUJEBESFMBUJWBEFHBTSF HFOFSBOUFTFSÃSB[POBCMF4JOFNCBSHP TJFMHBTEFBMJNFOUBDJÓOFTDPODFOUSBEP NÃTRVFQPDPT QVOUPTQPSDFOUVBMFT FMBETPSCFOUFTFTBUVSBSÃDPOCBTUBOUFSBQJEF[ZFMQBTPEFBMJNFOUBDJÓOTFSÃ SFMBUJWBNFOUFDPSUP$PNPTFSFRVJFSFMBNJTNBDBOUJEBEEFHBTSFHFOFSBOUFDBMJFOUFQBSBDBMFOUBS MBDPMVNOB TFWVFMWFFYDFTJWBMBSFMBDJÓO HBTSFHFOFSBOUFDBMJFOUF  HBTEFBMJNFOUBDJÓO   1BSBFTUVEJBSMPTTJTUFNBTEFBETPSDJÓODPOPTDJMBDJÓOEFUFNQFSBUVSBVTBOEPFMBOÃMJTJTEFNP WJNJFOUPEFTPMVUP EFCFNPTEFUFSNJOBSFMFGFDUPEFMPTDBNCJPTEFUFNQFSBUVSBTPCSFMBTPOEBTEF TPMVUP MBSBQJEF[DPORVFTFNVFWFVOBPOEBEFUFNQFSBUVSBQPSMBDPMVNOBZFMFGFDUPRVFUJFOFO MPTDBNCJPTEFUFNQFSBUVSBTPCSFMBDPODFOUSBDJÓO&MQSJNFSGFOÓNFOPFTTFODJMMP"MBVNFOUBSMB UFNQFSBUVSB MBTDPOTUBOUFTEFFRVJMJCSJP ,"Z, " EJTNJOVZFOBNCBTZDPOGSFDVFODJBTJHVFOVOB SFMBDJÓOEFMUJQPEFMBEF"SSIFOJVTFOMBFDVBDJÓO  4JTFDPOPDFFMFGFDUPEFMBUFNQFSBUVSB TPCSFMBTDPOTUBOUFTEFFRVJMJCSJP TFQVFEFODBMDVMBSOVFWPTWBMPSFTEFMBTDPOTUBOUFTEFFRVJMJCSJP ZTFQVFEFOEFUFSNJOBSOVFWBTWFMPDJEBEFTEFTPMVUP  "MDBNCJBSMBUFNQFSBUVSBEFVOBBMJNFOUBDJÓOBVOBDPMVNOBEFTPSDJÓOTFIBSÃRVFVOBPMB VPOEB UÊSNJDBSFDPSSBMBDPMVNOB-BWFMPDJEBEEFFTBPOEBUÊSNJDBTFDBMDVMBDPOVOQSPDF EJNJFOUPBOÃMPHPBMRVFTFVTBQBSBMBTPOEBTEFTPMVUP-BWFMPDJEBEEFMBPOEBUÊSNJDBTFSÃMB GSBDDJÓOEFMDBNCJPEFFOFSHÎBUÊSNJDBFOMBGBTFNÓWJM NVMUJQMJDBEBQPSMBWFMPDJEBEJOUFSTUJDJBM 

VUI GSBDDJÓOEFDBNCJPEFFOFSHÎBFOMBGBTFNÓWJM WJOUFS



$PNPMPTDBNCJPTFOMBFOFSHÎBDPOUFOJEBFOFMáVJEPFOMPTQPSPT FOFMTÓMJEPZFOMBTQBSFEFT  UPEPTFMMPTJONÓWJMFT FTUBGSBDDJÓOFT ;gVXX#YZXVbW^dYZ XVbW^dYZZcZg\†VZcaV[VhZb‹k^a 2 ZcZg\†VZcaV[VhZb‹k^a 8VbW^dYZZcZg\†VZc/;VhZB‹k# [aj^Yd^cbdk^a h‹a^Yd eVgZY



&OFTUBEFEVDDJÓOFTUBNPTTVQPOJFOEPVOBPOEBUÊSNJDBQVSB TJOBETPSDJÓO TJOSFBDDJPOFTZTJO DBNCJPTEFGBTF&OUPODFT MPTDBNCJPTEFFOFSHÎBTFEFCFOUPUBMNFOUFBMDBMPSFTQFDÎàDP1PSFKFN QMP MBDBOUJEBEEFMDBNCJPEFFOFSHÎBFOMBGBTFNÓWJMFT 

$UEEFDBNCJPEFFOFSHÎBFOMBGBTFNÓWJM F ["D G$Q G 5G



EPOEF$Q GFTMBDBQBDJEBEDBMPSÎàDBEFMáVJEPZ 5GFTFMDBNCJPEFUFNQFSBUVSBEFMáVJEP"MTVT UJUVJSMPTUÊSNJOPTBEFDVBEPT MBGSBDDJÓOEFMDBNCJPEFFOFSHÎBFOMBGBTFNÓWJMFT [gVXX^‹c2

εZΔo6Xρ[8e ΔI[ [

pΔo6XPεZΔI[ &− εXεeΔIe š[8e [

[

&− εZ&− εešh8e ΔIhR ΔoL8e ΔIlr

www.FreeLibros.me

h

l

  



$BQÎUVMP  *OUSPEVDDJÓOBMBBETPSDJÓO DSPNBUPHSBGÎBFJOUFSDBNCJPJÓOJDP

EPOEF8FTFMQFTPEFMBDPMVNOBQPSVOJEBEEFMPOHJUVE LHN Z 5QG  5TZ 5XTPOMPTDBNCJPT EFUFNQFSBUVSBFOFMáVJEPEFMPTQPSPT FOFMTÓMJEPZFOMBQBSFE JOEVDJEPTQPSFMDBNCJPFOMB UFNQFSBUVSBEFMáVJEP  4JEJWJEJNPTFMOVNFSBEPSZFMEFOPNJOBEPSEFMBFDVBDJÓO  FOUSF 5G UFOESFNPTMBT SFMBDJPOFTEF 5QG  5TZ 5XFOUSF 5G4JMBUSBOTGFSFODJBEFDBMPSFTNVZSÃQJEB FMTJTUFNBMMFHBSÃ BMFRVJMJCSJPUÊSNJDP 5G5QG5T5X1BSBFTUBJHVBMEBETFSFRVJFSFRVFUPEPTMPTDBNCJPTEF UFNQFSBUVSBTFBOJHVBMFT 

