https://journalcps.com/index.php/volumes Communication in Physical Science, 2021, 7(2): 97-114 Communication in Physical Science, 2021, 7(2): 97-114 9114114114 Thermodynamic properties and mass spectra of a quarkonium system with Ultra Generalized Exponential–Hyperbolic Potential Etido. P. Inyang, J. E. Ntibi, E. A. Ibanga, F. Ayedun, E. P. Inyang, E. E. Ibekwe, E. S. William and I.O. Akpan Received 28 March 2021/Accepted 13 May 2021/Published Online 15 May 2021 Abstract: We solved the N-dimensional Klein- Gordon equation analytically using the Nikiforov- Uvarov method to obtain the energy eigenvalues and corresponding wave function in terms of Laguerre polynomials with the ultra-generalized exponential –hyperbolic potential. The results were applied for calculating the mass spectra of heavy mesons including charmonium ( cc ) and bottomonium ( bb ) for different quantum states. Also, the thermodynamic properties such as free energy, mean energy, entropy, and specific heat were obtained. The data obtained in the study was in excellent agreement with experimental results and with results obtained from others with a maximum error of 0.0059 GeV . Keywords: Ultra generalized exponential– hyperbolic potential; Thermodynamic properties; Klein-Gordon equation; Heavy mesons; Nikiforov- Uvarov method Etido P. Inyang* 1 Department of Pure and Applied Sciences, National Open University of Nigeria, Abuja 2 Theoretical Physics Group, Department of Physics, University of Calabar,P.M.B 1115 Calabar, Cross River State, Nigeria Email: etidophysics@gmail.com Orcid id: 0000-0002-5031-3297 Joseph E. Ntibi 2 Theoretical Physics Group, Department of Physics, University of Calabar,P.M.B 1115 Calabar Nigeria Email: joseph.ntibi23@gmail.com Orcid id: 0000-0002-7908-2840 Efiong A. Ibanga Department of Pure and Applied Sciences, National Open University of Nigeria, Abuja Email: eibanga@noun.edu.ngg Orcid id:0000-0002-5452-0613 Funmilayo Ayedun Department of Pure and Applied Sciences, National Open University of Nigeria, Abuja Email: fayedun@noun.edu.ng Orcid id: 0000-0001-5421-9305 Ephraim P. Inyang Theoretical Physics Group, Department of Physics, University of Calabar, P. M. B 1115 Calabar, Cross River State, Nigeria Email: Inyang.ephriam@gmail.com Orcid id: 0000-0002-3803-7613 Etebong E. Ibekwe Department of Physics, Akwa Ibom State University, Ikot Akpaden, P. M. B 1167, Uyo, Akwa Ibom State, Nigeria Email: etebongibekwe@gmail.com Orcid id: 0000-0002-5031-3297 Eddy S. William Theoretical Physics Group, Department of Physics, University of Calabar,P.M.B 1115 Calabar, Cross River State, Nigeria Email: williameddyphysics@gmail.com Orcid id: 0000-0002-5247-5281 Ita O. Akpan Theoretical Physics Group, Department of Physics, University of Calabar,P.M.B 1115 Calabar, Cross River State, Nigeria Email: itayenakpan@yahoo.com Orcid id: 0000-0003-3953-1522 1.0 Introduction The study of thermodynamic properties is important in various areas of physical and chemical sciences. This is made possible through the solutions of the quantum mechanical problems, which contain all the essential data to portray the quantum system under study (Florkowski, 2010). The thermody- namic properties of systems are significance in the analyses of quark-gluon plasma and can provide