Because of the significance of the first pressure derivative of the isothermal bulk modulus (K'T,0) at temperature, T, and zero pressure, a thermodynamic model was developed to calculate K'T,0 and its temperature derivative ∂K'T,0/∂T. This model constructs a differential equation of K'T,0 with respect to temperature based on the well-known empirical linear relationship of the Anderson-Gr¿neisen parameter, δT, and the compression ratio, η. By solving this differential equation, we derived both K'T,0 and ∂K'T,0/∂T at a temperature, T, and zero pressure in terms of the known parameters of thermal expansivity, α, isobaric heat capacity, CP, and isothermal bulk modulus, KT at ambient pressure, and K'T at a reference temperature, T0, and ambient pressure. The reliability of this model was confirmed by comparing the modeled MgO results with previous data. This model will provide a powerful tool for determining the equation of state and the thermoelastic properties of solid materials at high temperatures and high pressures.