A Hill Equation for Solid Specific Heat Capacity Calculation

Abstract

The Hill Equation and Hill Coefficient have been used extensively in biochemistry for the description of noncovalent binding. Previously, the Hill Coefficient was correlated with the Gibbs free energy, which suggests that the Hill Equation might be extensible to covalent binding phenomena. To evaluate this possibility, the Hill Equation was compared to the Debye Model and Einstein Solid in the calculation of heat capacity for 53 covalent solids, which included stainless steels and refractory ceramics. Hill Equation specific heat predictions showed a standard error of 0.37 J/(mole⋅Kelvin), whereas errors from the Debye Model and Einstein Solid were higher at 0.45 J/(mole⋅Kelvin) and 0.81 J/(mole⋅Kelvin), respectively. Furthermore, the Hill Equation is computationally efficient, a feature that can accelerate industrial chemical process simulation(s). Given its speed, simplicity, and accuracy, the Hill Equation likely offers an alternative means of specific heat calculation in chemical process models.