Thermodynamic of the charged accelerating AdS black hole: P-V critical and Joule-Thomson expansion

In this paper, we study the thermodynamic of the charged accelerating AdS black hole in the extended phase space. Firstly, the thermodynamic quantities are derived and the state equation is obtained for this black hole. Through the investigate to the critical behavior, which shown that the charged accelerating AdS black hole as thermodynamic system is similar to the van der Waals system. The two systems share same critical exponents, and the black hole system also show that the large/small black hole phase transition. Then, we derive the inversion temperature of this black hole and plot the inversion and isenthalpic curves in the T-P plane. We find that the inversion temperature for a given pressure increases with $e$, and the acceleration parameter has the opposite effect, which the inversion curves decreases gradually with the the increases of $a$. Finally, we investigate the influence of acceleration parameter on isenthalpic curves, and obtain the ration between the minimum inversion temperature and critical temperature also is 0.5, which also means that the acceleration parameter has no effect on this universal ratio.