2.7 Other Equations of State for Gases

Van der Waals equation is not the only equation of state "dreamed up". There are a large number of others as well. Among the more useful are the Berthelot Equation:

$$\left( p + \frac{n^2 a}{TV^2} \right) \left( V - n b \right ) = n R T$$ (2.7.33)

which differs from van der Waals equation in that the "attractive force term" now is temperature dependent.

There is also the Dieterici Equation:

$$p e^{na/VRT} (V - nb) = nRT$$ (2.7.34)

which looks strange but again differs only in the "attractive force term". And there is the Redlich-Kwong Equation:

$$\left( p + \frac{n^2 a}{T^{1/2} V ( V + nb)} \right) ( V - nb) = nRT$$ (2.7.35)

which has a rather complex "attractive force term". In all four cases (these three and the van der Waals equation) the "repulsive force" term is the same, basically that for a hard sphere.