Quantum‐Mechanical Second Virial Coefficient of a Hard‐Sphere Gas at High Temperatures

1969 ◽  
Vol 51 (10) ◽  
pp. 4675-4676 ◽  
Author(s):  
Trygve S. Nilsen
Keyword(s):  
High Temperatures ◽  
Hard Sphere ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Quantum Mechanical

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

Using the second virial coefficient as physical criterion to map the hard-sphere potential onto a continuous potential

2018 ◽  
Vol 149 (16) ◽  
pp. 164907
Author(s):  
César Alejandro Báez ◽  
Alexis Torres-Carbajal ◽  
Ramón Castañeda-Priego ◽  
Alejandro Villada-Balbuena ◽  
José Miguel Méndez-Alcaraz ◽  
...  
Keyword(s):  
Hard Sphere ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Physical Criterion ◽  
Continuous Potential

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.

COMPRESSIBILITY OF GASES AT HIGH TEMPERATURES: I. METHODS OF MEASUREMENT AND APPARATUS

1949 ◽  
Vol 27b (4) ◽  
pp. 339-352 ◽  
Author(s):  
W. G. Schneider
Keyword(s):  
High Temperatures ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Temperature Range ◽  
Pure Helium ◽  
Methods Of Measurement

Methods and apparatus used for compressibility measurements of gases in the temperature range 0° to 600 °C. are described. A further method which can be used at temperatures above 600 °C. is also described. Data for some measurements with pure helium at 0° and at 600 °C. are given, from which the values (in Amagat units), 0.527 × 10−3 per atm. ± 0.003 × 10−3 and 0.439 × 10−3 per atm. ± 0.005 × 10−3 were obtained for the second virial coefficient at 0° and 600 °C. respectively.

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