Second Virial Coefficient of the 2cLJ, 3cLJ and 4cLJ Molecules

1994 ◽  
Vol 59 (4) ◽  
pp. 756-767 ◽  
Author(s):  
Tomáš Boublík
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Temperature Range ◽  
Lennard Jones ◽  
Pair Potentials ◽  
Error Bars ◽  
Experimental Values ◽  
The Individual

The second virial coefficient was evaluated for the two-centre, three-centre and four-centre Lennard Jones molecules with the site site distance l ∈ (0,1) at the reduced temperatures Tr = 0.6 - 3.0. The obtained data are correlated by an expression derived originally for the Kihara non-spherical molecules; the same value of the σ-parameter is considered for the both pair potentials whereas εKihara/εncLJ and lKihara / lncLJ vary with the increasing values of lncLJ. Values of the virial coefficient of the individual ncLJ molecules agree within error bars with experimental values in the whole temperature range studied; with only slightly higher deviations also data for the single 2cLJ, 3cLJ and 4cLJ molecules for all the lncLJ values can be correlated.

The second virial coefficient of a non-associating gas with anisotropic interactions

1980 ◽  
Vol 45 (9) ◽  
pp. 2375-2383 ◽  
Author(s):  
Miloš Ševčík ◽  
Tomáš Boublík
Keyword(s):  
Experimental Data ◽  
Perturbation Theory ◽  
Intermolecular Interactions ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Pair Potential ◽  
Lennard Jones ◽  
Different Temperatures ◽  
Anisotropic Interactions ◽  
Experimental Values

The second virial coefficient in systems with permanent and induced multipole interactions was studied by using a statistical-thermodynamics correlation based on the perturbation theory of fluids. Several pair potential combinations of the Lennard-Jones function with different, subsequently more complex anisotropic contributions, were considered; the improvement in the description of intermolecular interactions due to these non-central contributions brought about an improvement in the interpretation of experimental data. The characteristic dependence of the parameters ε/k on σ at different temperatures was obtained for all of the three systems studied (Ar, CH4 and CH3F). It was found that if experimental values of the second virial coefficient of methyl fluoride are correlated by a relation derived from the Stockmayer potential, two sets of the ε/k and σ can be employed.

The Second Virial Coefficients of Some Cyclic Hydrocarbons

1959 ◽  
Vol 12 (3) ◽  
pp. 309 ◽  
Author(s):  
HG David ◽  
SD Hamann ◽  
RB Thomas
Keyword(s):  
Interaction Potential ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Theoretical Curve ◽  
Cyclic Hydrocarbons ◽  
Second Virial Coefficients ◽  
Temperature Range ◽  
Lennard Jones ◽  
Law Of Corresponding States

This paper reports some measurements of the second virial coefficient B of cyclopropane in the temperature range 300 to 400°K . It also gives some values of B for cyclohexane and benzene, derived from critical analyses of the published vapour densities and P-V-T properties of these gases between 300 and 650°K . In each case the results have been fitted to the relation B = α + β/T + γ/T2 + δ/T3 The following conclusions can be drawn : (i) The values of B for benzene and cyclohexane are consistent with the effects of pressure on the enthalpies and heat capacities of the gases. (ii) cycloHexane and benzene show large and almost equal deviations from the law of corresponding states for monatomic gases, but cyclopropane shows a much smaller deviation. (iii) It is impossible to fit the second virial coefficients of benzene and cyclohexane to the theoretical curve for a Lennard-Jones (12,6) gas. But they can be fitted to the curve for a (28,7) gas, and the associated force constants are physically reasonable. It appears that the interaction potential for cyclopropane molecules is intermediate between the (12,6) and (28,7) potentials.

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.

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

Intermolecular forces and properties of fluid. I. The automatic calculation of higher virial coefficients and some values of the fourth coefficient for the Lennard-Jones potential

1960 ◽  
Vol 254 (1279) ◽  
pp. 487-498 ◽  
Keyword(s):  
Virial Coefficient ◽  
Mathematical Problem ◽  
Virial Coefficients ◽  
Intermolecular Forces ◽  
Lennard Jones Potential ◽  
Intermolecular Potentials ◽  
Jones Potential ◽  
Lennard Jones ◽  
Experimental Values ◽  
First Time

The prediction of the virial coefficients for particular intermolecular potentials is generally regarded as a difficult mathematical problem. Methods have only been available for the second and third coefficient and in fact only few calculations have been made for the latter. Here a new method of successive approximation is introduced which has enabled the fourth virial coefficient to be evaluated for the first time for the Lennard-Jones potential. It is particularly suitable for automatic computation and the values reported here have been obtained by the use of the EDSAC I. The method is applicable to other potentials and some values for these will be reported subsequently. The values obtained cannot yet be compared with any experimental results since these have not been measured, but they can be used in the meantime to obtain more accurate experimental values of the lower coefficients.

The Calibration of Thermocouples by Freezing-Point Baths and Empirical Equations

1959 ◽  
Vol 81 (2) ◽  
pp. 177-188 ◽  
Author(s):  
R. P. Benedict
Keyword(s):  
Digital Computer ◽  
High Speed ◽  
Freezing Point ◽  
Individual Characteristics ◽  
Empirical Equations ◽  
Test Results ◽  
Calibration System ◽  
Temperature Range ◽  
Experimental Values ◽  
The Individual

A calibration system is described which is based on the use of a few precisely determined experimental values obtained from freezing-point baths. Characteristics of the individual thermocouples at intermediate points are obtained by passing empirical equations of prescribed form through the test values. A program is reviewed, by which a high-speed digital computer accomplishes the necessary conversions, curve fittings, comparisons of individual characteristics with arbitrary reference tables, and the printing out of a table of differences. Test results for a series of iron-constantan thermocouples, over the temperature range 32–1225 F, are presented to illustrate the use of the system and the uncertainties involved. Comparisons are drawn between these results and those obtained by other methods.

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.

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