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