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- We investigate the extended phase space thermodynamics of nonsingular-AdS black holes minimally coupled to clouds of strings in which we consider the cosmological constant () as the pressure (P) of the black holes and its conjugate variable thermodynamical volume (V) of the black holes. Owing to the background clouds of strings parameter (a), we analyse the Hawking temperature, entropy and specific heat on horizon radius for fixed-parameter k. We find that the strings clouds background does not alter small/large black hole (SBH/LBH) phase transition but occurs at a larger horizon radius, and two second-order phase transitions occur at a smaller horizon radius. Indeed, the G–T plots exhibit a swallowtail below the critical pressure, implying that the first-order phase transition is analogous to the liquid–gas phase transition at a lower temperature and lower critical pressure. To further examine the analogy between nonsingular-AdS black holes and a liquid–gas system, we derive the exact critical points and probe the effects of a cloud of strings on criticality to find that the isotherms undergo liquid–gas like phase transition for at lower . We have also calculated the critical exponents identical with Van der Walls fluid, i.e., same as those obtained before for arbitrary other AdS black holes, which implies that the background clouds of strings do not change the critical exponents.
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- We get an exact nonlinear electrodynamics (NED) charged black holes endowed with the perfect fluid dark matter (PFDM) in the AdS background-charged PFDM AdS black holes with additional parameter charge parameter q and PFDM parameter β apart from mass M. We investigate the extended phase space thermodynamics wherein we identify the black hole mass with the chemical enthalpy rather than internal energy. We analysed it in a canonical ensemble to probe the effects of the parameter β on the thermodynamic quantities. The behaviour of heat capacity reveals the existence of two secondorder phase transitions for decreasing β, the former occurring at increasing horizon radii xc1 and the latter at reduced values of xc2, where x is ratio of radial coordinate r and AdS length l (x = r/l). Whereas an analysis of Gibbs’ free energy confirms our black hole exhibits first order (small to large black hole) phase transition. The behaviour of the solution is consistent with Van der Waals fluid, which can also result from the P − V criticality describing the liquid/gas phase transition observed by the isotherms for temperatures less than the critical temperature. Thus, we show black holes can be understood from the viewpoint of chemistry, in terms of concepts such as Van der Waals fluids and can undergo phase transitions.
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