A Statistical Theory of Liquids. I

Abstract

A theory is developed which deduces the elastic and thermal properties of a liquid from the expression of the mutual potential between two molecules, these being considered as centers of force. The two-phase system consisting of liquid and vapor is treated as a statistical unit and thus dynamical expressions for the vapor pressure and the surface tension are obtained. The characteristic parameter of the theory is the mean distance between nearest neighbors, $\ensuremath{\sigma}$. Its dependence on molecular density and temperature is determined by combining Boltzmann's theorem with a geometrical formula due to P. Hertz. The agreement with experimental data (after introduction of a specialized form of the potential) is satisfactory and will be further investigated in subsequent papers. The Introduction (Section I) exposes the general scope of the theory. In Section II the expression for the potential energy is established and suitably simplified by integration. In Section III the partition function for the two-phase system is formed without further neglections. In Section IV the co-existence of the two phases is shown to be possible only if surface tension is taken into account. Section V contains the determination of $\ensuremath{\sigma}$ as sketched above. In Section VI the general formulae for the liquid state are established. Section VII introduces a special form for the intermolecular forces and in Section VIII comparison with experimental data, covering heat of vaporization, compressibility, expansion, and specific heat, is carried through for ten liquids widely different in character.