The general class of accelerating, rotating and charged Plebanski-Demianski black holes as heat engine

Abstract

We first review the general class of accelerating, rotating and charged Plebanski-Demianski (PD) black holes in the presence of cosmological constant, which includes the Kerr-Newman rotating black hole and the Taub-NUT spacetime. We assume that the thermodynamical pressure may be described by the negative cosmological constant, and so the black hole represents anti-de Sitter (AdS) PD black hole. The thermodynamic quantities like surface area, entropy, volume, temperature, Gibb's and Helmholtz's free energies of the AdS PD black hole are obtained due to the thermodynamic system. Next, we find the critical point and corresponding critical pressure, critical temperature and critical volume for the AdS PD black hole. Due to the study of specific heat capacity, we obtain the specific heat capacity (with constant volume) CV=0 and the specific heat capacity (with constant pressure) CP≥0. From this result, we conclude that the AdS PD black hole may be stable. We examine the Joule-Thomson expansion of the PD black hole, and by evaluating the sign of the Joule-Thomson coefficient μ, we determine the heating and cooling nature of the PD black hole. Putting μ=0, we find the inversion temperature. Next, we study the heat engine for the AdS PD black hole. In the Carnot cycle, we obtain the work done and its maximum efficiency. Also, we describe the work done and its efficiency for a new engine. Finally, we analyze the efficiency of the Rankine cycle in the PD black hole heat engine.