The study of various relations between different quantities is of great importance in thermodynamics. Hence in this paper, we will discuss a specific thermodynamic relation between entropy (S) and temperature (T) of some of the black holes. Therefore, we will choose Kerr, Kerr–Newman and charged BTZ black holes. Then we will calculate the relations between the thermodynamic quantities and explain the results in detail. Here, we study a special type of duality-like behaviour that occurs in the thermodynamics of black holes while preserving the laws of thermodynamics. The relationship between entropy and temperature is calculated as S±T± = γ/2 for the Kerr and Kerr–Newman black holes and S±T± = γ 2/4 for the charged BTZ black holes.
