Thermodynamics of phase transition in higher-dimensional Reissner-Nordstrom-de Sitter black hole

It is well known that there are the black hole horizon and the cosmological horizon for the Reissner-Nordstrom-de Sitter (RN-dS) spacetime. The thermodynamic quantities on the both horizons satisfy the first law of the black hole thermodynamics, respectively; moreover, there are some additional connections between them. In this paper by considering the relations between the two horizons we give the effective thermodynamic quantities in (n + 2)-dimensional RN-dS spacetime. The thermodynamic properties of these effective quantities are analyzed; moreover, the critical temperature, critical pressure, and critical volume are obtained. We carry out an analytical check of the Ehrenfest equations and prove that both Ehrenfest equations are satisfied. So the spacetime undergoes a second-order phase transition at the critical point. This result is consistent with the nature of a liquid-gas phase transition at the critical point, hence deepening the understanding of the analogy of charged dS spacetime and liquid-gas systems.