Analytical Calculation of Thermodynamic Properties for Nonpolar Gases Using Formulaes Including Second Order Derivative of Virial Coefficients

The evaluation of second order derivative thermodynamic properties of nonpolar gases is carried out by constructing the analytical formulae of the second virial coefficient (SVC) with Morse potential and its first and second derivatives for the first time in the literature without any parameter restrictions. The acquired analytical formulae are used for obtaining the $$\Delta {{C}_{{v}}}{\text{/}}P$$ and $$\Delta {{C}_{p}}{\text{/}}P$$ values at the temperature range of 500–5000 K and 1 atm pressure for the gases of He, Ne, Ar, Kr, Xe, H2, N2, O2. Additionally, the speed of sound calculations are carried out for He and Xe gases for various temperature and pressure values. The Joule–Thomson coefficient (μ) and constant pressure heat capacities of a refrigerant gas of Ar are also obtained for six different temperature values for a temperature range of 193.15–383.15 K at 40 atm pressure. The $$\Delta {{C}_{{v}}}{\text{/}}P$$ and $$\Delta {{C}_{p}}{\text{/}}P$$ values of H2, N2 and O2 indicated good consistency with analytical literature data using Lennard-Jones (12-6) potential. The speed of sound calculations demonstrated that the analytical approach utilizing the Morse potential provides closer results to experimental data compared to the Lennard-Jones (12-6) potential, particularly for heavier atom Xe at all pressure and temperature values, especially in the lower pressure region, and lighter atom He at only calculated higher pressure values greater than 10 atm. The calculations of the Joule–Thomson coefficient for Ar displayed good consistency with experimental data.