SURFACE CORRECTIONS TO CLASSICAL PARTITION-FUNCTIONS

Surface corrections to partition functions for classical gases in thermodynamical equilibrium, close to the thermodynamical limit, are analysed. First, a gas without interparticle interactions but in a smooth external potential is considered in the canonical ensemble: the surface corrections (which, through the thermal wavelength, depend necessarily on Planck's constant) are evaluated explicity. Second, a dilute gas with interparticle interactions mediated by two-body potentials (but without external potential) is treated in the grand canonical ensemble. The surface corrections to the cluster integrals yielding the cluster expansion are studied. The free energy and the surface tension (for the external boundary) are computed explicity in both cases.