Extended phase space thermodynamics of black hole with non-linear electrodynamic field

Abstract: This paper deals with the thermodynamical properties of black hole formulated in Einstein theory of relativity and associated with a nonlinear electromagnetic field. The transition of the black hole is analyzed using the parameters mass, electric charge, coupling constant, and cosmological constant. We find-out the thermodynamical aspects of exact black hole solutions to compute the black hole mass, temperature, entropy, Gibbs free energy, specific heat and the critical exponents in the phase space. Further, we study the stability of the black hole solution by specific heat and Gibbs free energy. We look at the first and second phase changes and show a P-V criticality, which is like the Van der Waals phase change. We also examine the equation of the state and the critical exponents.