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Properties of pure materials

Presented by: Daniel Casas Orozco

Advanced Thermodynamics

Professor Rigoberto RosSeptember 7th 2012

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Gibbs related properties for pure

substances

dPPGdT

TGG

dPVSdTGd

Main idea: express some pure substances properties interms of PVT or PVTN relations (measurable data)

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TT

NP

GTSS

TG

,

PPNT GP

V

VP

G

,

NP

TPPTTVGG

,

P

TT

T

S

N

G

1

T

PP

P

V

NG

1

Entropy representation

Volume representation

Volume representation

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PVT relations for pure substances

Observed behavior of PVT for different

substances is nearly the same when

compared at reduced state:

c

r

T

TT

c

r

P

PP

RT

PVZ

NRT

VPZ

Theorem of corresponding states

c

r

V

VV

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Van der Waals equation

Van der Waals proposed that at Pr and Tr, Vr is

equal for all fluids

Correction of ideal gas expression vdW expression gets ideal gas as P tends to

zero

RTPV

2V

a

bV

RTP

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0@|

2

2

cTTVP

0@|

2

2

cTTV

P

c

c

P

TRa

64

27 22

c

c

P

RTb

8

23

13

8

rr

rr

VV

TP

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Pitzer contribution

Introduced acentric factor () concept:

deviation for sphericity in molecules

rrrr PTZPTZZ ,,10

1log7.0|,10

rTrvp

P

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EOS

Riguroustheoretical

models

Statisticalmechanics

Monte Carlomethod

Moleculardynamicsmethod

Empiricalexpressions

vdW typeformulations(cubic in V)

RK RKW - PR

Truncated Virial type

formulations

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vdW - type equations

bVVTa

bV

RTP

r

c

ca TkP

TRa

bVV

a

bV

RTP

1122

c

ca

P

RT

b

c

ca

P

TR

a

22

2

15613.055171.148508.0

k

Redlich

Kwong (RK EOS)

Redlich Kwong - Soave (RKS EOS)

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Volume translated cubic EOS: correct the high

pressure (r near to one) effects in cubic

type equations: Martin and later Peneloux,

Soave, Prausnitz

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Virial type models

Combination of statistical mechanics approachand experimental data fitting.

Based on the form

B, C constants calculed experimentally or

using principles from Corresponding States

Theorem

...32

V

CRT

V

BRT

V

RTP

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Specific developments for certain substances

made by several authors:

)1()0( BBP

RTB

BV

RTP

c

c

2.4

)1(

6.1

)0(

172.0139.0

422.0083.0

r

r

TB

TB

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Heat capacity for ideal gases

For ideal gases, Cp is only a function of T

VV

v T

U

T

S

TC

000

VVp T

H

T

STC

000

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Constants from data fitting, spectroscopy or

group contribution techniques

...320 dTcTbTaCv

RCC vp 00

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Statistical approach

Translational contribution: 3/2*R

Rotational contribution: 2/2*R

Vibrational contribution: rigid rotator, harmonic

oscillator model

Tx

xBxxxx

R

C

i

v

23

1

320

...

!22

1...

!3!2

12/22/3

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Departure functions

Describe how real state property for a

substance differs from ideal gas value

PTBPTBPTBPTB gasideal ,,,, 0

0000000

0000

,,

,,

,,

SSTHHVTGVTG

RTPVUUVTHVTH

SSTAAVTUVTU