 $I[ 2$Ie[ 2$Ih 2$Il  ZUPEBTMBTSFMBDJPOFTEFDBNCJPTEFUFNQFSBUVSBTPOJHVBMFTBVOP"MDPNCJOBSMBTFDVBDJPOFT 

  Z 

MBWFMPDJEBESFTVMUBOUFEFMBPOEBUÊSNJDBFT 

ji]2

K^ciZgš[8e

p

&

& EZ Ee š[8e  [ EZ

[

& EZ& Ee 8e šh h EZ

L 8 EZ6X el

r





&OVOBQSJNFSBBQSPYJNBDJÓO MBUFPSÎBEFMNPWJNJFOUPEFMTPMVUPFTVOBQSJNFSBBQSPYJNBDJÓO

 MBWFMPDJEBEEFMBPOEBUÊSNJDBFTJOEFQFOEJFOUFEFMBDPODFOUSBDJÓOZEFMBUFNQFSBUVSB-BUFN QFSBUVSBFTDPOTUBOUFBMPMBSHPEFMBTMÎOFBTDVZBQFOEJFOUFFTJHVBMBMWBMPSOVNÊSJDPEFVUI  &OMPTQSPDFTPTEFBETPSDJÓODPOPTDJMBDJÓOUÊSNJDB MBNFUBBMBVNFOUBSMBUFNQFSBUVSBFTTB DBSFMBETPSCBUPEFMBETPSCFOUF&TPTVDFEFDVBOEPMBPOEBUÊSNJDBTFDSV[BDPOMBPOEBEFTPMVUP 4VQPOHBRVFBMQSJODJQJPMBDPMVNOBFTUÃBVOBUFNQFSBUVSBVOJGPSNF5 DPODFOUSBDJÓODZDBSHBEF BETPSCFOUFR"MBDPMVNOBTFBMJNFOUBáVJEPBMBUFNQFSBUVSB5&TFDBNCJPEFUFNQFSBUVSBIBDF RVFDBNCJFOMBDPODFOUSBDJÓOZMBDBSHBEFBETPSCFOUFBDZR UPEBWÎBEFTDPOPDJEPT BNCPT $PNP FOMBUFPSÎBEFMNPWJNJFOUPEFMTPMVUPTFTVQPOFRVFIBZFRVJMJCSJPMPDBM DZRFTUÃOFOFRVJMJCSJP B5&MWPMVNFOEFDPOUSPMRVFNVFTUSBMBàHVSB# 8BOLBU  TFVTBSÃQBSBEFTBSSPMMBSFM CBMBODFEFNBTBDPOFTUFDBNCJPEFUFNQFSBUVSB"MQSJODJQJP MBPOEBUÊSNJDBFTUÃFOFMGPOEPEFM WPMVNFOEFDPOUSPM4FTVQPOFRVFMBPOEBUÊSNJDBTFNVFWFDPONÃTSBQJEF[RVFMBPOEBEFTPMVUP  MPDVBMFTDJFSUPQBSBMBNBZPSQBSUFEFMPTTJTUFNBTMÎRVJEPTEJMVJEPTZBMHVOPTTJTUFNBTHBTFPTPT EJMVJEPT1BSBVOBSFCBOBEBEJGFSFODJBMEFMBDPMVNOB EFBMUVSB [BSCJUSBSJB MBUFNQFSBUVSBEFMB SFCBOBEBWBBDBNCJBSEFTEFMBUFNQFSBUVSBJOJDJBM5IBTUBMBUFNQFSBUVSBàOBM5TJ U [VUI  &MCBMBODFEFNBTBQBSBMBSFCBOBEBEJGFSFODJBM EVSBOUFFMJOUFSWBMPEFUJFNQP U FT 

EZk^ciZg$iX' X& PEZ @YEe & EZRX' X&$o 

& EZ& Eešhf' f&$o2%



:BRVF U VUI FTUPTFTJNQMJàDBB  e&

Z



&

Z

&

Z

@Y

k ji]

Z ^ciZg

X'

X& 

šhP f'X'!I' f&X&!I&R2% 

e



-BFDVBDJÓO  ZMBFDVBDJÓOBQSPQJBEBEFMBJTPUFSNBTFQVFEFOSFTPMWFSTJNVMUÃOFBNFOUFQBSB EFTQFKBSMBTJODÓHOJUBTDZR1BSBVOBJTPUFSNBMJOFBM FDVBDJÓO C

MBTPMVDJÓOTJNVMUÃOFBFT 

XI' & & 2

XI& jhI& ji]

& & 

jhI' ji]



1BSBVOTJTUFNBMÎRVJEP EPOEFVUIVT FMVTPEFVOMÎRVJEPDBMJFOUFFOMBBMJNFOUBDJÓO 55  BVNFOUBSÃMBDPODFOUSBDJÓOFOMBTBMJEB&TUPTFJMVTUSBFOFMFKFNQMP

www.FreeLibros.me

  "OÃMJTJTEFMNPWJNJFOUPEFTPMVUPQBSBTJTUFNBTMJOFBMFT

&+&.1-0 3FHFOFSBDJÓOUÊSNJDBDPOJTPUFSNBMJOFBM 6TBSVOQSPDFTPEFBETPSDJÓODPOPTDJMBDJÓOUÊSNJDBQBSBFMJNJOBSIVFMMBTEFYJMFOPFO IIFQUBOPMÎRVJEP VTBOEPHFMEFTÎMJDFDPNPBETPSCFOUF&MBETPSCFEPSUSBCBKBBBUN -BBMJNFOUBDJÓOUJFOFEFYJMFOP GSBDDJÓOFOQFTPZEFOIFQUBOP GSBDDJÓO FOQFTP Bž$-BWFMPDJEBETVQFSàDJBMEFMBBMJNFOUBDJÓOFTDNNJO&TUFBETPSCFEPS UJFOFNEFMPOHJUVEZEVSBOUFFMQBTPEFBMJNFOUBDJÓOFTUÃBž$&MQBTPEFBMJNFOUB DJÓOTFDPOUJOÙBIBTUBRVFTFPCTFSWBFMFTDBQFEFYJMFOPBMBTBMJEB1BSBSFHFOFSBS VTBSO IFQUBOPQVSPBDPOUSBDPSSJFOUF Bž$ZDPOUJOVBSIBTUBRVFTFIBZBFMJNJOBEPFMYJMFOP -BWFMPDJEBETVQFSàDJBMEVSBOUFMBQVSHBFTDNNJO %BUPT"CBKBTDPODFOUSBDJPOFT MBTJTPUFSNBTQBSBYJMFOPTPORY!ž$RY !ž$RZYFTUÃOFOHTPMVUPHBETPSCFOUFZHTPMVUPHáVJEP SFTQFDUJWBNFOUF .BU[Z ,OBFCFM  0USPTEBUPTTPO TLHN QGLHN $QT+LHž$ $QG +LHž$  F  Q,E "TVNBRVF4FQVFEFOPUFOFSFODVFOUBMBTDBQBDJEBEFTDBMPSÎàDBTEFMBTQBSFEFT RVFFM DBMPSEFBETPSDJÓOFTEFTQSFDJBCMF RVFOPIBZBETPSDJÓOEFOIFQUBOPZRVFFMTJTUFNBFTUÃ FOFTUBEPFTUBCMFDÎDMJDP"QMJDBSMBUFPSÎBEFMNPWJNJFOUPEFMTPMVUP B  %FUFSNJOFFMUJFNQPQBSBRVFTFJOJDJFFMFTDBQFEFYJMFOPEVSBOUFFMQBTPEFBMJNFO UBDJÓO C %FUFSNJOF FM UJFNQP OFDFTBSJP QBSB RVF TBMHB MB POEB UÊSNJDB EVSBOUF MPT QBTPT EF BMJNFOUBDJÓOZEFQVSHB D  %FUFSNJOFFMQFSàMEFDPODFOUSBDJÓOEFYJMFOPBMBTBMJEBEVSBOUFFMQBTPEFQVSHB 4PMVDJÓO " %FGJOB&MQSPDFTPTFQBSFDFBMFTRVFNBEFMBàHVSB" QFSPTJOFMQBTPPQDJPOBMEF FOGSJBNJFOUP&MUJFNQPQBSBFMFTDBQFEFTPMVUPFTFMRVFUBSEBFMYJMFOPFOBQBSFDFS QPSQSJNFSBWF[FOMBTBMJEBEFMBDPMVNOBFO[-&MUJFNQPEFFTDBQFEFMBPOEBUÊS NJDBFTDVBOEPMBUFNQFSBUVSBDPNJFO[BBEJTNJOVJS EVSBOUFFMQBTPEFBMJNFOUBDJÓO  PBBVNFOUBS EVSBOUFFMQBTPEFQVSHB &MQFSàMEFDPODFOUSBDJÓOBMBTBMJEBRVFTF CVTDBFTMBDPODFOUSBDJÓOEFYJMFOPFOGVODJÓOEFMUJFNQP # &YQMPSF$PNPMBPQFSBDJÓOFTDÎDMJDBFOFTUBEPFTUBCMF DBEBDJDMPFTVOBSFQFUJDJÓOFYBD UBEFMDJDMPBOUFSJPS

MBDPMVNOBFTUBSÃDBMJFOUFDVBOEPTFJOJDJFMBBMJNFOUBDJÓOGSÎB-B BMJNFOUBDJÓOGSÎBQSPEVDFVOBPOEBUÊSNJDBGSÎBEVSBOUFFMQBTPEFBMJNFOUBDJÓO$BCF FTQFSBSRVFFTBPOEBTFNPWFSÃDPONÃTSBQJEF[RVFMBPOEBEFYJMFOP TFDPNQSPCBSÃ FTUBIJQÓUFTJTBMIBDFSMPTDÃMDVMPT "TÎ MBTPOEBTTPOJOEFQFOEJFOUFT$VBOEPTFJOWJFSUF MBEJSFDDJÓOEFáVKP MBDPODFOUSBDJÓOEFYJMFOPOPDBNCJB IBTUBRVFMBPOEBEFYJMFOP TFDSV[BDPOMBPOEBUÊSNJDB&TPDBVTBVOQFSJPEPEVSBOUFFMRVFFMMÎRVJEPSFHFOFSBEP RVFTBMFEFMGPOEPEFMBDPMVNOBFTUÃBMBDPODFOUSBDJÓOEFMBTBMJEB FTUVEJFMBàHVSB QBSBDPNQSFOEFSFTUP $VBOEPMBTEPTPOEBTTFDSV[BO DBNCJBMBUFNQFSBUVSB FM QBSÃNFUSPEFJTPUFSNBDBNCJBZDBNCJBMBWFMPDJEBEEFMBPOEBEFYJMFOP&OFTFNJTNP NPNFOUP FMYJMFOPTFEFTPSCFZBVNFOUBMBDPODFOUSBDJÓOEFYJMFOPFOFMáVJEP $ 1MBOFF$PNPTFVTBOGSBDDJPOFTEFNBTBFOMBFDVBDJÓOEFFRVJMJCSJP VTBSFNPTMBFDVB DJÓO D QBSBDBMDVMBSMBWFMPDJEBEEFMTPMVUPBZBž$-BWFMPDJEBEEFMBPOEB UÊSNJDBTFEFUFSNJOBDPOMBFDVBDJÓO  DPO8&MFGFDUPEFMDBNCJPEFUFN QFSBUVSBTPCSFMBDPODFOUSBDJÓOEFMáVJEPTFEFUFSNJOBZBTFBDPOVOCBMBODFEFNBTB EVSBOUFVODJDMP PDPOMBFDVBDJÓO   % )ÃHBMP

