Enthalpy and Entropy Departure Functions for Gases

​
gas
argon
benzene
carbon dioxide
compare departure functions
​
plot
enthalpy
enthalpy departure function
entropy
entropy departure function
pressure (MPa)
15
This Demonstration plots the enthalpies and entropies for a real gas and an ideal gas as a function of temperature, relative to a reference state at a selected pressure and temperature, using the Peng–Robinson equation of state and ideal-gas heat capacities. Select argon, benzene, or carbon dioxide with buttons. For each gas, the temperature scale is adjusted so the plots are only shown above the critical temperature. Select enthalpy or entropy departure function, which is the difference between the thermodynamic property (enthalpy, entropy) for a real gas and an ideal gas at the same temperature and pressure. You can vary the pressure with the slider. Select "compare departure functions" to view departure functions for all three gases as a function of temperature at 10 MPa. Click "show labels" to label each departure function curve with the corresponding gas.

Details

Enthalpy
H
and entropy
S
are calculated using the Peng–Robinson equation of state (EOS) for a real gas and the ideal gas law for an ideal gas:
H=(H-
ig
H
)+
ig
H
-
ig
H
R
+
ig
H
R
,
S=(S-
ig
S
)+
ig
S
-
ig
S
R
+
ig
S
R
,
where
H
is in kJ/mol and
S
is in kJ/[mol K]; the superscript
ig
represents an ideal gas, the subscript
R
refers to the reference state, and
(H-
ig
H
)
and
(S-
ig
S
)
are the enthalpy and entropy departure functions for a real gas calculated from the Peng–Robinson EOS, while
ig
H
R
and
ig
S
R
are the ideal gas enthalpy and entropy at the reference state.

ig
H
-
ig
H
R
=
Cp
A
(T-
T
R
)+
1
2
Cp
B

2
T
-
2
T
R
+
1
3
Cp
C

3
T
-
3
T
R
+
1
4
Cp
D

4
T
-
4
T
R

,

ig
S
-
ig
S
R
=
Cp
A
ln(T/
T
R
)+
Cp
B
(T-
T
R
)+
1
2
Cp
C

2
T
-
2
T
R
+
1
3
Cp
D

3
T
-
3
T
R
-Rln(P/
P
R
)
,
where
Cp
A
,
Cp
B
,
Cp
C
, and
Cp
D
are heat capacity constants (
Cp=
Cp
A
+
Cp
B
T+
Cp
C
2
T
+
Cp
D
3
T
),
T
is temperature (K), and
P
is pressure (MPa).
(H-
ig
H
)=RTZ-1-
A
2
2
B
(1+κ
Tr/α
)ln
Z+(
2
+1)B
Z-(
2
-1)B
,
(S-
ig
S
)=Rln(Z-B)-
AR
2
2
B
κ
Tr/α
ln
Z+(
2
+1)B
Z-(
2
-1)B
,
Tr=T/Tc
,
κ=0.375+1.542ω-0.270
2
ω
,
α=
2
(1+κ(1-
Tr
))
,
where
Z
is the compressibility factor,
Tr
is the reduced temperature (dimensionless, not to be confused with
T
R
),
Tc
is the critical temperature (K),
ω
is the acentric factor, and
κ
and
α
are constants.
A=0.457
Pr
2
Tr
α
,
B=0.0778
Pr
Tr
,
Pr=P/Pc
,
where
A
and
B
are constants,
Pr
is the reduced pressure (dimensionless, not to be confused with
P
R
), and
Pc
is the critical pressure (MPa).
These equations are used to calculate the compressibility factor
Z
:
Z=
1/3
-q2+
r

+
1/3
-q2-
r

,
r=
2
q
4+
2
m
/27
,
q=2
3
a
2
-
a
2
a
1
+27
a
0
27
,
m=3
a
1
-
2
a
2
3
,
where
q
,
r
,
m
,
a
2
,
a
1
, and
a
0
are constants used for simplification.
a
2
=B-1
,
a
1
=A-3
2
B
-2B
,
a
0
=
2
B
+
3
B
-AB
.
The screencast video at[1] explains how to use this Demonstration.

References

[1] Enthalpy and Entropy Departure Functions for Gases. www.colorado.edu/learncheme/thermodynamics/EntropyEnthalpyDepartureFunctions.html.

Permanent Citation

Rachael L. Baumann, Neil Hendren, John L. Falconer, Derek M. Machalek, Nathan S. Nelson, Garrison J. Vigil
​
​"Enthalpy and Entropy Departure Functions for Gases"​
​http://demonstrations.wolfram.com/EnthalpyAndEntropyDepartureFunctionsForGases/​
​Wolfram Demonstrations Project​
​Published: May 13, 2015