This file illustrates the use of the Redlich-Kwong equation of state to obtain the compressibility factor of real gases.

1. Compressibility factor, Z, of real gas using the Redlich-Kwong equation of state
by Julio C. Banks, P. E.
Consultant
The Redlich-Kwong equation of state can be rearranged [1] to yield a two-equation set
The use of these equations is illustrated via the following three (3) examples.
Example 2.7 [Reference 2, page 26] Calculate the compressiblility factor, Z, of steam using the
Redlich-Kwong equation of state.
T :=773 K
T c :=647.3 (Critical Temperature of steam) Pc 22.09,106
(Critical Pressure of steam)
(Reduced Temperature of steam) (Reduced Pressure of steam)
Guess: Z 1 Given
Z-ZRK(PR' TR,Z)
Z(PR,TR)' Find(Z)
Therefore the compressiblility factor, Z, of steam using the Redlich-Kwong equation ofstate is
Where PR =0.362 and TR = 1.194
Solved Problem 2.8 [Reference 2, page 28] Calculate the compressiblility factor, Z, and corresponding
temperature, T of steamusing the Redlich-Kwong equation of state.
P :=3.998.105
Pa v := 1.541 m3/kg R. 461.9 joule/kg
Guess: Z 1 and T 1.334.103
K (guess from ideal-gas law)
P T
(Reduced Pressure of steam) TR :=r (Reduced Temperature of steam)
c c
P
c: --'v Given
R·T c
(Z) (0.999)
TR 2.062
Postprocess: T = 1.334-103
K
Julio C. Banks, P.E. ZRK.MCD Page 1

2. Solved Problem 3.2 [Reference 2, page 42] Calculate the compressiblility factor, Z, and corresponding
temperature, T of steamusing the Redlich-Kwong equation of state.
T :=673 K v:=0.458 m3/kg
Guess: Z and P :=678.7.103
Pa (from the ideal-gas equation)
PR'
P
-
Pc
(Reduced Pressure of steam) T R
T
c
(Reduced Temperature of steam)
P = 6.787-105
Pa
Given
Z=ZRK(PR,TR'Z)
Z ) = (0.991 )
(pZR)· Find(Z,PR) (PR 0.03)
Postprocess: P = 6.724-105
Pa
Reference
1. Kenneth Wark, Jr. ''Thermodynamics''. 5th Edition, Pages 479, and 837
2. M. C. Potter, C. W. Somerton. "Engineering Thermodynamics", Pages 26, 28, 42.
Julio C. Banks, P.E. ZRK.MCD Page 2

3. 6-16 THERMODYNAMICS
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PIPe
Figure 6.11 Compresslblllty Factors for.Low P.ressure~
As originally presented by Professor Edward F. Obert and L.C. Nelson In "Generallzed P-V-T Properties of
Gases," ASME Trans~ctlons, 76,1057 (1954).
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PIP.,.
Figure 8.12 Compresslbll1ty Factors for HIgh - Pressures

4. Z.cpp
#pragma hdrstop
#include <condefs.h>
#include <iostream.h>
#include <math.h>
#include <conio.h>
#include <iomanip.h>
/
#pragma argsused
int main(int argc, char **argv)
{
float Pr = 1.0, //Reduced Pressure
Tr = 1.0, //Reduced Temperature
A, B,
Tol 0.00005,
Zi 0.6
Dz 1.0
C O.
FO O.
dFOdZ O.
Zj 1.0
int i 1;
A 0.0867*Pr/Tr;
B 4.934/pow(Tr,1.5);
if ((1.0 <= Pr && Pr <= 3.0) && (1.0 <= Tr && Pr <= 1.125)) Zi 0
.35;
while (Dz > Tol)
{ C B/(A + Zi);
FO 1.0 - Zi + A*(1.0 - C*(1.0 - A/Zi));
dFOdZ A*C*(1.0 - A*(2.0*Zi + A)/pow(Zi,2))/(A + Zi} - 1.0;
Zj Zi - FO/dFOdZ;
Dz abs(Zj - Zi);
i += 1;
cout « "Compressibility Factor of Air" « endl;
cout « "Solution Converged in " « i « " iterations"
« endl « endl;
cout « setiosflags(ios::fixed ios::showpoint)
« setprecision(4);
cout « "Pr " « Pr « endl;
cout « "Tr = " « Tr « endl « endl;
cout « " Z = " « setw(6)« Zj « endl;
cout « endl;
cout « endl « "Press any key to continue . .. " ,.
getch();
return 0;
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