www.FreeLibros.me





$BQÎUVMP  *OUSPEVDDJÓOBMBBETPSDJÓO DSPNBUPHSBGÎBFJOUFSDBNCJPJÓOJDP

k^ciZg!; 2

khjeZg!; -#% 2 2&-#+%Xb$b^c EZ %#)(

k^ciZg!ejg\V 2



1BSBDBMDVMBSMBWFMPDJEBEEFMTPMVUPTFVTBMBFDVBDJÓO D  k^ciZg

jh2

EZ

&

EZ

&

Ee šh @a%o8 š[

&'%Xb 2(&*#-*b^c %#(,..Xb$b^c

-BWFMPDJEBEEFMBPOEBUÊSNJDB EFBDVFSEPDPOMBFDVBDJÓO 

DPO8FT ji]!;2  &

k^ciZg & ¾EZ& ¾Ee šh8šh & ¾E Ee  š[8š[ EZ EZ

2 &#+(+



EZ EZ

EPOEF,  ž$  &MUJFNQPEFFTDBQFEFYJMFOPFT iWg!mn2



Ee@Y

&-#+% 2%#(,.. Xb$b^c %#*,%#)-&#% %#*,%#*' '&%% ''#(+ %#)( #)( +-)

jh!;%o82

 

&&#% 2 '*#*-Xb$b^c %#)(

&-#+% 2)#,%& Xb$b^c #*,#*' '&%% '%%% #)( +-) &-)&

ZFMUJFNQPEFFTDBQFEFMBPOEBUÊSNJDBFT iWg!i]!; 2 &'%Xb )#,%&Xb$b^c 2'*#*(b^c



1BSBFMQBTPEFQVSHB VUI QVSHB−DNNJO&TOFHBUJWBQPSRVFTFJOWJFSUFMBEJSFD DJÓOEFMáVKP&TUFUJFNQPEFFTDBQFFT ii]!Wg!ejg\V 2 &'%

+#)++ 2&-#*+b^c



0CTFSWFRVFMBPOEBUÊSNJDBTFNVFWFDPOCBTUBOUFNBZPSSBQJEF[RVFMBPOEBEFMTP MVUP ZFMFTDBQFUÊSNJDPFTNÃTSÃQJEP%FTQVÊTEFMDBNCJPEFUFNQFSBUVSB ,  ž$  ZMBWFMPDJEBEEFMTPMVUPZFMUJFNQPEFFTDBQFEVSBOUFMBQVSHBTPO jh-%°2 &#+(+ iWg!mn!ejg\V 2

'*#*'*#*2 2 )#()(Xb$b^c &#+(+ )#'*( %#*,%#*' '&%% '#%& #)( +-)

&'% 2',#+'.b^c )#()(

www.FreeLibros.me

  "OÃMJTJTEFMNPWJNJFOUPEFTPMVUPQBSBTJTUFNBTMJOFBMFT





&MCBMBODFEFNBTBEFYJMFOPFOVODJDMP FOFTUBEPFTUBCMFDÎDMJDPFT&OUSBEBT4BMJEBT



:cigVYVh 2-#%Xb b^c) 6X !Xb'(&*#-*b^cš[ \hdak# Xb(%#%%%.\m^a $\hdac#







-BDPSSJFOUFEFTBMJEBRVFNVFTUSBMBàHVSBDPOTJTUFFOVOBQBSUFBY'ZVOBQBSUF RVFFTDPODFOUSBEB

 

HVa^YVh 2&&#%Xb b^c6X!Xb'&-#*+ b^cš[ \hdakZciZ $Xb(%#%%%.\mna $\hdac &&#%Xb b^c6XXb'',#+'. &-#*+ b^cš[ \hdakZci$Xb(mXdcX



"MJHVBMBS&OUSBEBT4BMJEBT EJWJEBFOUSF"DZrG RVFTFTVQPOFODPOTUBOUFT ZEFT QFKFYDPOD RVFEB mXdcX 2

-#%(&*#-*%#%%%. &&#%&-#*+%#%%%. %#%'%.* \m^a 2 \hdac &&#%',#+'. &-#*+





&MYJMFOPRVFTBMFQPSFMGPOEPEFMBDPMVNOBUJFOFYTBMY'EVSBOUFMPTQSJ NFSPTNJOVUPTEFMQBTPEFSFHFOFSBDJÓO%FTQVÊT EFBNJOVUPT  MBSFHFOFSBDJÓODPOUJFOFYTBMYDPODEFYJMFOP4JMBSFHFOFSBDJÓODPOUJOÙB EVSBOUFNÃTEFNJOVUPT YTBM&MQSPNFEJPEFGSBDDJPOFTFOQFTPEVSBOUFMB SFHFOFSBDJÓOFTYTBM QSPN & $PNQSVFCF 4F QVFEF DPNQSPCBS MB GSBDDJÓO EF YJMFOP FO QFTP  B MB TBMJEB  DPO MB FDVBDJÓO  &TUBFDVBDJÓOTFBQMJDBFOFMQVOUPFOFMRVFFMBETPSCFOUFDBNCJB EFUFNQFSBUVSB%FBDVFSEPDPOMBàHVSB FTPTVDFEFEVSBOUFFMQBTPEFQVSHBZ BTÎUPEBTMBTWFMPDJEBEFTTFEFCFODBMDVMBSBMBWFMPDJEBEEFQVSHB:BRVFMBWFMPDJEBE EFMTPMVUPFTEJSFDUBNFOUFQSPQPSDJPOBMBMBUFNQFSBUVSB n-heptano puro

Purga, 80°C

uxy (vpurga, 80º)

uth (vpurga)

Alimentación, 0°C

'*(63" 40-6$*¶/%&.07*.*&/50%&40-6501"3""%403$*¶/"$0/53"$033*&/5& $0/04$*-"$*¶/%&5&.1&3"563"%&-&+&.1-0

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMBBETPSDJÓO DSPNBUPHSBGÎBFJOUFSDBNCJPJÓOJDP

jhkejg\V!I2%2jhk;!I2%kejg\V$k;2%#(,.. &&#%$-#%2 %#*'')Xb$b^c#

mmnI' 2-% & 2 mmnI& 2% jhI2% 2

& %#*'')

& +#)++

& ji]

& jhI2-%

& ji]

& 2'(#',, +#)++



ZYYZ 5ž$     RVFDPODVFSEBDPOFMSFTVMUBEPEFMCB MBODFEFNBTB ' (FOFSBMJDF&TUFHSBOBVNFOUPFOMBDPODFOUSBDJÓOEFMTPMVUPEVSBOUFMBSFHFOFSBDJÓO UÊSNJDBFTVOGFOÓNFOPHFOFSBMDPOTPMVUPTGVFSUFNFOUFBETPSCJEP TJMBBMJNFOUBDJÓO FTEJMVJEB-BFOFSHÎBOFDFTBSJBQBSBDPODFOUSBSFMYJMFOPEJMVJEPFOFMOIFQUBOP QPS BETPSDJÓO FTCBTUBOUFNFOPSRVFMBOFDFTBSJBQBSBPCUFOFSMBNJTNBDPODFOUSBDJÓO QPSEFTUJMBDJÓO 1VFEFQBSFDFSRVFOPFTHSBODPTBQBTBSEFGSBDDJPOFTEFQFTP B QFSPFTOFDFTBSJPFMJNJOBSVOBDBOUJEBENVZHSBOEFEFOIFQUBOPQBSBPC UFOFSFTFHSBEPEFDPODFOUSBDJÓO 

