Derivation of the Kelvin Equation

Abstract

The exact Kelvin equation is deduced from the equilibrium condition of liquid drops. It is easily translated into the classical macroscale expression. The relationship between surface tension and curvature radius is a key point in microscale. Use of the Tolman equation allows us to obtain formulae for incompressible liquid drops and this relates the curvature radius to saturation vapor pressure,vapor density,and vapor molar volume. The Kelvin equation for a compressible liquid is also given while the compression coefficient and the Tolman length are introduced into the expression.