For most applications, such a detailed analysis is "over-kill" and the ideal gas approximation is used. Real-gas models have to be used near condensation point of gases, near critical point, at very high pressures, and in several other less usual cases.
Real gases are often modelized by taking into account their molar weight and molar volume
Where P is the pressure, T is the temperature, R the ideal gas constant, and Vm the molar mass. a and b are parameters that are determined empirically for each gas, but are sometimes estimated from their critical temperature (Tc) and critical pressure (Pc) using these relations:
The Redlich-Kwong equation is another two-parameters equation that is used to modelize real gases. It is almost always more accurate than the Van der Waals equation, and ofter more accurate than some equation with more than two parameters. The equation is
where a and b two empirical parameters that are not the same parameters as in the Van der Waals equation.
The Berthelot Equation is very rarely used,
but the modified version is somewhat more accurate
This modelisation fell out of usage in recent years
The Clausius equation is a very simply three-parameter equation used to modelize gases.
where A, B, C, A′, B′, and C′ are temperature dependent constants.
This two parameter equation has the interesting property being useful in modelizing some liquids as well as real gases.
The Wohl equation is formulated in terms of critial values, making it useful when real gas constants are not available.
The Beattie-Bridgeman equation
where d is the molal density and a, b, c, A, and B are empirical parameters.
The BWR equation, sometimes referred to as the BWRS equation
Where d is the molal density and where a, b, c, A, B, C, α, and γ are empirical constants.