4JMBTPOEBTEFTPMVUPTFNVFWFONÃTSÃQJEPRVFMBPOEBUÊSNJDB MPDVBMQVFEFTVDFEFSFO MPTTJTUFNBTDPOHBTFTEJMVJEPT TFQVFEFEFEVDJSVOBFDVBDJÓOEFCBMBODFEFNBTBZVOBTPMVDJÓO QBSFDJEB QFSPMJHFSBNFOUFEJTUJOUB BMBTFDVBDJPOFT  B   WFBFMQSPCMFNBEFUBSFB $ &OFTUFDBTP FMTPMVUPDPODFOUSBEPTBMFBEFMBOUFEFMBPOEBUÊSNJDB FOMVHBSEFBUSÃT DPNP JOEJDBOMBTFDVBDJPOFT  B  0USPDBTPRVFTFQVFEFQSFTFOUBS QFSPFTSBSPFOTJTUFNBT EJMVJEPT FTDVBOEPVT 5DBM VUIVT 5GSÎP &OFTUFDBTP RVFTBMFEFMBMDBODFEFFTUBFYQPTJDJÓOFMF NFOUBM FMTPMVUPTFDPODFOUSBPTFFOGPDB FOMBGSPOUFSBEFUFNQFSBUVSB 8BOLBU    )BZWBSJPTDJDMPTUÊSNJDPTRVFTFVTBOFOMBJOEVTUSJB-BàHVSBNVFTUSBVODJDMPBMUFSOPEF BETPSDJÓODPOPTDJMBDJÓOEFUFNQFSBUVSB RVFTFVTBDPOGSFDVFODJBQBSBSFDVQFSBSTPMWFOUFT RVF TVFMFOTFSDPNQVFTUPTPSHÃOJDPTWPMÃUJMFTEFQFTPNPMFDVMBSJOUFSNFEJP FTEFDJSEF BVNB  FOPQFSBDJPOFTEFTFDBEPZEFDVSBEP #BTNBEKJBO 'VMLFS 8BOLBU  4FVTBDBSCÓO Solvente orgánico Condensador

Gas de alimentación

Agua

'*(63" 3&$61&3"$*¶/ %&40-7&/5&$0/ $"3#¶/"$5*7"%0: 3&(&/&3"$*¶/$0/ 7"103%&"(6"

Aire limpio

Vapor de agua

Paso de alimentación

Regeneración con vapor de agua

www.FreeLibros.me

  "OÃMJTJTEFMNPWJNJFOUPEFTPMVUPQBSBTJTUFNBTMJOFBMFT



BDUJWBEPDPNPBETPSCFOUFZWBQPSEFBHVBDPNPHBTSFHFOFSBOUF$POGSFDVFODJB TFFNQMFBOMFDIPT IPSJ[POUBMFTDPOQSPGVOEJEBEEFVOPBEPTNFUSPT QPSRVFMBGVFSUFBETPSDJÓOEFMTPMWFOUFFOFMDBS CÓOBDUJWBEPQFSNJUFRVFMPTMFDIPTTFBOCBTUBOUFDPSUPTZMPTHSBOEFTáVKPTEFHBTFTSFRVJFSFOHSBO EFTÃSFBTUSBOTWFSTBMFTQBSBFWJUBSVOBDBÎEBEFQSFTJÓOFYDFTJWB4JTFEFCFUSBUBSDPOUJOVBNFOUFFM HBTEFBMJNFOUBDJÓO TFVTBOEPTPNÃTBETPSCFEPSFTFOQBSBMFMP VOUJFNQPUÎQJDPEFBMJNFOUBDJÓO FTIPSBT BQSPYJNBEBNFOUF$PNPFMDBMPSMBUFOUFEFMWBQPSEFBHVBFTBMUP TFQVFEFUSBOTGFSJS VOBHSBODBOUJEBEEFFOFSHÎBBMBETPSCFEPSQBSBDBMFOUBSMPDPOSBQJEF[4VFMFRVFEBSVOiUBMÓOuEF TPMWFOUFFOFMMFDIP QPSRVFVOBSFHFOFSBDJÓODPNQMFUBEFMNJTNPOFDFTJUBSÎBDBOUJEBEFTFYDFTJWBT EFWBQPSEFBHVB$PNPMBSFHFOFSBDJÓOFTJODPNQMFUBZEFCJEPBMBDPNQFUFODJBDPOFMWBQPSEF BHVBQBSBMMFHBSBMPTTJUJPTEFBETPSDJÓO MBDBQBDJEBEEFEJTFÒPDBSBDUFSÎTUJDBRVFTFVTBQBSBFMDBS CÓOBDUJWBEPFTEFVOBEFTVDBQBDJEBENÃYJNB-BDBQBDJEBEEFMMFDIPQVFEFBVNFOUBSTF SFEVDJFOEPMBIVNFEBESFMBUJWBEFMHBTEFBMJNFOUBDJÓOBNFOPTEFM  &O BQMJDBDJPOFT JEFBMFT EF FTUF QSPDFTP DPNP FMJNJOBS QFRVFÒBT DBOUJEBEFT EF UPMVFOP FO BJSF

MBTGSBDDJPOFTNPMBSFTNÃYJNBTEFMUPMVFOPTFBDFSDBOB #BTNBEKJBO  ZFMUPMVFOP FT DBTJ UPUBMNFOUF JONJTDJCMF DPO BHVB "TÎ  TF QVFEF SFDVQFSBS FM BETPSCBUP EFM WBQPS EF BHVB  DPOEFOTBOEPMBDPSSJFOUFEFBETPSCBUPZEFKBOEPTFQBSBSFMMÎRVJEP GPSNÃOEPTFVOBDBQBPSHÃOJDB ZVOBDBQBEFBHVB4JFMBETPSCBUPFTNJTDJCMFDPOBHVB QPSFKFNQMP FUBOPM

FMDPOEFOTBEPSTF EJNFOUBEPS RVF NVFTUSB MB àHVSB  TF EFCF TVTUJUVJS QPS VOB DPMVNOB EF EFTUJMBDJÓO  MP DVBM BVNFOUBDPOTJEFSBCMFNFOUFMPTDPTUPTEFDBQJUBMZEFPQFSBDJÓO  5FOHBFODVFOUBRVFQVFEFIBCFSSJFTHPTDPOMBTFHVSJEBEFOMBPQFSBDJÓOEFMFRVJQPEFSF DVQFSBDJÓOEFTPMWFOUFDPODBSCÓOBDUJWBEP RVFNVFTUSBMBàHVSB4JFMTPMWFOUFRVFTFFTUÃ SFDVQFSBOEPFTJOáBNBCMF EFCFUFOFSTFDVJEBEPQBSBFWJUBSVOJODFOEJP4JFMHBTEFBMJNFOUBDJÓO FTBJSF MBDPODFOUSBDJÓOEFMTPMWFOUFFOFMNJTNPEFCFNBOUFOFSTFBCBKPEFMMÎNJUFJOGFSJPSEFFY QMPTJWJEBEZDPOGSFDVFODJBTFNBOUJFOFBCBKPEF›EFFTFMÎNJUFQBSBUFOFSVONBSHFOEFTFHVSJEBE &TUFSFRVJTJUPFRVJWBMF EFNBOFSBJOWBSJBCMF BRVFFMHBTEFBMJNFOUBDJÓOEFCBTFSCBTUBOUFEJMVJEP ZRVFMPTáVKPTTFBOHSBOEFT4JFMHBTEFBMJNFOUBDJÓOFTUÃDBMJFOUF DPOGSFDVFODJBTFFOGSÎBBOUFT EFMBETPSCFEPS QBSBBNFOUBSFMNBSHFOEFTFHVSJEBEZUBNCJÊOMBDBQBDJEBEEFMBETPSCFEPS6OB BMUFSOBUJWBFTPQFSBSBDPODFOUSBDJPOFTNVDIPNBZPSFT VTBOEPOJUSÓHFOPPEJÓYJEPEFDBSCPOP DPNPHBTQBSBMBPQFSBDJÓOEFTFDBEPPEFDVSBEP QFSPFOUPODFTFMHBTQPSUBEPSEFCFSFDVQFSBSTF ZSFDJSDVMBSTF4JFMDBSCÓOBDUJWBEPDBMJFOUFQVFEFDBUBMJ[BSVOBSFBDDJÓODPOMBBMJNFOUBDJÓO TF BÒBEFVOQBTPEFFOGSJBNJFOUPBMQSPDFTP"WFDFT TFBHSFHBVOQBTPEFTFDBEPBOUFTEFMQBTPEF FOGSJBNJFOUP QPSRVFQVFEFJOUFSGFSJSFMBHVBDPOMBBETPSDJÓOPSFBDDJPOBSDPOMBBMJNFOUBDJÓO4J FMHBTEFBMJNFOUBDJÓOFTDPODFOUSBEP FMBETPSCFOUFQVFEFDBMFOUBSTFNVDIP QPSFMHSBODBMPSEF BETPSDJÓO%FTBGPSUVOBEBNFOUF MPTMFDIPTEFDBSCÓOTFJODFOEJBOBWFDFTDVBOEPFTPTVDFEF&TP TFQVFEFFWJUBSFOGSJBOEPCBTUBOUFFMHBTEFBMJNFOUBDJÓO JODPSQPSBOEPVOQBTPEFFOGSJBNJFOUP FOFMDJDMPPTVTUJUVZFOEPFMBJSFEFMQSPDFTPQPSVOHBTJOFSUF  %FCJEPBRVFWBSJBTFNQSFTBTTVNJOJTUSBOVOJEBEFTQBRVFUFQBSBSFDVQFSBSTPMWFOUFTDPODBS CÓOBDUJWBEP FTNÃTQSPCBCMFRVFMPTJOHFOJFSPTKÓWFOFTJOUFSWFOHBOFOMBDPNQSBFJOTUBMBDJÓOEF VOBVOJEBEZOPFOFMEJTFÒPEFVOBOVFWBVOJEBE.JFOUSBTNÃTTFDPOP[DBTPCSFSFDVQFSBDJÓOEF TPMWFOUFTDPODBSCÓOBDUJWBEP TFQPESÃFMFHJSNFKPSMBVOJEBEZOFHPDJBSNFKPSMBPGFSUBQBSBCJFO EFMBDPNQBÒÎB  1BSBMPTTJTUFNBTMÎRVJEPTUBNCJÊOTFFNQMFBOWBSJPTDJDMPTUÊSNJDPT BVORVFUJFOEFOBTFSBMHP EJGFSFOUFTEFMPTRVFTFVTBOQBSBMPTHBTFT-BQSJODJQBMBQMJDBDJÓOEFMBBETPSDJÓOEFMÎRVJEPTFT FMVTPEFDBSCÓOBDUJWBEPQBSBUSBUBSBHVBQPUBCMFZBHVBSFTJEVBM 'BVTUZ"MZ  :BRVFMBT DPODFOUSBDJPOFTEFDPOUBNJOBOUFTTPONVZCBKBTZMBBETPSDJÓOUJFOEFBTFSNVZGVFSUF MBQBSUF EFMBBMJNFOUBDJÓOFOFMDJDMPQVFEFEVSBSBMHVOPTNFTFT&TEJGÎDJMSFHFOFSBSFMDBSCÓOBDUJWBEP -PRVFTFIBDFFTTBDBSFMDBSCÓOEFMBDPMVNOBZNBOEBSMPBVOIPSOPQBSBRVFNBSZFMJNJOBSMPT

