Quantum Mechanical Second Virial Coefficient of a Lennard‐Jones Gas. Helium

1969 ◽  
Vol 50 (9) ◽  
pp. 4034-4055 ◽  
Author(s):  
M. E. Boyd ◽  
S. Y. Larsen ◽  
J. E. Kilpatrick
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Quantum Mechanical ◽  
Lennard Jones

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

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.

The analytical evaluation of the first-order density cluster integral in the radial distribution function

1970 ◽  
Vol 320 (1542) ◽  
pp. 323-348 ◽  
Keyword(s):  
Hard Sphere ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Scattering Data ◽  
X Ray ◽  
Lennard Jones ◽  
X Ray Scattering ◽  
Cluster Integrals ◽  
Square Well ◽  
Three Body

It is shown how to evaluate the two-body, and three-body cluster integrals, ɳ 3 , ɳ * 3 , β 3 , β * 3 (equations (1.1) to (1.4)) for the hard-sphere, square-well and Lennard-Jones ( v :½ v ) potentials; the three-body potential used is the dipole-dipole-dipole potential of Axilrod & Teller. Explicit expressions are presented for the integrals ɳ * 3 , β * 3 using the above potentials; in the case of the first integral, its values for both small and large values of the separation distance are also given, for the Lennard-Jones ( v :½ v ) potential. Similar considerations have been carried out for ɳ 3 and β 3 , except that explicit expressions for the hard-sphere, and square-well potentials are not given, since these had been done before by other authors. The intermediate expressions for the four cluster integrals, are in terms of single integrals, and such expressions are valid for any continuous potential. Numerical results based on some of the expressions in this paper are compared with the results of numerical evaluation of the above integrals by other authors, and the agreement is seen to be good. Making use of the Mikolaj-Pings relation, the above results are used to obtain relationships between the second virial coefficient, and X-ray scattering data, as well as a means of deducing the pair potential at large separations, directly from a knowledge of X-ray scattering data, and the second virial coefficient.

Takahasi Nearest-Neighbour Gas Revisited III; Lennard-Jones Gases

2013 ◽  
Vol 68 (12) ◽  
pp. 773-776
Author(s):  
Akira Matsumoto
Keyword(s):  
Virial Coefficient ◽  
Analytical Formula ◽  
Second Virial Coefficient ◽  
Thermodynamic Quantities ◽  
Inflexion Point ◽  
Lennard Jones ◽  
First Order Phase Transition ◽  
Higher Temperature ◽  
Lower Temperature ◽  
First Order Phase

Some thermodynamic quantities for the Lennard-Jones (12,6) potential are expressed as analytical formula at an isobaric process. The parameters of Lennard-Jones gases for 18 substances are obtained by the second virial coefficient data. Also some thermodynamic quantities for benzene are calculated numerically and drawn graphically. The inflexion point of the length L which depends on temperature T and pressure P corresponds physically to a boiling point. L indicates the liquid phase from lower temperature to the inflexion point and the gaseous phase from the inflexion point to higher temperature. The boiling temperatures indicate reasonable values comparing with experimental data. The behaviour of L suggests a chance of a first-order phase transition in one dimension.

Second virial coefficient of a generalized Lennard-Jones potential

2015 ◽  
Vol 142 (3) ◽  
pp. 034305 ◽  
Author(s):  
Alfredo González-Calderón ◽  
Adrián Rocha-Ichante
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Lennard Jones
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