A general model for isochoric heat capacity of matter in different states by introducing thermodynamic dimension concept

Abstract

Using the Maxwell-Boltzmann distribution function and considering Frenkel's theory of liquids; a substance is approached as a fractal lattice. We introduce a new concept that we call it thermodynamic dimension DT to generalize both Einstein and Debye models, so that both models are a special case of the general model (DT = 3). The thermodynamic dimension DT of a fluid is a dimensionless quantity whose value can be a number between zero and three (0 ≤ DT ≤ 3). In a wide range of temperature and pressure comparison of calculated results with experimental data for isochoric heat capacities in dense region show good agreement in the studied fluids. Based on the obtained results, we illustrate existence of the principle of the corresponding states for simple fluids. Finally, in addition to introducing a new condition (DT = 1/2) to plotting the Frenkel line, we predict solid-like features for around of the critical point.