Equations of state for Real Gas

EQUATIONS OF STATE FOR REAL GAS

1. Van der Waals equation:

The scientist Van der Waals considered these two corrections to analyse the behaviour of real gases during 1879.

⸫ The equation of state for real gases is given by

For ideal gas, the constants a and b are zero. The values of a and b are dependent on the type of fluid or gases used.

If molar volume is considered in the analysis, the equation of state becomes

Van der Waals equation has some limitations as follows:

1. The study had not been made closely under actual conditions and its validity bias failed.

2. The values of a and b are assumed to be constant but they will vary with temperature which is experimentally found.

3. At critical point, Van der Waals equation becomes

2. Beattie-Bridgeman equation of state:

This equation is based on five experimentally determined constraints in the form of

The Beattie-Bridgeman equation is known to be reasonably accurate for densities values up to 0.8ρcr, where ρcr is the density of the substance at critical point.

3. Benedict-Webb-Rubin equation of state:

The equation of state is expressed as

It can take up substances at densities up to about 2.5 ρcr.

4. Virial equation of state:

Virial or virtual expansions are only applicable to gases of low and medium densities.

The equation state of a substance is given by

The coefficient of a(T), b(T), c(T), d(T) are virial coefficients. The virial coefficient will vanish when the pressure becomes zero. Finally, the equation of state reduces to the ideal-gas equation.

5. Berthelot and Dieterici equations of state:

1. Berthelot equation of state:

2. Dieterici equation of state:

where a and b are constants

p = Pressure, Pa

v = Volume, m3

R = Gas constant, J/kgK

T = Temperature, K.