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7/28/2019 Properties of Pure Materials
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Properties of pure materials
Presented by: Daniel Casas Orozco
Advanced Thermodynamics
Professor Rigoberto RosSeptember 7th 2012
7/28/2019 Properties of Pure Materials
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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