In this work, we attempt to study the thermodynamic behavior of static Van der Waals (VdW) black hole with an anti-de Sitter (AdS) background in the extended phase space. Treating the negative cosmological constant as thermodynamic pressure, we obtain the expressions for enthalpy, Gibb’s free energy and Helmholtz free energy. We study the stability and Joule–Thomson expansion for the black hole. Next, we construct a heat engine by considering the VdW black hole as the working substance. We investigate the maximum efficiency of the black hole heat engine for the Carnot cycle. We also discuss the work done and the efficiency of a new heat engine. Finally, we study the efficiency of the black hole heat engine for the Rankine cycle.

In this paper, we have explored the thermodynamic properties of static Modified Bardeen black hole in the background of Anti-de Sitter (AdS) extended phase space. Thermodynamic pressure is taken as a thermodynamic variable, defined by the negative cosmological constant. We have discussed the thermodynamic quantities like Hawking temperature, Gibbs energy and Helmholtz free energy along with specific heat capacity to analyze the stability. Next, Joule–Thomson expansion has been evaluated to determine cooling-heating phase transition. Followed by these, we have constructed a new heat engine where the black hole is considered as the working substance. We have determined the efficiency through a heat cycle in the [Formula: see text]-[Formula: see text] plane. As a result, we have been able to show the efficiency of a new heat engine and measure it against the Carnot efficiency. After evaluating the efficiency of the Rankine cycle, the paper has been concluded with a comparison analysis between the heat engine efficiencies of Modified Bardeen AdS Black hole and Regular Bardeen AdS Black hole.

This paper reflects a study on the thermodynamic features of charged rotating Kerr–Sen–AdS black holes discussed with an extended phase space, where the negative cosmological constant is accounted for pressure. Thermal stability/instability and dependency of the phase transition points on the parameters of a black hole have been discussed further. The authors have systematically studied the throttling process of the black hole considering its mass is identified by its enthalpy. Moreover, the phenomenon of Joule–Thomson expansion has been explored, and inversion temperature for the black hole has been investigated using a numerical approach. Next, a heat engine is constructed by considering the black hole as a working object and subsequently, its efficiency is calculated by considering a rectangular heat cycle in the [Formula: see text]–[Formula: see text] plane. Then the effects of the black hole parameters on its efficiency and their respective roles are studied, followed by a careful comparison of the efficiency with that of a Carnot engine so that the second law of thermodynamics holds true.

Inspired by the pronounced effect of gravity’s Rainbow on black hole thermodynamics, entropy relations and bounds have been investigated for [Formula: see text]-dimensional Reissner–Nordström (RN) black hole in the framework of Rainbow gravity. Basic thermodynamic properties of the black hole have been derived for the event horizon and Cauchy horizon. Except for the horizon radius, they all crucially depend on the Rainbow functions. Bounds of the aforesaid thermodynamic quantities have been deduced for both horizons. Analyzing the specific heat capacity, stability conditions have been obtained. Also, the extremal phase of the black hole has been explored. Further, a comparative study has been carried out to distinguish between the effects of Rainbow gravity model parameters on the entropy bound by considering different Rainbow gravity functions. For massless scalar perturbation, quasinormal modes have been computed using modified WKB approach. We have investigated the quantum correction of the black hole in a Rainbow gravity background to obtain the effects of Extended Uncertainty Principle (EUP) and Generalized Uncertainty Principle (GUP) parameters. We have derived the Hawking temperature, specific heat, entropy and remnant masses of the black hole in the Extended General Uncertainty Principle (EGUP) framework, and with the help of graphical methods, we have compared our findings.