Rapando B. W., Tonui J. K., Khanna K. M., Mang’are P. A.2026-09-212026ISSN (Online) : 2378-5714, www.arjonline.orghttps://repository.nrf.go.ke/handle/123456789/1621The Bogliubov transformation was used in this study to diagonalize the t-J model Hamiltonian yielding the quasi-particle Hamiltonian and the thermodynamic properties of high temperature superconductors. Formulae for ground state Energy , specific heat, , and entropy, , of high temperature superconductors have been derived in the framework of the t-J model. Transition temperature for Lanthanum Strontium Copper Oxide (LSCO) in the t-J formalism is obtained . Transition temperature for Yttrium Barium Copper Oxide (YBCO) in the t-J formalism is obtained . Calculated Tc that is higher than the experimental value has been obtained for the LSCO and YBCO Cuprates. Highest heat capacity of the superconducting state in the t-J model is found to be while the highest entropy value is 3.15×10-3eV/K for high-Tc superconductors. The total energy of the system increases exponentially with the temperature.enKeywords: Bogliubov Transformationt-J model HamiltonianTransition temperatureSuperconducting StateGround State Energy.Article