Ideal Bose Gas in Some Deformed Types of Thermodynamics. Correspondence between Deformation Parameters

Two approaches to the construction of thermodynamics in the framework of the q- and м-formalisms, which correspond to certain deformations of the algebra of the creation–annihilation operators, have been considered. By comparing the obtained results, an approximate, independent of the space dimension, correspondence was revealed between the second virial coefficients for the ideal q- and м-deformed Bose gases. The corresponding discrepancy arises only at the level of the third virial coefficient. A method for emulating the м-deformed Bose gas up to the third virial coefficient inclusive by means of the two-parametric nonadditive Polychronakos statistics is demonstrated.

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The Bender Equation of State and Virial Coefficients

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc20001464 ◽

2000 ◽

Vol 65 (9) ◽

pp. 1464-1470 ◽

Cited By ~ 1

Author(s):

Anatol Malijevský ◽

Tomáš Hujo

Keyword(s):

Equation Of State ◽

Virial Coefficient ◽

Virial Coefficients ◽

Low Density ◽

Second Virial Coefficients ◽

The Third ◽

Temperature Dependences ◽

Experimental Values

The second and third virial coefficients calculated from the Bender equation of state (BEOS) are tested against experimental virial coefficient data. It is shown that the temperature dependences of the second and third virial coefficients as predicted by the BEOS are sufficiently accurate. We conclude that experimental second virial coefficients should be used to determine independently five of twenty constants of the Bender equation. This would improve the performance of the equation in a region of low-density gas, and also suppress correlations among the BEOS constants, which is even more important. The third virial coefficients cannot be used for the same purpose because of large uncertainties in their experimental values.

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Approximate method for calculating the third virial coefficient of a gaseous mixture

Canadian Journal of Chemistry ◽

10.1139/v67-066 ◽

1967 ◽

Vol 45 (4) ◽

pp. 373-378 ◽

Cited By ~ 7

Author(s):

M. Orentlicher ◽

J. M. Prausnitz

Keyword(s):

Experimental Data ◽

Virial Coefficient ◽

Virial Coefficients ◽

Gaseous Mixture ◽

Pure Component ◽

Spherically Symmetric ◽

Experimental Uncertainty ◽

Symmetric Potential ◽

The Third ◽

Third Virial Coefficient

An approximation is suggested for calculating the third virial cross-coefficient Cijk from available generalized tables for pure-component third virial coefficients Ciii which are based on any one of several, spherically symmetric potential functions. A comparison of calculated results with the very limited experimental data now available indicates that the suggested approximation can reproduce the experimental results essentially within the probable (large) experimental uncertainty.

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Multipolar third-order non-pairwise additivity of intermolecular forces: Effects on crystal properties and third virial coefficients

Australian Journal of Chemistry ◽

10.1071/ch9712205 ◽

1971 ◽

Vol 24 (11) ◽

pp. 2205 ◽

Cited By ~ 9

Author(s):

CHJ Johnson ◽

TH Spurling

Keyword(s):

Cohesive Energy ◽

Virial Coefficient ◽

Virial Coefficients ◽

Intermolecular Forces ◽

Higher Order ◽

The Third ◽

Dipole Term ◽

Third Virial Coefficient ◽

Three Body ◽

Body Potential

In this paper we give the results of computing the third virial coefficient and the cohesive energy of the crystal for argon taking into account the higher-order multipole terms in the long-range three- body interaction as recently calculated by Bell. The Barker-Pompe potential has been used as the two-body potential function. We find that the third virial coefficient values for argon computed with this more complete non-additive energy function agree very much better with the experimental values than when only the triple-dipole term is used. This is particularly true at lower temperatures. The results also show that better agreement would be obtained if some form of repulsive non- addivity were included in the computation. For the cohesive energy of the crystal we find that the dipole-dipole-quadrupole energy is one-third as large as the triple-dipole energy and so cannot be neglected in these lattice computations. Furthermore, we find that these higher- order three-body forces do not stabilize the face-centred-cubic lattice for argon, the hexagonal-close-packed lattice having a slightly lower energy.

