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Published: Kem. Ind. 55 (11) (2006) 445–456
Paper reference number: KUI-06/2006
Paper type: Professional paper

The Equations of State of Real Gases

V. Butorac and V. Simeon+


The properties of classical real gases, especially their deviations from ideal behaviour, are reviewed. After a brief overview of molecular interactions, the so-called traditional (‘primitive’) model is presented and shown to be applicable not only to monoatomic but also for many polyatomic classical gases. Two-coefficient equation of state was derived by using virial theorem. The best known equation of state for real gases – van der Waals equation – was derived by using canonical partition function. Among the empirical equations of state, Kamerlingh-Onnes’ virial expansion was described, as well as some equations of state frequently used in technical thermodynamics (Redlich-Kwong, Peng-Robinson and Benedict-Webb-Rubin). A review of statistical models of real gases is given. Cluster model is presented where all deviations from perfect gas behaviour are described by configuration integral. In addition, the limits of the cluster model are given. The Kirkwood’s model of integral equation is also discussed. This model, unlike the Mayer’s cluster model, is based on a hierarchy of radial distribution functions for many molecules. Finally, the methods of numerical simulation (Monte Carlo and molecular dynamics) are shortly reviewed.

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real gases, critical point, molecular interactions, virial expansion, configuration integral, cluster model, numerical simulations