An Accurate and Efficient Theoretical Assessment of the Thermodynamic Properties of Non-polar Gases

Abstract

Investigation of the intermolecular interactions and thermodynamic properties of real nonpolar gases is of high importance and can be evaluated through virial equation of state. A new, practical and general analytical method is obtained for the evaluation of the second virial coefficient (SVC) with Morse potential, which is significant for the investigation of all thermodynamic properties of gases. The first derivative of SVC with Morse potential analytical formulae is also established since it appears in the thermodynamic expressions. One of the significances of obtained formulae is their validity of all ranges of parameters providing accurate and precise results quickly. The accuracy of the applied method is tested by the calculations of SVC of  gas for a wide temperature range with both experimental and analytical data for comparison and Boyle temperature (T_B) of He, Ne, Ar, Kr, Xe, H₂, N₂, and О₂ gases with included highly accurate corresponding literature data for the comparison and proved to be consistent. In this study, we also used the acquired analytical formulae to obtain the changes in entropy, enthalpy, internal energy and free energy per pressure for the gases of He, Ne, Ar, Kr, Xe, H₂, N₂, and О₂. The results of (∆S)/P, ∆H/P, ∆E/P and ∆F/P are compared with literature data that utilizes most commonly used potential Lennard-Jones (12-6) to acquire thermodynamic properties of gases for SVC calculations. The results proved that including previously ignored higher order term in the (∆S)/P formula improved accuracy but still can be disregarded due to small contributions.