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 , the volume , and the chemical potential . The and equations of state of the lattice fluid, where is the volume per particle, are derived from the grand canonical partition function in the mean-field approximation. We distinguish between the integral pressure and the differential pressure , where 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.
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