Evaluation of specific heat capacity and speed of sound of fluids by using the quantum correction to second virial coefficient with Kihara potential

In this work, an analytical formula for the quantum corrections to second virial coefficient over Kihara potential is proposed to evaluate correct and precision the specific heat capacities and speed of sound of fluids by using analytical expression. Also, analytical formulae are presented for the first and second derivatives of the quantum corrections to second virial coefficient. As an example, the suggested approach has been applied to Xe,Ne,Ar,N2,H2,CO2,CF4,C6H6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{Xe}},\;{\text{Ne}},\;{\text{Ar}},\;{\text{N}}_{2} ,\;{\text{H}}_{2} ,\;{\text{CO}}_{2} ,\;{\text{CF}}_{4} ,\;{\text{C}}_{{6}} {\text{H}}_{6} $$\end{document}, n–C4H10, and n–C5H12 fluids for the evaluation of the quantum corrections to second virial coefficient with Kihara potential, specific heat capacity, and speed of sound as a function of temperature and pressure. The analytical formula leads to a rapid and correct evaluation and enables fluids precision calculations of thermodynamic properties (entropy, enthalpy, and internal energy) even in complex molecules due to the Kihara potential. Agreement of the obtained results with the available literature data demonstrates that the proposed formulae are accurate and effective.