4_PVT_Sub_puras_AulaZecão-Termo-II-Mar16

TERMODINÂMICA II – UNIFACS ENGENHA ENGE NHARIA RIA QUÍMICA 2016 2016.1 .1 Aulas  – Mar/16

COMPORTAMENTO PVT DE SUBSTÂNCIAS PURAS EQUAÇÕES CÚBICAS DE ESTADO

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O QUE VAI SER VISTO... VISTO... Comportamento

PVT de Substâncias Puras Equações de Estado Para

lí quidos quidos A Equ Equaçã açãoo do Viria Viriall Aplicações da Equação da Equação do Virial Equações Cúbicas de Estado

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COMPORTAMENTO PVT DE SUBSTÂNCIAS PURAS  Porque

estudar o comportament comportamentoo PVT de substâncias

 puras? 1 - Cálculo de Cálculo de Q e W: W:  Essenciais para a indústria química, são calculados em  função de U e H. Entretanto, essas propriedades não podem  ser medidas diretamente, mas são função de parâmetros de  fácil medição P, V e T (para sistemas em equilíbrio),  conforme RELAÇÕES  conforme RELAÇÕES TERMODINÂMICAS . TERMODINÂMICAS .

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COMPORTAMENTO PVT DE SUBSTÂNCIAS PURAS  RELAÇÃO

PVT 

 Para

substâncias puras, simples e compressíveis, experimentos demonstram que:  Duas

propriedades são são independentes  regra das fases  Pressão P pode ser determinada como função função de T e v

 P = f (v, (v, T)

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COMPORTAMENTO PVT DE SUBSTÂNCIAS PURAS  DIAGRAMA P-T 

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COMPORTAMENTO PVT DE SUBSTÂNCIAS PURAS  DIAGRAMA P-T  Curvas

de condições P e T onde coexistem 2 fases

 fronteiras  Ponto

triplo

 Ponto

crítico

 3 fases em equilíbrio (S-L-V) –  Ponto  Ponto 2  região de fluido  T e V são propriedades

independentes –  Ponto  Ponto C  Tc

e Pc - máximas T e P para equilíbrio L- V 

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COMPORTAMENTO PVT DE SUBSTÂNCIAS PURAS  DIAGRAMAS

P x V 

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COMPORTAMENTO PVT DE SUBSTÂNCIAS PURAS  DIAGRAMAS

P x V 

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COMPORTAMENTO PVT DE SUBSTÂNCIAS PURAS  DIAGRAMAS

P x V 

 Regiões  Líquido

sub-res friado: Líquido a uma temperatura inferior à  de saturação à uma dada p

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PROPRIEDADES DOS SISTEMAS BIFÁSICOS  PROPRIEDADES Quando

DO VAPOR VAPOR ÚMIDO:

as fases líquida e vapor coexistem à  temperatura de saturação define-se o título:

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PROPRIEDADES DOS SISTEMAS BIFÁSICOS  PROPRIEDADES

DO VAPOR VAPOR ÚMIDO:

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EQUAÇÕES DE ESTADO (EDE)

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EQUAÇÕES CÚBICAS DE ESTADO  Ponto Crítico Comportamento real   P c

T  c

 3 raízes

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EQUAÇÕES CÚBICAS DE ESTADO  EQUAÇÃO CÚBICA DE VAN VAN DER WAALS WAALS Precursora das equações cúbicas (1873)  P

 RT  v

 Parâmetros

 b

 a v

2

ou

 Z

de Van der Waals  características de cada cada gás

 Pv  RT 

v v

 a  b

 RTv

a e b são constantes

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EQUAÇÕES CÚBICAS DE ESTADO

 a e b   de e b   de de Van der Waals de RK. Ambos são experimentais ou calculados através de:  a

 P

2

 P

0

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EQUAÇÕES CÚBICAS DE ESTADO  PARÂMETROS ARÂMETROS  P 2

 a

27 R T  c 64 P c

DE VAN VAN DER WAALS: WAALS: 2

 b

 RT  c 8 P c

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EQUAÇÕES CÚBICAS DE ESTADO  PARÂMETROS ARÂMETROS  P

DE VAN VAN DER WAALS: WAALS:

Para Para chegar ch egar no a, b e Vc de Van der Walls: 1º)Deriva 2 vezes e iguala a zero: ( p / V)Tc = -RT/(Vc - b )2 + 2a/Vc 3 = 0 (1) ( 2p / V2)Tc = 2RT/(Vc - b )3 - 6a/Vc 4 = 0 (2) 2º) 2º) Tir Tira a o valor de a em (1) (1) e su bsti bs titu tuii em (2). (2). Com is so acha Vc = 3b 3º) 3º) Com Com esse valor de Vc, substitu i no valor valor encontrado para a com (1), (1), com co m iss i sso o acha a em em fun f unção ção de R, Tc e b a = 27bRTc /8 (3) 4º) 4º) subst itui itu i este a na equação equação de Van Van der Waa Waals ls e enco encontr ntra a o valor valor final fin al de b em funç ão de T , p e R.

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EQUAÇÕES DE ESTADO GENERALIZADAS  EDE’S   GENERALIZADAS

volumétricas com apenas Tc e Pc.

Pred Prediç ição ão de prop propri ried edad ades es

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EQUAÇÕES DE ESTADO GENERALIZADAS  Alternativa:   uso

de Gráficos Generalizados de Z vs P r a T  r Válidos para to d o s os gases diversas (aproximação razoável). Não usar para líquidos

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EQUAÇÕES DE ESTADO GENERALIZADAS As   EDE’s  generalizadas

aliadas à observações experimentais

indicam que:

“Todos os

fluidos, quando comparados à mesma Tr e Pr, têm o

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FATOR AC NTRICO E CORRELAÇÕES GENERALIZADAS Aproximação Melhor Ainda

dos estados correspondentes: Z= f (Tr,Pr) (Tr,Pr)

que o modelo do gás ideal

apresenta desvios significativos dos resultados

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FATOR AC NTRICO E CORRELAÇÕES GENERALIZADAS Correlação Sabe-se

de Pitzer

que a relação entre o  logP rsat vs 1/ T  linear ( Eq. T r  é linear (  Eq. de Clapeyron), ou seja,

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Prof. José Antonio Cunha