Statistical Mechanics of Liquid-Vapor Equilibrium

Abstract

The configuration integral of a pure fluid is approximated by considering configurations in which the N particles are distributed in two sub‐volumes of the volume V, the potential energy per particle in each sub‐volume being taken to be a function, u(v_i), of the volume per particle in that region, and interaction between sub‐volumes being ignored. When all possible distributions of particles between sub‐volumes are considered, and when u(v_i) has the form suggested by physical considerations, then the pressure as a function of v=V/N is found to be equal to π(v)=kT/v—u′(v) whenever π(v) is stable, but to be equal to the constant vapor pressure which satisfies the equal‐areas criterion whenever π(v) is metastable or unstable. The functions π(v) themselves have the form of a set of isotherms of van der Waals type.