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMBBETPSDJÓO DSPNBUPHSBGÎBFJOUFSDBNCJPJÓOJDP

BETPSCBUPT FOVOJEBEFTQFRVFÒBT  DPNPMBTRVFTFVTBOQBSBQVSJàDBSBHVBEFMBMMBWFFOMPTIPHB SFT FMDBSCÓOTFEFTFDIBEFTQVÊTEFVTBSMP&MDBSCÓOBDUJWBEPFTEFVTPDPNÙOFOMBTQMBOUBTFN CPUFMMBEPSBT QBSBFMJNJOBSFMDMPSPEFMBHVBRVFSFBDDJPOBDPOFMDBSCÓOZQSPEVDF)$M 8BOLBU   &MBHVB MJHFSBNFOUFÃDJEB EFCFVTBSTFEFJONFEJBUP QVFTZBOPDPOUJFOFDMPSPRVFEFUJFOF FMDSFDJNJFOUPNJDSPCJBOP  6OBEFMBTQSJODJQBMFTBQMJDBDJPOFTEFMBBETPSDJÓOMÎRVJEBFOMBJOEVTUSJBFTFMTFDBEPEFTPM WFOUFTPSHÃOJDPT #BTNBEKJBO  &OMBàHVSBTFWFVOQSPDFTPUÎQJDP%VSBOUFMPTQBTPT EFSFMMFOPZBMJNFOUBDJÓOTFVTBáVKPBTDFOEFOUF$PNPFMDPOUFOJEPEFBHVBFOMBTVTUBODJBPSHÃOJ DBTVFMFTFSCBKP FMQBTPEFBMJNFOUBDJÓOQVFEFTFSSFMBUJWBNFOUFMBSHP6OBWF[RVFTFQSFTFOUBFM FTDBQF BQBSFDFODBOUJEBEFTBQSFDJBCMFTEFBHVBFOFMTPMWFOUFRVFTBMF

TFDJFSSBMBBMJNFOUBDJÓO ZTFESFOBMBDPMVNOB4FIBDFMBSFHFOFSBDJÓODPOáVKPEFTDFOEFOUFEFVOHBTDBMJFOUFZEFTQVÊT TVFMFIBDFSTFVOQBTPEFFOGSJBNJFOUP&MTFDBEPQPSBETPSDJÓODPNQJUFDPOFMTFDBEPQPSEFTUJMB DJÓO DBQÎUVMP -PTDPTUPTEFPQFSBDJÓOEFMTFDBEPQPSBETPSDJÓOTFEFCFOQSJODJQBMNFOUFBMDPT UPEFMBFOFSHÎBQBSBFWBQPSBSFMMÎRVJEPSFTJEVBMZEFTBETPSCFSFMBHVB&OHFOFSBM FMTFDBEPQPS BETPSDJÓOUJFOFWFOUBKBTFDPOÓNJDBTFODPNQBSBDJÓODPOMBEFTUJMBDJÓODVBOEPMBTDPODFOUSBDJPOFT EFBHVBFOFMTPMWFOUFTPOCBKBT  &OMPTTJTUFNBTDPODFOUSBEPT MBFOFSHÎBHFOFSBEBQPSBETPSDJÓOFTUBOHSBOEF PBQSFDJBCMFNFOUF NBZPS RVFFMDBMPSFTTFOTJCMFEFCJEPBMDBNCJPEFUFNQFSBUVSB&TUPQSPWPDBVOBDPQMBNJFOUPEFMBT POEBTEFDPODFOUSBDJÓOZEFUFNQFSBUVSBRVFDPOGSFDVFODJBTFEFTQMB[BOKVOUBT#BTNBEKJBO   QSFTFOUBVONÊUPEPTFODJMMPQBSBDBMDVMBSFMBVNFOUPNÃYJNPEFUFNQFSBUVSBFOFMTJTUFNB 

5 NÃYZBETPSCBUP BMJN )BET $1 G



&MJOUFSWBMPUÎQJDPQBSBMPTDBMPSFTEFBETPSDJÓO  )BET FTEFBL+LH QSPNFEJP  L+LH ZMBTDBQBDJEBEFTDBMPSÎàDBTUÎQJDBTFOMPTHBTFT $1 G TPOL+LH BQSPYJNBEBNFOUF&TUB FTUJNBDJÓOEBDPNPSFTVMUBEPVOBVNFOUPNÃYJNPBQSPYJNBEPEFUFNQFSBUVSBEFž$QBSBVOB BMJNFOUBDJÓORVFDPOUFOHBFOQFTPEFBETPSCBUPZVOBVNFOUPNÃYJNPEFUFNQFSBUVSBEF ž$QBSBVOBBMJNFOUBDJÓORVFDPOUFOHBFOQFTPEFBETPSCBUP#BTNBEKJBO  SFDP NJFOEBVTBSVOBOÃMJTJTJTPUÊSNJDPTJFMBVNFOUPNÃYJNPDBMDVMBEPEFUFNQFSBUVSBFTNFOPSRVF Pž$&TPCWJPRVFMPTDBTPTFORVFIBZBHSBOEFTBVNFOUPTEFUFNQFSBUVSBEFCFOEJTFÒBSTF UFOJFOEPFTPFODVFOUB ZBEFNÃTUJFOFOJNQPSUBODJBFDPOÓNJDB QFSPFMUSBUBNJFOUPUFÓSJDPEF UBMMBEPTBMFEFMBMDBODFEFFTUFDBQÎUVMPEFJOUSPEVDDJÓO-PTMFDUPSFTJOUFSFTBEPTEFCFODPOTVMUBS

