Thermodynamical Fundamental Equation for Spherical Interface

Abstract

The relation between the radius of the Gibbs dividing surface and the superficial density is investigated in detail and the generalized Kelvin relation is obtained. Consequently the fundamental equation for spherical interface is expressed by ${\mathrm{dE=TdS+\mu dN-p}}_{\alpha }{\mathrm{dV}}_{\alpha }{\mathrm{-p}}_{\beta }{\mathrm{dV}}_{\beta }{\mathrm{+\gamma dA+(\partial }}_{\gamma }{\mathrm{/\partial }}_a\mathrm{)Ada}$ . The generalized Kelvin relation is the explicit differential equation for determining the location of the surface of tension which does not contradict with the conventional one. Thus the mathematical formalism of thermodynamics will be completed for treating spherical interface in a rigorous and self‐consistent manner, the last ambiguous point being eliminated from the conventional Gibbs treatments.