New Kinetic Theory for Absorption and Emission Rates of Radiation and New Equations for Lattice and Electronic Heat Capacities, Enthalpies and Entropies of Solids: Application to Copper

Abstract

New equations, which have analytical solutions, for lattice and electronic heat capacities, entropies and enthalpies at constant volume and constant pressure were derived by using kinetic theory, Kirchhoff and Stefan-Boltzmann laws and Wien radiation density equation. These equations were applied to the experimental constant volume heat capacity data of copper. The temperature ΘV corresponding to 3R/2 was found to be 78.4 K for copper. Copper shows the dimensionality crossover from 3 to 2 at about 80 K. The ΘV (T ) is proportional to Debye temperature. The relationship between dimension and ΘV was given. Temperature dependence of Debye temperature and nonmonotonic behavior were discussed. The heat capacity and entropy values, predicted by the proposed models were compared with the values predicted by the Debye models. The results have shown that the proposed models fit the data better than the Debye models. Enthalpy equations derived in this study were compared with the polynomial model and a good fitting was obtained. The equation for the photon absorption equilibrium constant of copper was derived.

New Kinetic Theory and New Equations for Lattice and Electronic Heat Capacities, Enthalpies and Entropies of Solids: Application to Tungsten

“…A plot of C V /T versus T 2 should be a straight line with slope A and intercept γ and allows the determination of Debye temperature Θ D (0) through A = 12π 4 Rs/5Θ 3 D (0). In this study, the heat capacity, enthalpy and entropy equations proposed in [13] will be applied to the constant volume and constant pressure heat capacity data of tungsten. The temperature and dimension dependence of Debye temperature and the deviation from monotonicity will be explained.…”