A note on Maxwell's equal area law for black hole phase transition

The state equation of the charged AdS black hole is reviewed in the T-r(+) plane. With a view on the the phase transition, the T-S, P-V, P-nu graphs are plotted and then the equal area law is used in the three cases to get the phase transition point (P, T). The analytical phase transition point relations for P-T of a charged AdS black hole has been obtained successfully. By comparing the three results, we find that the equal area law possibly cannot be used directly for the P-nu plane. According to the T-S, P-V results, we plot the P-T-Q graph and find that for a highly charged black hole a very low temperature condition is required for the phase transition.