A general kinetic theory of liquids. II. Equilibrium properties

The object of this paper is to expand and develop the equilibrium theory outlined in the first part of this series, within the framework of a general kinetic theory of fluids. The entropy of the fluid is first defined in such a way that agreement with the definition of statistical mechanics is obtained in equilibrium conditions. It is then found possible, provided care is taken to avoid certain well-known fallacies in the application of statistics to mechanical systems, to prove that the quantity defined will in general increase with time towards a certain maximum. The equilibrium solution of the fundamental equations is thereby derived without any appeal to statistical mechanics. At the same time a direct proof is offered of certain general formulae in statistical thermodynamics . The second half of the paper is devoted to a more detailed study of the equilibrium state by a method proposed in part I of the series. It is shown that the liquid state is distinguished from the gaseous state by the existence of real roots of a certain transcendental equation. Approximate but tractable expressions are found for all the virial coefficients in the gaseous phase. An equation of state is derived with two branches, which are identified with the gaseous and liquid states respectively.