ON THE KINETIC THEORY OF A VAN DER WAALS GAS

Abstract

A kinetic equation is proposed that leads, in equilibrium, to the Van der Waals equation of state. It is shown that this kinetic equation obeys an H theorem, and that its equilibrium solutions are, in the condensation region, of two types, (i) inhomogeneous equilibrium solutions which are absolutely stable and correspond to the two phases in equilibrium, (ii) homogeneous equilibrium solutions which are not absolutely stable but are, if the compressibility is positive, stable against small dynamical (i.e. nonquasi-static) perturbations, and correspond to the metastable states of the system. As a result, it is seen that a linear theory cannot explain the transition from the metastable to the stable states. A system of simplified nonlinear equations for the first three velocity moments of the distribution function is obtained in the hope that its study will contribute to the understanding of the mentioned transition.