Charged accelerating AdS black hole of $f(R)$ gravity and the Joule-Thomson expansion

Abstract: In this paper, the thermodynamical properties and the phase transitions of the charged accelerating anti-de Sitter (AdS) black holes are investigated in the framework of the $f(R)$ gravity. By studying the conditions for the phase transitions, it has been shown that the $P-V$ criticality and the van der Waals like phase transitions can be achieved for $T \approx T_{c}$. The Joule-Thomson expansion effects are also examined for the charged accelerating AdS black holes of the $f(R)$ gravity. Here, we derive the inversion temperatures as well as the inversion curves. Then, we determine the position of the reverse point for different values of mass $M$ and parameter $b$ for the corresponding black hole. At this point, the Joule-Thompson coefficient is zero. So, in such case, we can say that such point is very important for the finding of cooling - heating regions. Finally, we calculate the ratio of minimum inversion temperature and critical temperature for such black hole.