  The thermodynamical properties of the Reissner-Nordstr\"om-anti-de Sitter
black hole in the grand canonical ensemble are investigated using York's
formalism. The black hole is enclosed in a cavity with finite radius where the
temperature and electrostatic potential are fixed. The boundary conditions
allow us to compute the relevant thermodynamical quantities, e.g. thermal
energy, entropy and charge. The stability conditions imply that there are
thermodynamically stable black hole solutions, under certain conditions.
Instantons with negative heat capacity are also found.
