Translation of J. D. van der Waals' ?The thermodynamik theory of capillarity under the hypothesis of a continuous variation of density?

Abstract

Van der Waals justifies the choice of minimization of the (Helmholtz) free energy as the criterion of equilibrium in a liquid-gas system (Sections 1–4). If densityρ is a function of heighth then the local free energy density differs from that of a homogeneous fluid by a term proportional to (d 2 ρ/dh 2); the extra term arises from the energy not from the entropy (Section 5). He uses this result to show howρ varies withh (Section 6), how this variation leads to a stable minimum free energy (Section 7), and to calculate the capillary energy or surface tensionσ (Section 9). Near the critical pointσ varies as (τ k -τ)3/2, whereτ k is the critical temperature (Section 11). The paper closes with short discussions of the thickness of the surface layer (Section 12), of the difficulty of assuming thatρ varies discontinuously with height (Section 14), and of the possible effect of derivatives of higher order than (d 2 ρ/dh 2) on the free energy and surface tension (Section 15).