P-Vcriticality and Joule-Thomson expansion of charged AdS black holes in the Rastall gravity

We discuss the P - V criticality and the Joule-Thomson expansion of charged AdS black holes in the Rastall gravity. We find that although the equation-of-state of a charged AdS black hole in the Rastall gravity is related to the Rastall parameter lambda, its reduced equation-of-state at the critical point is independent of the Rastall parameter lambda, as is the case in the Einstein gravity where lambda = 0. This is the reason why the critical exponents are not related to the Rastall parameter lambda. We also find that the inversion temperature T-i is related to the Rastall parameter lambda, but that the minimum inversion temperature T-i(min) and the ratio epsilon between the minimum inversion temperature and the critical temperature are both independent of the Rastall parameter lambda. At the critical point, the thermodynamic evolution of a charged AdS black hole in the Rastall gravity behaves as in the van der Waals fluid and charged AdS black hole in the Einstein gravity. We show the inversion curves and isenthalpic curves in the T - P plane and analyze the effect of the Rastall constant lambda on the inversion curves of a charged AdS black hole during the Joule-Thomson expansion.