On the Statistical Mechanics of Liquids, and the Gas of Hard Elastic Spheres

Abstract

Because of the extreme complications arising from a direct deductive approach, the theory of the liquid state requires the use of a model involving simplifying assumptions. In this paper an attempt is made to formulate general principles which any such model must follow. The first step is a general discussion of ``communal'' entropy, arising from the sharing of available space by all the atoms. Arguments are advanced to support the contention that for a gas of hard elastic spheres the communal entropy is fully excited in each direction of space, and amounts in all to 3R per mole. The communal entropy of assemblages of atoms exerting normal attractive and repulsive forces (in particular, the Debye solid) is considered. The geometry, the equation of state, and the partition function for an assemblage of hard elastic spheres are considered in detail. By extension of these ideas, allowing for the type of force actually exerted on each other by real atoms, a general form of partition function for a monatomic liquid is set up. This partition function involves a sum of two parts, one corresponding to a vibrational motion expressed in terms of the Debye characteristic temperature of the solid, and the other being a translational term, each part carrying with it its own communal entropy.