University of Babylon /College Of Engineering
Electrochemical Engineering Dept.
Second Stage /Thermodynamics
Equation of state
PV=nRT is the simplest equation of state and is called ideal gas equation
Virial EQUATIONS OF STATE
For an isothermal such as T 1 as pressure increase , volume decrease , thus PV
product for gas or vapor should be more nearly constant and this lead to suggest
that PV along isotherm can be represented as a power series equation , this called
Virial equation state
PV
 1  BP  C P 2  DP 3  .....
RT
PV
B C
D
z
 1   2  3  ....
RT
V V
V
B
B 
RT
C  B2

C 
( RT ) 2
z
D 
D  3BC  2 B 2
( RT ) 3
B,B are second Virial coefficients ,C,C are third Virial coefficients and so on.
Values of C, like those of B, depend on the gas and , temperature.
The below figure shows a compressibility-factor graph for methane. Values of the
compressibility factor Z (as calculated from P VT data for methane by the defining
equation Z = P V / RT) are plotted vs. pressure for various constant temperatures.
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University of Babylon /College Of Engineering
Electrochemical Engineering Dept.
Second Stage /Thermodynamics
 all isotherms originate at value z=1 for P =0.
 the isotherms are nearly straight at low pressure .
 Thus the equation of the tangent lines is z = 1+ B P
dz
 B  2C P  3DP 3  ....
dP
 dz 
 B  slop


dP

 P 0
z 
PV
BP
 1
RT
RT

This equation satisfactorily the PVT behavior of many vapors at subcritical
temperature up to pressure of about 5 bar. for pressure the range applicability of
Eq.  but below the critical pressure, the Virial equation truncated to three terms
often provides excellent results.
PV
B C 
z 
 1  2
RT
V V
2
University of Babylon /College Of Engineering
Electrochemical Engineering Dept.
Second Stage /Thermodynamics
This equation can be solved directly for pressure, but is cubic in volume. Solution
for V is easily done by an iterative scheme with a computer. The effect of
temperature on C and B for Nitrogen are illustrated on below figure
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