Question

What is the difference between the virial equation of state and the SRK equation of state? When would you use one versus the other?

Answer 1

Virial Equations of State

Virial equations are a family of equations of state of the general form:

The parameters in the equation (B,C,D = c_i) are called "virial coefficients". If c_i=0 for i>0, the virial equation reduces to the ideal gas equation. Just as with the ideal gas equation, the temperatures and pressures used must be absolute.

The accuracy required determines the number of terms that are kept -- more terms makes the equation more accurate, but also more complicated to work with. Virial coefficients are different for each gas, but other than that are functions of temperature only.

Coefficients are normally obtained by making measurements of P, V, and T, and fitting the equation. These values are then published so that others may use them.

Many forms of the virial equation exist. Often, we will truncate the virial equation to

A number of methods (correlations, etc.) are available to determine B. In order to improve accuracy and capture more behaviors, additional parameters are sometimes added. One example is the Benedict-Webb-Rubin (BWR) equation of state.

All the constants must be supplied if you are to use this equation for a particular gas. It isn't always easy to find BWR coefficients for the gas you are interested in.

Cubic Equations of State

Virial equations cannot represent thermodynamic systems where both liquid and vapor are present. A "cubic" EoS is need to do this. One such is the Soave-Redlich-Kwong (SRK) equation.

where the constants are given by

In this equation, the b term is a volume correction, while the a is a molecular interaction parameter. The constants all depend on the critical temperature and pressure of the gas. These can be looked up easily in a data table.

The "acentric factor", omega, is also easily looked up. It is related to the geometry of the gas molecule.

To use the SRK equation:

1. look up T_c, P_c, and the acentric factor
2. plug in and find a, b, and alpha
3. plug these into the SRK equation; the result will be a cubic equation in P, T, and V
4. solve for the unknown you seek