This manuscript deals with a mathematical analysis of the functions that should be used in the Clausius-Clapeyron thermodynamic modeling, which is usually modeled as a linear fit; this research emphasizes that the thermal models are nonlinear even taking into account the heat capacity functions as a constant. Specifically, the mathematical analysis of the thermal models proposes what equations should be used depending on the type of enthalpy function. Consequently, the enthalpy functions depend on the model of the heat capacity proposed by Albert Einstein. The magnitude of the errors that would be committed by using linear regressions was also estimated, as is the case for the vast majority of publications in this area. This study also shows how the models behave in a wide temperature range and how they are becoming apparently linear as the temperature range decreases.