A comparative evaluation of speed of sound and specific heat capacities of gases by using the quantum mechanical and classical second virial coefficients

In this paper, we propose a new approach for accurate evaluation of speed of sound and specific heat capacities of gases by using analytical formulae of the quantum mechanical and classical second virial coefficients with the Lennard-Jones (12-6) potential. Also, the first and second derivatives of the virial coefficient have been established. The efficiency of the methods is thoroughly examined by applying obtained formulae to the evaluation of some properties of molecules He, Ne, Kr, Xe, Ar, H2, D2, O2 and CH4. The results of the analytical and literature calculations in the case of arbitrary temperature are compared. The suggested method can be used to improve the correctness of quantum correction to classical second virial coefficient evaluation and their first and second derivatives. The proposed approach allows us to calculate the thermodynamic parameters using quantum second virial coefficients with more accuracy and reliability.