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

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 < T_{c} $. The Joule-Thomson expansion effects are also examined for the considered black hole. Here, we derive the inversion temperatures as well as the inversion curves. In the following, 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.