  We study the thermodynamic properties of the RN-AdS black hole in full phase
space and propose a generalized thermodynamic identity. As an example, we use
it to find relations of thermodynamical coefficients between the grand
canonical and canonical ensembles. We also show, for the first order phase
transition, that the usual Maxwell's equal area law should be extended to a new
form for the RN-AdS black hole.
