Analytical evaluation of third virial coefficient with Lennard-Jones (12-6) potential and its applications

In this paper we give the results of computing the effect of non-additivity of long range forces on the fourth virial coefficient of a Lennard-Jones 12-6 gas. We have considered only dipolar effects but have included all terms up to the fourth order of perturbation theory. We have also calculated the effect of the fourth-order triple-dipole term on the third virial coefficient. For the fourth virial coefficient we find that the dispersion non-additivity, while being positive at low reduced temperatures, goes through a negative minimum at a reduced temperature of about 1.25 before becoming small and positive at high temperatures. This is in contradistinction to the behaviour of the third virial co-efficient where the dispersion non-additivity is always positive.

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Characteristic Curves of the Lennard-Jones Fluid

10.31219/osf.io/9xwsn ◽

2021 ◽

Author(s):

Simon Stephan ◽

Ulrich K. Deiters

Keyword(s):

Virial Coefficient ◽

Equations Of State ◽

Virial Coefficients ◽

Intermolecular Potential ◽

Intermolecular Potentials ◽

Characteristic Curves ◽

The Past ◽

Lennard Jones ◽

Physically Based ◽

Third Virial Coefficient

Equations of state based on intermolecular potentials are often developed about the Lennard-Jones (LJ) potential. Many of such EOS have been proposed in the past. In this work, 20 LJ EOS were examined regarding their performance on Brown’s characteristic curves and characteristic state points. Brown’s characteristic curves are directly related to the virial coefficients at specific state points, which can be computed exactly from the intermolecular potential. Therefore, also the second and third virial coefficient of the LJ fluid were investigated. This approach allows a comparison of available LJ EOS at extreme conditions. Physically based, empirical, and semi-theoretical LJ EOS were examined. Most investigated LJ EOS exhibit some unphysical artifacts.

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Theoretical Assessment of Compressibility Factor of Gases by Using Second Virial Coefficient

Zeitschrift für Naturforschung A ◽

10.1515/zna-2017-0225 ◽

2018 ◽

Vol 73 (2) ◽

pp. 121-125

Author(s):

Bahtiyar A. Mamedov ◽

Elif Somuncu ◽

Iskender M. Askerov

Keyword(s):

Virial Coefficient ◽

Second Virial Coefficient ◽

Compressibility Factor ◽

Analytical Approximation ◽

Accurate Evaluation ◽

Numerical Examples ◽

Lennard Jones ◽

Theoretical Assessment ◽

Good Agreement

AbstractWe present a new analytical approximation for determining the compressibility factor of real gases at various temperature values. This algorithm is suitable for the accurate evaluation of the compressibility factor using the second virial coefficient with a Lennard–Jones (12-6) potential. Numerical examples are presented for the gases H2, N2, He, CO2, CH4 and air, and the results are compared with other studies in the literature. Our results showed good agreement with the data in the literature. The consistency of the results demonstrates the effectiveness of our analytical approximation for real gases.

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