Solvente seco producto

'*(63" 4&$"%0 %&40-7&/5&4-±26*%04 103"%403$*¶/

Alimentación de solvente húmedo Paso de alimentación

gas caliente

Solvente húmedo gas húmedo (a reprocesamiento) Drenado

Regeneración

www.FreeLibros.me

gas frío

gas caliente

Enfriamiento (opcional)

gas

Alimentación líquida Rellenado

  "OÃMJTJTEFMNPWJNJFOUPEFTPMVUPQBSBTJTUFNBTMJOFBMFT



#BTNBEKJBO 

-F7BOFUBM 

3VUIWFO  P:BOH  &TUPTTJTUFNBTNÃTDPODFO USBEPTUBNCJÊOTFQVFEFOTJNVMBSDPOQSPHSBNBTDPNFSDJBMFT 17.3.2

Adsorción con oscilación de presión

-PTDJDMPTEFBETPSDJÓODPOPTDJMBDJÓOEFQSFTJÓO 14" EFQSFTTVSFTXJOHBETPSQUJPO ZMBBETPSDJÓO DPOPTDJMBDJÓOEFWBDÎP 74" EFWBDVVNTXJOHBETPSQUJPO TPOBMUFSOBUJWBTQBSBDJDMPTUÊSNJDPTFO TJTUFNBTHBTFPTPT­TUPTUJFOFOFTQFDJBMVUJMJEBEQBSBBMJNFOUBDJPOFTNÃTDPODFOUSBEBTZPBETPS CBUPTRVFOPTFBETPSCFONVZGVFSUFNFOUF-BàHVSB"NVFTUSBMPTQBTPTFOFMDJDMPCÃTJDPEF 4LBSTUSPN QPS$IBSMFT4LBSTUSPN JOWFOUPSEFMQSPDFTP

FO14" 3VUIWFOFUBM 8BOLBU   &OHFOFSBM FMQSPEVDUPRVFTFEFTFBFTFMHBTQVSPQSPEVDJEPEFTQVÊTEFFMJNJOBSBETPSCBUP &OUSFMBTBQMJDBDJPOFTUÎQJDBTFTUÃOFMTFDBEPEFHBTFT MBQVSJàDBDJÓOEFIJESÓHFOPZMBQSPEVDDJÓO EFPYÎHFOPPOJUSÓHFOPBQBSUJSEFBJSF  %FTQVÊTEFMQBTPEFBMJNFOUBDJÓOBMBQSFTJÓONBZPS TFSFEVDFMBQSFTJÓOFOMBDPMVNOBIBTUB MMFHBSBMBQSFTJÓOJOGFSJPS IBDJFOEPVOBTPQMBEB TBMJEBWJPMFOUBEFHBT BDPOUSBDPSSJFOUF"FTUB QSFTJÓOSFEVDJEB MBDPMVNOBTFQVSHB FODPOUSBDPSSJFOUFDPOMBBMJNFOUBDJÓO VTBOEPQBSUFEFMHBT QSPEVDUPQVSP$PNPFMHBTQSPEVDUPQVSPTFVTBDPNPQVSHB FMHBTEFQVSHBQSPEVDUP PEFTFDIP  DPOUJFOFBETPSCBUPZUBNCJÊOHBTEFBSSBTUSF&MWPMVNFOEFMHBTEFQVSHBOFDFTBSJPQBSBFMDJDMP EF4LBSTUSPNFT 

7QVSHB 7BMJN



EPOEF RVFEB UÎQJDBNFOUF FOUSFZ%FCJEPBMBEJMBUBDJÓOWPMVNÊUSJDBEFMHBTQSPEVDUP  EFTEFQIIBTUBMBQ-EFQVSHB TFOFDFTJUBONFOPTNPMFTEFHBTEFQVSHBRVFEFHBTEFBMJNFOUBDJÓO "MCBKBSMBQSFTJÓOUBNCJÊOTFSFEVDFMBQSFTJÓOQBSDJBM MPRVFBZVEBBEFTPSCFSFMBETPSCBUP&M QBTPàOBMFOFMDJDMPEF4LBSTUSPNFTMBSFQSFTVSJ[BDJÓO PBVNFOUPEFMBQSFTJÓOEFMBDPMVNOB &TUFQBTPTFIBDÎBFOGPSNBPSJHJOBMDPOHBTGSFTDPEFBMJNFOUBDJÓO BVORVFDPOTJTUFNBTDPODFO USBEPTIPZFTNVDIPNÃTGSFDVFOUFVTBSHBTQSPEVDUPEFBMUBQSFTJÓO DPNPTFWFFOMBàHVSB &OHFOFSBM TFPQFSBOFOQBSBMFMPEPTPNÃTDPMVNOBT QFSPDPODJDMPTEFTGBTBEPTQBSBRVFEFVOB DPMVNOBTBMHBFMQSPEVDUPNJFOUSBTRVFMBPUSBOFDFTJUBQVSHBSTFPFMFWBSTVQSFTJÓO6ONÊUPEPEF IBDFSMPTFNVFTUSBFOMBàHVSB#&OMBJOEVTUSJBTFVTBOTJTUFNBTEFBETPSDJÓODPOPTDJMBDJÓO EFQSFTJÓOEFVOBBEPDFDPMVNOBT&TUFTJTUFNBUJFOFMBWFOUBKBEFRVFMPTDJDMPTQVFEFOTFSNVZ SÃQJEPTTPODPNVOFTFOMBJOEVTUSJBUJFNQPTEFVOPPEPTNJOVUPTZFOBMHVOPTDBTPTTPOIBTUB EF BMHVOPT TFHVOEPT &TPT DJDMPT DPSUPT QFSNJUFO UFOFS BMUBT QSPEVDUJWJEBEFT Z FO DPOTFDVFODJB  BETPSCFEPSFTSFMBUJWBNFOUFQFRVFÒPT  -BàHVSBJMVTUSBVODJDMPTFODJMMPEFPTDJMBDJÓOEFWBDÎP-BBMJNFOUBDJÓOFOUSBBMBQSF TJÓOBMUB RVFFOFTFODJBQVFEFTFSMBQSFTJÓOBUNPTGÊSJDB4JQIFTCBTUBOUFNBZPSRVFMBQSFTJÓO BUNPTGÊSJDB QVFEFJOUFSDBMBSTFVOQBTPDPSUPZPQDJPOBMEFTPQMBEB&OUPODFTTFVTBVOBCPNCBEF WBDÎPQBSBSFEVDJSMBQSFTJÓOBWBMPSFTNVZCBKPT"QSFTJPOFTNVZCBKBT MBQSFTJÓOQBSDJBMFTNVZ CBKBZTFQVFEFBETPSCFSNVZQPDPBETPSCBUP WFBMBàHVSB %FTBGPSUVOBEBNFOUF FTUFQBTP FTMFOUPZMBTQSPEVDUJWJEBEFTEFMPTTJTUFNBTEFBETPSDJÓODPOPTDJMBDJÓOEFWBDÎPTPOCBKBT4JO FNCBSHP FTUFTJTUFNBUJFOFMBWFOUBKBRVFTFQVFEFOPCUFOFSVOHBTQSPEVDUPSFMBUJWBNFOUFQVSP ZVOBETPSCBUPQSPEVDUPSFMBUJWBNFOUFQVSP1PSFKFNQMP MBTVOJEBEFTEFBETPSDJÓODPOPTDJMBDJÓO EFWBDÎPQVFEFOTFQBSBSBJSFFOVOPYÎHFOPQSPEVDUPZVOOJUSÓHFOPQSPEVDUP&MQBTPàOBMFTFM BVNFOUPEFMBQSFTJÓOFOMBDPMVNOB-BTVOJEBEFTEFBETPSDJÓODPOPTDJMBDJÓOEFWBDÎPTFTVFMFO USBCBKBSDPOWBSJBTDPMVNOBTFOQBSBMFMP4FIBJOWFOUBEPVOBHSBODBOUJEBEEFWBSJBDJPOFTEFMPT TJTUFNBT 14"  74" Z DPNCJOBDJPOFT EF DJDMPT 14" Z 74" ,VNBS   3VUIWFO FU BM   5POEFVSZ8BOLBU  1PSFKFNQMP FMQBTPEFQVSHBFOVODJDMPEFBETPSDJÓODPOPTDJMBDJÓOEF QSFTJÓOTFQVFEFIBDFSBVOBQSFTJÓONFOPSBMBBUNPTGÊSJDB

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMBBETPSDJÓO DSPNBUPHSBGÎBFJOUFSDBNCJPJÓOJDP

6# dc6

@67

>dc9

@97

>dc6

@67

>dc9

A^ = CV C= ) @ 8h 6\

&#% &#( '#% '#+ '#. (#( -#*

B\ Oc 8d 8j 8Y C^ Bc 8V Hg EW 7V

(#( (#* (#, (#(#. (#. )#& *#' +#* .#. &&#*

; 8=(8DD =8D( T 7gD ( 8a 8C T CD ' T =HD) 7g T CD ( >

%#& %#' %#) &#% &#% &#( &#( &#+ ( ) -

HD) TT 8D ( TT =ED)

