WOLFRAM|DEMONSTRATIONS PROJECT

Thermodynamic Properties of Acetylene Using Cubic Equations of State

​
equation of state
Redlich-Kwong
residual functions
Z vs. reduced pressure
temperature in Kelvin
415
pressure in bars
1
Z = 0.9977
R
V
(​
3
m
/kmol)
-0.0781294
ig
V
(​
3
m
/kmol)
34.5031
V (​
3
m
/kmol)
34.425
R
H
(J/mol)
-24.9856
ig
H
(J/mol)
5613.46
H (J/mol)
5588.47
R
S
(J/mol·K)
-0.0413822
ig
S
(J/mol·K)
15.9252
S (J/mol·K)
15.8838
R
G
(J/mol)
-7.812
ig
G
(J/mol)
-995.502
G (J/mol)
-1003.31
R
U
(J/mol)
-17.1727
ig
U
(J/mol)
2163.15
U (J/mol)
2145.97
R
A
(J/mol)
0.00094171
ig
A
(J/mol)
-4445.81
A (J/mol)
-4445.81
Any thermodynamic property,
M
, can be expressed as the sum of an ideal gas contribution and a residual non-ideal contribution:
M=
ig
M
+
R
M
, where
ig
M
and
R
M
are the ideal gas and residual contributions, respectively. For a given equation of state, the residual contribution can then be expressed as a function of
T
,
P
, and compressibility factor
Z
. In this Demonstration, the compressibility factor for a single gas chemical species (acetylene) is computed, from which the enthalpy (
H
in
J/mol
) and entropy (
S
in
J/mol·K)
can be determined for given
T
and
P
. You can select from one of three cubic equations of state (Redlich–Kwong, Soave–Redlich–Kwong, or Peng–Robinson) as well as the temperature (in
K
) and the pressure (in
bar
). The reference state is taken an ideal gas at
1bar
and
298.15K
. This information is then used to obtain the molar volume (in
3
m
/kmol
) as well as additional thermodynamics properties such as the Gibbs free energy (
G
in
J/mol
), Helmholtz free energy (
A
in
J/mol
), and internal energy (
U
in
J/mol
). In addition,
Z
is plotted versus reduced pressure
(
P
r
=P/
P
c
)
for a user-specified reduced temperature (
T
r
=T/
T
c
), where
P
c
and
T
c
are the critical pressure and temperature for acetylene. For an ideal gas
Z=1
.