University of Babylon /College Of Engineering
Electrochemical Engineering Dept.
Second Stage /Thermodynamics
Equation of state
PV=nRT is the simplest equation of sate 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 - 3 BC - 2 B 2
D¢=
( 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.
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 + 3 D ¢P 3 + ....
dP
æ dz ö
= B ¢ = slop
ç
÷
è dP ø 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
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