A curious result concerning the Clausius virial

Abstract

For a sample of liquid confined in a hard-walled spherical container it is shown by computer simulation and by statistical mechanics that the conventional virial pressure for a notional sphere of radius r is not the correct thermodynamic normal pressure on the surface of the sphere but is the local kinetic contribution only, ρ(r)kT. In other words, ρ̄(r)kT+[1/3V(r)]〈𝒥iri⋅Fiθ(r −ri)〉=ρ(r)kT, where ρ̄(r) is the mean density inside the sphere of radius r and volume V(r). This result is true for any intermolecular interaction derivable from a potential and is a good approximation for any reasonable wall potential for regions outside the range of the wall potential.