Phase transition of RN-AdS black hole with dark energy

This paper focuses on the examination of various thermodynamic properties of RN-AdS black hole surrounded by quintessence, which is considered as one of the most widely accepted models of dark energy. The investigation involves the determination of temperature, entropy, heat capacity, pressure, equation of state, and Gibbs free energy for this particular black hole. By employing the laws of thermodynamics pertaining to black holes and considering the influence of quintessence, the impact on these quantities is thoroughly analyzed. Additionally, graphical representations of these quantities are depicted, and based on the critical points obtained, the stability and phase transition of the system are assessed. The study further delves into the examination of stability, instability, and the Swallowtail behavior of the system. Notably, due to the discontinuity in the heat capacity, a phase transition occurs within the system, resembling Van der Waals-like phase transitions that transpire between small, intermediate, and large black holes.