The Imperfect Gas

The partition function of the classical imperfect gas is approximated by means of a generalized cell model in which the number of particles in a cell is taken as the statistical variable. The limiting free energy per particle exhibits critical phenomena, and, for temperatures less than the critical temperature, the $p-v$ isotherm is a nonanalytic function of $v$ consisting of three pieces. These properties depend only on the interparticle potential energy having the general features usually assigned to it. However, the condensation pressure is not constant, and, for temperatures sufficiently low, the isotherm shows thermodynamic instability. The model allows the calculation of the limiting free energy per particle for all values of the temperature and specific volume.