For thermodynamic performance to be optimized particular attention must be paid to the fluid's thermal pressure coefficients and thermodynamic properties. A new analytical expression based on the statistical mechanics is derived for R11, R13, R14, R22, R23, R32, R41, and R113 refrigerants, using the intermolecular forces theory. In this paper, temperature dependency of the parameters of R11, R13, R14, R22, R23, R32, R41, and R113 refrigerants to calculate thermal pressure coefficients in the form of first order has been developed to second and third orders and their temperature derivatives of new parameters are used to calculate thermal pressure coefficients. These problems have led us to try to establish a function for the accurate calculation of the thermal pressure coefficients of R11, R13, R14, R22, R23, R32, R41, and R113 refrigerants based on statistical-mechanics theory for different refrigerants.