Ambient heat capacities and entropies of ionic solids: a unique view using the Debye equation

Entropies of solids are obtained experimentally as integrals of measured heat capacities over the temperature range from zero to ambient. Correspondingly, the Debye phonon distribution equation for solids provides a theoretical connection between these two chemical thermodynamic measures. We examine how the widely applicable Debye equation illuminates the relation between the corresponding experimental measures using more than 250 ionic solids. Estimation of heat capacities for simple ionic solids by the Dulong-Petit heat capacity limit, by the Neumann-Kopp elemental sum, and by the ion sum method is examined in relation to the Debye equation. We note that, and explain why, the ambient temperature heat capacities and entropies of ionic solids are found to be approximately equal, and how deviations from equality may be related to the Debye temperature, ΘD, which characterizes the Debye equation. It is also demonstrated that Debye temperatures may be readily estimated from the experimental ratio of ambient heat capacity to entropy, C(p)/S(p), rather than requiring resort to elaborate theoretical or experimental procedures for their determination. Correspondingly, ambient mineral entropies and heat capacities are linearly correlated and may thus be readily estimated from one another.