TT

@97

%#&* %#%( %#%&

%FFTUBFDVBDJÓOTFQVFEFEFTQFKBSGÃDJMNFOUFZ%QBSBDVBMRVJFSWBMPSFTQFDJàDBEPEFY% VTBOEP MBGÓSNVMBDVBESÃUJDB0CTFSWFRVFFMQBSÃNFUSPFGFDUJWPEFFRVJMJCSJPFOMBFDVBDJÓO  FT ,%#D35D5  :B RVF TF QVFEF DBNCJBS DPO GBDJMJEBE MB DPODFOUSBDJÓO UPUBM FO FM áVJEP  TF QVFEF DBNCJBSFTUFQBSÃNFUSPFGFDUJWPEFFRVJMJCSJP&TUFDPNQPSUBNJFOUPTFJMVTUSBFOFMFKFNQMPZ FOMBàHVSB  -PTQBSÃNFUSPTEFFRVJMJCSJPEFQFOEFOEFMBUFNQFSBUVSB4JOFNCBSHP FMJOUFSDBNCJPJÓOJDP TFTVFMFPQFSBSBVOBUFNQFSBUVSBDPOTUBOUF DFSDBOBBMBUFNQFSBUVSBBNCJFOUF 17.5.2

Movimiento de los iones

-BUFPSÎBEFMNPWJNJFOUPEFMTPMVUP EFTBSSPMMBEBFOMBTTFDDJPOFTZ TFBNQMÎBDPOGBDJMJ EBEBMNPWJNJFOUPEFMPTJPOFT1BSBMBTSFTJOBTEFJOUFSDBNCJPJÓOJDPEFUJQPHFM RVFTPOMBTNÃT QPQVMBSFT OPIBZQPSPTQFSNBOFOUFTZ Q&MEFTBSSPMMPEFMBUFPSÎBEFMNPWJNJFOUPEFMTPMVUP  BQBSUJSEFMBTFDVBDJPOFT  B  TFNPEJàDB IBDJFOEPRVF QZFYQSFTBOEPMBTDPO DFOUSBDJPOFTFOGVODJPOFTEFGSBDDJPOFTFRVJWBMFOUFTYZZFJODMVZFOEPVOGBDUPSEFFYDMVTJÓOEF %POOBO,%&&MSFTVMUBEPFT 

k^ciZg

j^dc!^2 &

& XGI $n^ @ EZ XI $m^ 9:!^





-PTDPJPOFT JPOFTDPOMBNJTNBDBSHBRVFMPTJPOFTàKPTBMBSFTJOB TFFYDMVZFOZUJFOFO,%& -PTJPOFTRVFTFJOUFSDBNCJBOOPTFFYDMVZFOZ,%&0CTFSWFRVFMBEFOTJEBEEFMTÓMJEP  T OP BQBSFDFFOMBFDVBDJÓO 

QPSMBTVOJEBEFTWPMVNÊUSJDBTRVFTFTVFMFOVTBSFOMBTDPODFOUSB DJPOFTEFMPTJPOFTFOTPMVDJÓOZFOMBSFTJOB  4FQVFEFBQMJDBSMBFDVBDJÓO  BPOEBTEJGVTBTPEFDIPRVF-BTPOEBTEJGVTBTTFQSFTFO UBOTJBVOBDPMVNOBRVFFTUÃDPODFOUSBEBFOFMJPO" P% TFBMJNFOUBVOBTPMVDJÓOEF" P% EF

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMBBETPSDJÓO DSPNBUPHSBGÎBFJOUFSDBNCJPJÓOJDP

CBKBDPODFOUSBDJÓOZ,"#4J,"# TFQSPEVDFO POEBTEJGVTBTDVBOEPBVOBDPMVNOBRVFUJFOFVOBEJMVDJÓOCBKBEFMJPO" PFM% TFBMJNFOUBDPO VOBTPMVDJÓODPODFOUSBEBFO" PFO% 1BSBMBTPOEBTEJGVTBT MBWFMPDJEBEEFMPTJPOFTFT 

k^ciZg

jh!^dc!^2 &

Yn^ & XGI @ EZ XI 9:!^ Ym^





-BEFSJWBEBEZJEYJTFDBMDVMBBQBSUJSEFMBFDVBDJÓODPSSFTQPOEJFOUFEFFRVJMJCSJP DPNPMBFDVB DJÓO C PMB C   -BTPOEBTEFDIPRVFTFQSPEVDFODVBOEPMBTDPOEJDJPOFTEFFRVJMJCSJPTPODPOUSBSJBTBMBTEF MBTPOEBTEJGVTBT1PSFKFNQMP TJ,"#ZTFBMJNFOUBVOBTPMVDJÓODPO DFOUSBEBFO" PFO% BVOBDPMVNOBRVFDPOUJFOFVOBTPMVDJÓOEJMVJEBEFMJPO DBCFFTQFSBSRVF TFQSPEV[DBVOBPOEBEFDIPRVF-BFDVBDJÓOEFMBPOEBEFDIPRVFFT 

k^ciZg

jh]!^dc!^2 &

n −n^!VciZh  & XGI @9:!^ ^!YZhej‚h m ^!YZhej‚h −m ^!VciZh  εZ XI





-BTDPODFOUSBDJPOFTFRVJWBMFOUFTEFMJPO" PFM% FOTPMVDJÓO YJ ZFOMBSFTJOB ZJ TFTVQPOFOFO FRVJMJCSJPBOUFTZEFTQVÊTEFMBPOEBEFDIPRVF  -BTWFMPDJEBEFTEFMPTJPOFTEFQFOEFOEFMBSFMBDJÓOD35D5 JOEFQFOEJFOUFNFOUFEFMBGPSNBEF MBJTPUFSNB&TUPDPODVFSEBDPOOVFTUSBJOUVJDJÓOGÎTJDB4JMBDBQBDJEBED35EFMBSFTJOBFTHSBOEFZ MBDPODFOUSBDJÓOD5EFMJÓOFOTPMVDJÓOFTCBKB DBCFFTQFSBSRVFMBTPOEBTTFNVFWBODPOMFOUJUVE  :BRVFMPTDBNCJPTEFMBDPODFOUSBDJÓOJÓOJDBUPUBMQVFEFOBGFDUBSUBOUPFMFRVJMJCSJPDPNP MBT WFMPDJEBEFT EF MPT JPOFT  EFCFNPT CBMBODFBS MB DPODFOUSBDJÓO EF JPOFT UPUBMFT $VBOEP FTUB DPODFOUSBDJÓOUPUBMDBNCJBFOMBBMJNFOUBDJÓO QPSMBDPMVNOBQBTBVOBPMBJÓOJDB1BSBTPMVDJPOFT SFMBUJWBNFOUFEJMVJEBT MBSFTJOBZBFTUÃTBUVSBEBDPOJPOFTDPOUSBSJPTZOPQVFEFOSFUFOFSTFNÃT JPOFT1BSBIBDFSVOCBMBODFEFUPEPTMPTJPOFT TFFYDMVZFOMPTJPOFTUPUBMFT ,%&ZMBFDVBDJÓO  TFUSBOTGPSNBFO 

jidiVa^dc 2k^ciZg 



­TUFFTFMNJTNPSFTVMUBEPRVFFMRVFTFPCUJFOFQBSBMPTDPJPOFT-BTPOEBTJÓOJDBUPUBMZEFDP JPOFTBUSBWJFTBOSÃQJEBNFOUFMBTDPMVNOBT-BPOEBJÓOJDBUPUBMBGFDUBBMBTWFMPDJEBEFTEFJPODPO USBSJP V"PV% FOUPEPTMPTTJTUFNBTEFJOUFSDBNCJPJÓOJDPZBMFRVJMJCSJPEFMJOUFSDBNCJPEFJPOFT DPOEJTUJOUBTDBSHBT QPSFKFNQMP EJWBMFOUFNPOPWBMFOUFPUSJWBMFOUFNPOPWBMFOUF &MDÃMDVMPEF FTUPTFGFDUPTTFJMVTUSBFOFMFKFNQMP &+&.1-0 .PWJNJFOUPEFJPOFTQBSBJOUFSDBNCJPEJWBMFOUFNPOPWBMFOUF 6OBDPMVNOBEFJOUFSDBNCJPJÓOJDPFTUÃMMFOBDPOVOBSFTJOBÃDJEBGVFSUF D35FRVJWB MFOUFT-  F "MQSJODJQJP MBDPMVNOBFTUÃBVOBDPODFOUSBDJÓOJÓOJDBUPUBMD5/  DPOY/BZY$V&MDPJPOFTFMDMPSVSP$VBOEPU TFBMJNFOUBVOBTPMVDJÓO BDVPTBEF/B$M/ Y/B -BTDPOTUBOUFTEFTFMFDUJWJEBE DPOTUBOUFTEFFRVJMJCSJP QBSBJOUFSDBNCJPJÓOJDP TFQVFEFODBMDVMBSDPOMBUBCMB-BDPMVNOBUJFOFDNEF MPOHJUVE/PTFFYDMVZFOMPTJPOFTDPOUSBSJPT ,& -BWFMPDJEBETVQFSàDJBMEVSBOUFFM FYQFSJNFOUPFTDNNJO

