Liquid-vapor coexistence and the PVT surface of a lattice fluid

Abstract

The lattice fluid model in the grand canonical ensemble is presented as a useful system for teaching liquid-vapor coexistence and the PVT surface of a fluid. The state of the fluid in the grand canonical ensemble is specified by the temperature T, the volume V, and the chemical potential μ. The p̂(T,V,μ) and v(T,V,μ) equations of state of the lattice fluid, where v is the volume per particle, are derived from the grand canonical partition function in the mean-field approximation. We distinguish between the integral pressure p̂≡−Ω/V and the differential pressure p≡−(∂Ω/∂V)T,μ, where Ω is the Landau potential so that we can discuss finite size effects near first-order phase transitions. The nonequivalence of the canonical and grand canonical ensembles for describing the liquid-vapor phase transition is also discussed.