This thesis studies the thermodynamic and heat engines of black holes in F(R) gravity's rainbow. General relativity and some properties of black holes such as Schwarzschild, Reissner–Nordström, Kerr, and Kerr-Newman black holes will be studied. We also evaluate two modified theories of gravity namely F(R) gravity and gravity's rainbow and also introduce the heat engine which is one of the interesting properties of thermodynamics. Considering F(R) gravity’s rainbow coupled with Maxwell field and in the presence of energy-dependent spacetime with topological structure, we obtain black hole solutions. Then, we evaluate the effects of different parameters on the event horizon of these black holes. We calculate the conserved and thermodynamic quantities of the topologically charged black hole solutions in F(R) gravity's rainbow to check the first law of thermodynamics both in non-extended and extended phase space. Considering the black hole as thermodynamic systems in the extended phase space, we investigate the heat engine efficiency of these black holes. To study the effects of different parameters of the topologically charged black holes in F(R) gravity's rainbow on the heat engine, we will plot η versus different parameters.
