Curved Fluid Interfaces. III. The Dependence of the Free Energy on Parameters of External Force

The parameter of external force dependence of the free energy Ω appearing in the grand partition function is first illustrated on the basis of ideal gas models. In order to obtain a corresponding asymptotic estimate of Ω for real fluids in the presence of external fields, our earlier hydrostatic results are transcribed into thermodynamic terms. The resulting expression for Ω is shown to yield work elements in agreement with the detailed theory and, furthermore, when Ω is subjected to an appropriate variational principle the earlier relations describing the surfaces are obtained. These asymptotic formulas demonstrate that for macroscopic applications the classical equations are completely valid. Since these equations determine the spatial distribution of fluids, their connection with Duhem's theorem is described.