Critical behavior and Joule-Thomson expansion of charged AdS black holes surrounded by exotic fluid with modified Chaplygin equation of state

By considering the concept of a unified single fluid model, referred to as the modified Chaplygin gas (MCG), which amalgamates dark energy and dark matter. In this study, we explore the thermodynamic characteristics of charged anti-de Sitter (AdS) black holes existing in an unconventional fluid accompanied by MCG. To accomplish this objective, we derive the equations of state by regarding the charge $Q^{2}$ as a thermodynamic variable. The impact of MCG parameters on the critical thermodynamic quantities ($\psi_{c}$, $T_{c}$, $Q_{c}^{2}$) are examined, followed by a detailed analysis of the $Q^{2}-\psi$ diagram. To provide a clearer explanation of the phase transition, we present an analysis of the Gibbs free energy. It is important to note that if the Hawking temperature exceeds the critical temperature, there is a distinct pattern observed known as swallowtail behavior. This indicates that the system undergoes a first-order phase transition from a smaller black hole to a larger one. The critical exponent of the system is found to be in complete agreement with that of the van der Waals fluid system. Furthermore, we investigate the impact of MCG parameters and black hole charge on the Joule-Thomson (J-T) expansion in the extended phase space. The J-T coefficient is examined to pinpoint the exact region experiencing cooling or heating, the observation reveals that the presence of negative heat capacity results in the occurrence of a cooling process. In addition, it is worth noting that the certain parameters exert a significant influence on the ratio $\frac{T_{min}}{T_{c}}$. The parameters $\gamma$ and $\beta$ have a non-negligible effect on the isenthalpy curve.