Morse potential specific heat with applications: an integral equations theory based

Abstract

The specific heat in its molar form or mass form is a significant thermal property in the study of the thermal capacity of the described system. There are two basic methods for the determination of the molar specific heat capacity, one of them is the experimental procedure and the other is the theoretical procedure. The present study deals with finding a formula of the molar specific heat capacity using the theory of the integral equations for Morse interaction which is a very important potential for the study of the general oscillations in the quantum mechanics. We use the approximation (Mean-Spherical) for finding the total energy of the compositions described by Morse interaction. We find two formulas of the heat capacity, one at a constant pressure and the other at a constant volume. We conclude that the Morse molar specific heat is temperature dependent via the inverse square low with respect to temperature. Besides, we find that the Morse molar specific heat is proportional to the square of the Morse interaction well depth. Also, we find that the Morse molar specific heat depends on the particles’ diameter, the bond distance of Morse interaction, the width parameter of Morse interaction, and the volumetric density of the system. We apply the formula of the specific heat for finding the specific heat of the vibrational part for two dimer which are the lithium and caesium dimers and for the hydrogen fluoride, hydrogen chloride, nitrogen, and hydrogen molecules.

Morse oscillator equation of state: An integral equation theory based with virial expansion and compressibility terms

“…The main equation in the study of the simple fluids using the integral equation theory is Ornstein–Zernike equation (OZE) which has two different terms: the first term is resulted from the direct correlation and the other is resulted from the indirect one, the OZE is worded via following formula ( Al-Raeei, 2022b , Al-Raeei, 2022c ): Where the distance of the particles is r , the particle density number is τ , and are correlation functions. From the formula of the equation (2) , it is clear that the finding of solutions of this equation needs another equation which is resulted from multiple types of the approximations used in the simple fluids theory where some have linear form, some have exponential form, and others have natural logarithmic form.…”

Morse potential specific bond volume: a simple formula with applications to dimers and soft–hard slab slider

“…However, the bond volume of Morse potential itself is for the three dimension of the space. We apply the boundary conditions on the solutions of the Ornstein-Zernike equation for the Morse potential where the Morse potential has multiple applications in lots of chemical physics subjects, for instance: the discussing of the thermal properties of a specific system such as the diamond class materials and finding the constants of the vibrational force and the elastic properties, the discussing of the correlations in alloys phases, the discussing of the spectral analysis, in the study of some quantum effect, discussing the energy vibrational states, discussing the alpha decay, the study of the structures with other potentials, the study of the some dimers where this potential has wide applications [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. In the second section of this work, we show the theoretical method of the derivation of the bond volume formula, and in the third section, we show some applications of the formula which we derive, and in the last one, we show the conclusions of the work.…”