Critical behavior and Joule-Thomson expansion of charged anti-de Sitter black hole in four-dimensional Rastall gravity

In this work, we investigate the thermodynamics of four-dimensional charged anti-de Sitter (AdS) black hole surrounded by perfect fluids in the context of Rastall theory. We derive the equations of state by considering the charge square Q2 and the metric parameter Ns as the thermodynamic variables. The Q2-& phi; and Ns-& UTheta;s figures for some special surrounding fields were analyzed in detail. To better explain the phase transition, the behavior of the Gibbs free energy is presented. Note that the critical exponents are in perfect agreement with the van der Waals (vdWs) fluid system. In addition, we discuss Joule-Thomson (J-T) expansion in extended phase space. We determine the region where cooling or heating by investigating J-T coefficient. The inversion curves and the isenthalpic curves are plotted in the T-P plane. Also, we calculate the minimum inversion temperature Tmin and find that the ratio Tmin/Tc is independent of the radiation field parameter Nr.