van der Waals Gas -- from Eric Weisstein's World of Physics

V v

van der Waals Gas

An empirical equation of state which represents the behavior of real gases better that the ideal gas law.

where

is the molar volume. The term accounts for long-range attractive forces which increase pressure, and the b term accounts for short range repulsive forces which decrease the volume available to molecules. For , the van der Waals law reduces to

which is the ideal gas law. The internal energy of a van der Waals gas is computed from

but

so

Because

It is also true that

so is independent of volume and the molar internal energy is given by