Accurate Evaluation Of Internal Energy, Free Energy, Entropy, And Enthalpy Of Non-Polar Molecules Using Virial Coefficients

The theoretical assessments of thermodynamic quantities are of great significance for the accurate prediction of the many chemical processes, optimizing equipment, industrial applications, and designing engineering systems. The equations of state are very important for real gases because they are widely used both as initial and intermediate materials in modern technologies.

The Lennard-Jones (12-6) is well-known for having the potential to be successfully applied to the study of various properties gases and liquids. In this study, we have provided useful perspectives of an analytical approach for thermodynamics parameters determination of gases by using the second virial coefficient over the Lennard-Jones (12-6) potential in the wide temperature ranges.


The established expressions were basic and general for arbitrary applications of real systems. The calculated thermodynamics quantities (internal energy, free energy, entropy and enthalpy) of gases ( Cl2, N2O, CH4, C2H2, AsH3, C6H6, Br2, COS, C2N2, Air, CH2, HCl, I2, SO2, He, Ne, Kr, Xe, H2, O2, N2, A, and CO2) were then presented as functions of temperature in terms of a new set of second virial coefficients and their first derivatives, which are shown to provide correct results and are suitable for enough use in the wide temperature range. 

The advance of this study was to use series expansion formulae of the exponential functions for the established formulae of second virial coefficients with Lennard-Jones (12-6) potential. It is well known that the series of formulas for the exponential functions are general and provide accurate results of arbitrary values of parameters. Therefore, the obtained formulae for the second virial coefficient and related thermodynamic quantities are valid in the arbitrary values of parameters.

Image courtesy of Bahtiyar A. Mamedov

As seen from the applications our approach, we present some advantages in the determination of thermodynamic properties of real gases. Within this framework, it is now possible to evaluate any thermodynamic properties for an arbitrary temperature, including a wide pressure range. Therefore, the formulae presented in the study will be useful in wide areas of the engineering sciences.

From the 19th century, the humans have progressively influenced the earth’s temperature and climate by burning fossil fuels. This has added greenhouse gases in enormous quantities that create the greenhouse effect on the atmosphere and increase global warming. Hence, in the Earth’s atmosphere, the gases either trap the sun’s heat or behave as a mirror, causing the rays to reflect back into space. Such theoretical studies may allow us to estimate the change in other thermodynamic properties and the speed of gases, especially in different layers of the atmosphere, depending on changes of temperature and pressure, without the use of any technological equipment.


These findings are described in the article entitled Accurate evaluation of internal energy, free energy, entropy and enthalpy of non-polar molecules by using virial coefficients, recently published in the Chinese Journal of Physics. This work was conducted by B. A. Mamedov from the University of Gaziosmanpaşa and E. Somuncu from Giresun University.



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