Thermodynamics of charged black hole

This paper investigates thermodynamics as well as thermal stability of the Reissner-Nordstrom black hole with the effects of non-linear electrodynamics. We first calculate the expressions for Hawking temperature, Helmholtz free energy, internal energy, enthalpy and Gibbs free energy of this black hole and then study their graphical behavior in the presence of non-linear electrodynamic effects. We also investigate thermal stability of the considered system with two different methods, i.e., through heat capacity and through Hessian matrix. It is found from both the methods that the considered system is thermodynamically stable in the presence of non-linear electrodynamic parameter (alpha). Finally, we analyze the phase transitions of Hawking temperature as well as heat capacity in terms of entropy for different values of charge (q), horizon radius (r+) and coupling parameter. We obtain that Hawking temperature changes its phase from positive to negative for increasing values of q and r+ while it shows opposite trend for higher values of alpha. The heat capacity changes its phase from negative to positive for large values of charge, horizon radius and coupling parameter.