www.FreeLibros.me

  *OUFSDBNCJPJÓOJDP



$BMDVMF B &MDPNQPSUBNJFOUPFOFRVJMJCSJPDPOD5/ZD5/ C &MUJFNQPRVFUBSEBMBPOEBEFJPOFTUPUBMFT D -PTWBMPSFTEFY$VZZ$VEFTQVÊTEFTBMJSMBPOEBEFJPOFTUPUBMFT E &MUJFNQPFORVFTBMFMBPOEBEFTPEJP ZTVGPSNB 4PMVDJÓO " %FGJOB1SJNFSPFTOFDFTBSJPDBMDVMBSMPTQBSÃNFUSPTEFFRVJMJCSJPDVBOEPD5/ ZD5/ QBSBEFTQVÊTHSBàDBSMPTSFTVMUBEPTEFMFRVJMJCSJP"DPOUJOVBDJÓO EFUFS NJOFFMUJFNQPEFFTDBQFQBSBMBPOEBEFJPOFTUPUBMFT MBTGSBDDJPOFTFRVJWBMFOUFTEF DPCSFFOD5/ZFMQFSàMEFDPODFOUSBDJÓOEFTPEJPBMBTBMJEB # &YQMPSF-BEFUFSNJOBDJÓOEFMDPNQPSUBNJFOUPEFFRVJMJCSJP MBPOEBEFJPOFTZMPT WBMPSFTEFY$VZZ$VTFBQFHBBMBTFDVBDJPOFT QFSPFMPSEFOQVFEFTFSCBTUBOUFDPOGV TP6OBSB[ÓOQBSBQSFTFOUBSFTUFFKFNQMPFTBDMBSBSDÓNPTFDPODBUFOBOMPTDÃMDVMPT "WFDFT FMNBZPSEFTBGÎPFTUÃFOEFUFSNJOBSTJMBPOEBEFTPEJPFTVOBPOEBEFDIP RVFPVOBPOEBEJGVTB $ 1MBOFF4FQVFEFDBMDVMBSMBTFMFDUJWJEBEDPOMBFDVBDJÓO  ZFMQBSÃNFUSPEFFRVJ MJCSJPFT ,%#D35D5 -BTDVSWBTEFFRVJMJCSJPTFDBMDVMBODPOWBMPSFTBSCJUSBSJPTEFY DPOMBFDVBDJÓO  -BWFMPDJEBEEFMBPOEBEFJPOFTUPUBMFTFTJHVBMBMBWFMPDJEBE JOUFSTUJDJBM -BT GSBDDJPOFT FRVJWBMFOUFT EF DPCSF TF DBMDVMBO SFTPMWJFOEP MB FDVBDJÓO  DPOY$V BOUFTZD5/ QBSBEFUFSNJOBSZ$V BOUFT$VBOEPQBTBMBPOEBEF JPOFTUPUBMFT TFJHVBMBZ$V EFTQVÊTZ$V BOUFT ZTFEFTQFKBY$V EFTQVÊTEFMBFDVBDJÓO  DPO FTUFWBMPSEFZ$V EFTQVÊTZD5/1PSÙMUJNP FMUJFNQPEFFTDBQFEFTPEJPTFQVFEF DBMDVMBSZBTFBDPOMBFDVBDJÓO  PMB 

EFTQVÊTEFEFDJEJSTJFTVOBPOEB EJGVTBPEFDIPRVF SFTQFDUJWBNFOUF1BSBFMMP WFSFNPTMBGPSNBEFMBJTPUFSNBQBSB FTUBEJTNJOVDJÓOEFDPODFOUSBDJÓOEFDPCSFFOMBBMJNFOUBDJÓO % )ÃHBMP  1SJNFSP EFUFSNJOFMBDVSWBEFFRVJMJCSJPDPOD5/$PNPFMDPCSFFTEJWBMFOUF ZFMTPEJPFTNPOPWBMFOUF TFVTBOMBTFDVBDJPOFT  Z  %FMBFDVBDJÓO 

@8jA^ (#2 2%#.* ' @CVA^ '#%' @ %#.*'#% X 2&.% 6iX I 2%#%& C! 8jC^ GI 2 XI %#%& :cidcXZh!aVZXjVX^‹c&,")(k^ZcZVhZg m8j n8j 2&.% & n8j' & m8j' @8jC^ 2

8jVcYdm8j2%#&aVXdcXZcigVX^‹c^c^X^Va n8j %#& 2&.% 2'(#)+ & n8j' %#.'



-BDBOUJEBEZ$VTFEFUFSNJOBDPOVOBIPKBEFDÃMDVMP ZFMSFTVMUBEPFTZ$V-B UBCMBEFFRVJMJCSJPRVFTJHVF QBSBD5/ TFHFOFSÓVTBOEPFTUBIPKBEFDÃMDVMP m8j n8j

www.FreeLibros.me



$BQÎUVMP  *OUSPEVDDJÓOBMBBETPSDJÓO DSPNBUPHSBGÎBFJOUFSDBNCJPJÓOJDP

8jVcYdXI 2'#*!

@8jC^XGI %#.*'#% 2 2%#,+% naVZXjVX^‹c&,")(Zh XI '#*

nXj mXj 2%#,+% adhgZhjaiVYdhYZaZfj^a^Wg^dhdc & nXj' & mXj' m8j n8j



&TUBTEPTUBCMBTTFHSBàDBOFOMBàHVSB0CTFSWFRVFDPOD5/ SFTVMUBVOB JTPUFSNBNVZGBWPSBCMF NJFOUSBTRVFDPOD5/MBJTPUFSNBFTEFTGBWPSBCMF



-BWFMPDJEBEEFMBPOEBEFJPOFTUPUBMFTFTVUPUBM@JPOWTVQFS FDNNJO&M UJFNQPEFFTDBQFEFFTBPOEBFTUFTD-VUPUBM@JPONJO



%F BDVFSEP DPO MB UBCMB EF WBMPSFT EF FRVJMJCSJP  DPO D5   /  DVBOEP Y$V BOUFT   Z$V BOUFT&OUPODFT DVBOEPMBPOEBEFJPOFTUPUBMFTQBTB BIPSBD5/

 Z$V EFTQVÊTZ$V BOUFT$POD5/ZZ$V EFTQVÊT TFEFTQFKBY$V EFTQVÊTEFMB FDVBDJÓO D  m8j 2 & m8j '

& @97X GI XI

%#-&) n8j & 2 %#,+ %#&-+' & n8j '



&MSFTVMUBEPFTY$V EFTQVÊT



0CTFSWFFMHSBOBVNFOUPFOMBGSBDDJÓOFRVJWBMFOUFEFDPCSFFOFMMÎRVJEP QPSRVFTF EFTBETPSCFEFMBSFTJOBBMBNBZPSDPODFOUSBDJÓOEFJPOFTUPUBMFT



$VBOEP TF BMJNFOUB MB TPMVDJÓO EF DMPSVSP EF TPEJP  / B MB DPMVNOB  MB GSBDDJÓO FRVJWBMFOUFEFDPCSFZMBDPODFOUSBDJÓOFOMBBMJNFOUBDJÓOEJTNJOVZFO$PNPMBDP MVNOBFTUÃDPOTPMVDJÓO/DVBOEPMBPOEBEFTPEJPMMFHBBDVBMRVJFSQBSUFEFFMMB  VTBSFNPTFTBDVSWBEFFRVJMJCSJPEFMBàHVSB&TVOBJTPUFSNBEFTGBWPSBCMFQBSB FMDPCSFZFOUPODFT BMCBKBSMBDPODFOUSBDJÓOEFDPCSFFOMBBMJNFOUBDJÓOSFTVMUBVOB &#' & %#nXj