  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, and heat capacities are calculated at constant pressure not at constant
volume. The Euclidean action is associated with a bridge equation for the Gibbs
free energy and not the Helmholtz free energy. Quantum corrections to the
enthalpy and the equation of state of the BTZ black hole are studied.
