Joule–Thomson expansion of a specific black hole in f ( R ) gravity coupled with Yang–Mills field

Abstract In this paper, we study the Joule–Thomson expansion of a specific black hole in f ( R ) gravity coupled with Yang–Mills field. Firstly, four-dimensional equation of state and the Joule–Thomson coefficient are derived from thermodynamic quantities, the critical temperature and the inversion temperature are obtained, and the isenthalpic curves and the inversion curves are plotted in the T − P plane. Then, by considering the higher dimensions black hole, the inversion temperature is obtained, the isenthalpic curves and the inversion curves are also plotted, and the effect of nonlinear term η and dimension for the Joule–Thomson expansion is demonstrated visually by depicting different curves. Finally, we compare the ratio of the inversion temperature to the critical temperatures with the van der Waals fluid and other black hole, which the ratio is not equal to 0.5, and it decreases with the dimensionality d .