In this paper, we first review the equal area laws and Clapeyron equations in the extended phase space of charged anti–de Sitter black holes. With different fixed parameters, the Maxwell’s equal area law holds not only in the pressure-thermodynamic volume oscillatory line, but also in the charge-electric potential and temperature-entropy oscillatory lines. The conventional Clapeyron equation is generalized and two extra equations are found. Moreover, we show that the coexistence curve of the small and large charged black holes is charge independent in the reduced parameter space for any dimension of spacetime. The highly accurate fitting formula for the coexistence curve is also presented. Using this fitting formula of the coexistence curve, we find that the Clapeyron equations are highly consistent with the calculated values. The fitting formula is also very useful for further study on the thermodynamic property of the system varying along the coexistence curve.

• Received 8 December 2014

DOI:https://doi.org/10.1103/PhysRevD.91.044018