The thermodynamics of the surfaces of solutions

Abstract In his classical treatment of the thermodynamics of capillarity* Gibbs considered the equilibrium of the matter contained within a closed surface (A, fig. 1), drawn so as to cut the dividing surface (S) between the two phases normally everywhere and to include part of the homogeneous mass on each side. The matter contained within this surface is divided into three parts by two surfaces (B, B), one on each side of S and very near to that surface, although at such a distance as to lie entirely beyond the influence of the discontinuity in its vicinity. If ε, ε', ε'' and η, η', η" are the value of the energy and entropy of the part between the surfaces BB, and of the homogeneous parts outside these surfaces respectively, the condition of internal equilibrium of the whole mass is dε + dε' + dε" ≧ 0, (1) for all possible variations for which the total entropy remains constant, i. e., for which dη + dη' + dη'' = 0. (2)