P-V criticality and Joule-Thomson expansion of charged AdS black holes in the Rastall gravity * * Supported by the Program for NCET-12-1060, by the Sichuan Youth Science and Technology Foundation (2011JQ0019), and FANEDD (201319), and by Ten Thousand Talent Program of Sichuan Province, and by Sichuan Natural Science Foundation (16ZB0178), and the starting funds of China West Normal University (17YC513,

Abstract

We discuss the 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 , its reduced equation-of-state at the critical point is independent of the Rastall parameter , as is the case in the Einstein gravity where . This is the reason why the critical exponents are not related to the Rastall parameter . We also find that the inversion temperature is related to the Rastall parameter , but that the minimum inversion temperature and the ratio between the minimum inversion temperature and the critical temperature are both independent of the Rastall parameter . 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 plane and analyze the effect of the Rastall constant on the inversion curves of a charged AdS black hole during the Joule-Thomson expansion.