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We investigate the thermodynamical properties of charged torus-like black holes and take it as the working substance to study the heat engines. In the extended phase space, by interpreting the cosmological constant as the thermodynamic pressure, we derive the thermodynamical quantities by the first law of black hole thermodynamics and obtain the equation of state. Then, we calculate the efficiency of the heat engine in the Carnot cycle as well as the rectangular cycle, and investigate how the efficiency changes with respect to volume. In addition, to avoid a negative temperature, we emphasize that the charge of this black hole cannot be arbitrary. Last, we check the calculation accuracy of a benchmark scheme and discuss the upper bound and lower bound for charged torus-like black hole in the scheme.

In this paper, we study the Joule–Thomson expansion for RN-AdS black holes immersed in perfect fluid dark matter. As perfect fluid dark matter is one of the dark matter candidates, we are interested in how it influences the thermodynamic properties of black holes. Firstly, the negative cosmological constant could be interpreted as thermodynamic pressure and its conjugate quantity as the thermodynamic volume, which give us more physical insights into the black hole. Moreover, we derive the thermodynamic definitions and study the critical behaviour of the black hole. Secondly, the explicit expression of Joule–Thomson coefficient is obtained from the basic formulas of the pressure, the volume, the entropy and the temperature. Then, we obtain the inversion curves in terms of charge Q and parameter λ. Furthermore, we analyse the isenthalpic curve in T–P graph with the cooling–heating region determined by the inversion curve. At last, we derive the ratio of minimum inversion temperature to critical temperature and compare the result with that in the RN-AdS case.