Statistical Mechanics Basis of Macleod Formula

TL;DR

This paper derives the theoretical foundation of the Macleod formula, connecting liquid-vapor surface tension to one-particle densities using statistical mechanics, and confirms its approximation validity.

Contribution

It provides a rigorous statistical-mechanical derivation of the Macleod formula, clarifying its theoretical basis and approximation scope.

Findings

Macleod formula is supported by statistical mechanics

Surface tension relates to one-particle densities in equilibrium

First approximation validity of the Macleod formula is demonstrated

Abstract

In this work the theoretical basis for the famous formula of Macleod, relating the surface tension of a liquid in equilibrium with its own vapor to the one-particle densities in the two phases of the system, is derived. Using the statistical- mechanical definition of the surface tension, it is proved that this property is, at the first approximation, given by the Macleod formula.