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Mixture virial coefficients for the Hamann-Lambert model for globular molecules

Australian Journal of Chemistry ◽

10.1071/ch9712449 ◽

1971 ◽

Vol 24 (12) ◽

pp. 2449 ◽

Cited By ~ 2

Author(s):

CHJ Johnson ◽

TH Spurling

Keyword(s):

Experimental Data ◽

Least Squares ◽

Virial Coefficient ◽

Virial Coefficients ◽

Second Virial Coefficients ◽

The Third ◽

Lennard Jones ◽

Atomic Interactions ◽

Lambert Model ◽

Experimental Values

The Hamann-Lambert model for globular molecules using Lennard-Jones 12- 6 potential functions for the atomic interactions has been used to obtain second virial coefficients for CH4, CF4, SF6, SiF4, CMe4, SiMe4, and the mixtures CH4-CF4, CH4-SF6, CH4-CMe4, CH4-SiMe4, and CF4-SF6. Additive third virial coefficients have been computed where experimental data are available. Of the 18 parameter sets needed for the 12-6 interactions in the above molecules and their combinations ten were obtained by a least-squares fitting process using experimental values of second virial coefficients, five were obtained from combining rules, and the remaining three from sources independent of virial coefficient data. The computed values of the virial coefficients agree well with the experimental data although in the case of the third virial coefficients improved agreement would be obtained if some form of non-additivity could be allowed for.

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The second virial coefficients of mixed polar vapours

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1959.0033 ◽

1959 ◽

Vol 249 (1258) ◽

pp. 414-426 ◽

Cited By ~ 21

Keyword(s):

Methyl Acetate ◽

Virial Coefficient ◽

Methyl Formate ◽

Second Virial Coefficient ◽

Virial Coefficients ◽

Ethyl Formate ◽

Carbonyl Oxygen ◽

Second Virial Coefficients ◽

Theoretical Significance ◽

Boyle’S Law

The second virial coefficients of binary mixtures of chloroform with methyl formate, n -propyl formate, methyl acetate, ethyl acetate and diethylamine have been measured in a ‘Boyle’s law apparatus’ at temperatures between 50 and 95 °C. The measured values are consistently higher than predicted by the theory of corresponding states, and a quantitative interpretation is proposed, based on the hypothesis that the esters and amine are partially dimerized and are involved in association with the chloroform by hydrogen bonding. A linear relation is shown to exist between the heats and entropies of association for the various mixtures, and the theoretical significance of this is discussed. There is some evidence that hydrogen bonds are formed through the alkoxyl oxygen by formate esters and through the carbonyl oxygen by acetate esters. The paper includes data on the second virial coefficient for the pure esters and for ethyl formate and methyl propionate.

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Parameters of the Bender Equation of State for Chloro Derivatives of Methane and Chlorobenzene

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc20010833 ◽

2001 ◽

Vol 66 (6) ◽

pp. 833-854 ◽

Cited By ~ 1

Author(s):

Ivan Cibulka ◽

Lubomír Hnědkovský ◽

Květoslav Růžička

Keyword(s):

Experimental Data ◽

Equation Of State ◽

Virial Coefficient ◽

Second Virial Coefficient ◽

Virial Coefficients ◽

Liquid Equilibrium ◽

Second Virial Coefficients ◽

Equilibrium Data ◽

State Behaviour ◽

Derivatives Of

Values of adjustable parameters of the Bender equation of state evaluated for chloromethane, dichloromethane, trichloromethane, tetrachloromethane, and chlorobenzene from published experimental data are presented. Experimental data employed in the evaluation included the data on state behaviour (p-ρ-T) of fluid phases, vapour-liquid equilibrium data (saturated vapour pressures and orthobaric densities), second virial coefficients, and the coordinates of the gas-liquid critical point. The description of second virial coefficient by the equation of state is examined.

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