The thermodynamics of black holes in various dimensions are described in the presence of a negative cosmological constant which is treated as a thermodynamic variable, interpreted as a pressure in the equation of state. The black hole mass is then identified with the enthalpy rather than the internal energy, the Euclidean action is the Gibbs free energy rather than the Helmoholtz free energy and heat capacities are calculated at constant pressure not at constant volume. Quantum corrections to the enthalpy and the equation of state of the BTZ black hole are studied.