scholarly journals Third Virial Coefficients for Helium

1978 ◽  
Vol 33 (9) ◽  
pp. 1095-1096
Author(s):  
R. E. Caligaris ◽  
J . C. Grangel
Keyword(s):  
Experimental Data ◽  
Virial Coefficient ◽  
Quantum Correction ◽  
Pair Potential ◽  
Virial Coefficients ◽  
Dispersion Interaction ◽  
Third Virial Coefficient

Third virial coefficient for helium is calculated using the realistic Beck pair potential. The first quantum correction and the triple-dipole dispersion interaction are included. The results are compared with experimental data and with theoretical values obtained using the MDD-2 pair potential.

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

1967 ◽  
Vol 45 (4) ◽  
pp. 373-378 ◽  
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.

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

2001 ◽  
Vol 66 (6) ◽  
pp. 833-854 ◽  
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.

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

2020 ◽  
Vol 65 (6) ◽  
pp. 500
Author(s):  
O. M. Chubai ◽  
A. A. Rovenchak
Keyword(s):  
Virial Coefficient ◽  
Space Dimension ◽  
Virial Coefficients ◽  
Bose Gas ◽  
Bose Gases ◽  
Second Virial Coefficients ◽  
The Third ◽  
Deformation Parameters ◽  
Third Virial Coefficient ◽  
The Ideal

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.

Pairwise additive third virial coefficients for multipolar molecules : Application to water vapour

1971 ◽  
Vol 24 (8) ◽  
pp. 1567 ◽  
Author(s):  
CHJ Johnson ◽  
TH Spurling
Keyword(s):  
Water Vapour ◽  
Potential Function ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Axially Symmetric ◽  
Multidimensional Integration ◽  
Third Virial Coefficient ◽  
Qualitative Effect ◽  
Experimental Values

Pairwise additive third virial coefficients for axially symmetric multipolar molecules have been calculated using a non-product multidimensional integration formula. Results for the Stockmayer potential agree with the corrected results of Rowlinson. It is found that the inclusion of the dipole-quadrupole and quadrupole-quadrupole terms in the potential function has a marked qualitative effect on the shape of the C-T curve. Values of the third virial coefficient for water vapour calculated using a potential function derived from gaseous viscosity and second virial coefficient data are in good agreement with the experimental values.

A new combining rule for fluid mixtures

2009 ◽  
Vol 74 (2) ◽  
pp. 363-391 ◽  
Author(s):  
José Alfredo González-Calderón ◽  
Fernando del Río
Keyword(s):  
Experimental Data ◽  
Small Molecules ◽  
Binary Mixtures ◽  
Electrostatic Interactions ◽  
Virial Coefficient ◽  
Virial Coefficients ◽  
Interaction Parameters ◽  
Effective Interactions ◽  
Fluid Mixtures ◽  
The Cross

We present evidence for the regular behaviour of the Boyle temperature TB in gaseous binary mixtures of small molecules with negligible multipolar moments. We use this regularity to construct a new combining rule for the prediction of the cross interaction u12(r) in those mixtures. The combining rule gives TB of the cross interaction as the harmonic mean of the Boyle temperatures of the pure components. The validity of this harmonic rule is based on experimental data of 28 binary mixtures, whose TB have been obtained from experimental data of the cross virial coefficient B12(T). In determining TB we make use of non-conformal potentials that have been proven to represent very accurately the effective interactions of the molecules investigated. The new combining rule is used to give interaction parameters of several dozens of binary mixtures involving noble gases (Ne, Ar, Kr and Xe), diatomic molecules (N2, O2 and CO) and n-alkanes (from methane to n-octane). These interaction parameters lead to a prediction of cross virial coefficients B12(T) within experimental error. Electrostatic interactions, originating in permanent dipolar, quadrupolar, octupolar and hexadecapolar moments and exemplified by molecules of HCl, CO2, CF4 and SF6, depart from the regular non-polar behaviour.

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.

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

1971 ◽  
Vol 24 (11) ◽  
pp. 2205 ◽  
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.

Virial coefficients of nitrogen from a quadrupolar site–site potential function

2016 ◽  
Vol 15 (03) ◽  
pp. 1650024
Author(s):  
Kenneth Osondu Monago ◽  
Charles Otobrise
Keyword(s):  
Experimental Data ◽  
Low Temperatures ◽  
Pair Potential ◽  
Virial Coefficients ◽  
Site Model ◽  
Wide Range ◽  
Dipole Term ◽  
Linear Molecules ◽  
A Site ◽  
Model Pair

This work describes a procedure for the numerical calculation of third virial coefficients of simple linear molecules. The method is applied to nitrogen using a site–site model pair-potential and the triple dipole term. Values of volumetric and acoustic second and third virial coefficients of nitrogen are reported over a wide range of temperature and compared with experimental data of several authors. The effect of including the quadrupole–quadrupole energy to the pair potential is investigated and the results suggest that the contributions of the quadrupole moment to second and third virial coefficients are non-negligible at low temperatures.

scholarly journals Characteristic Curves of the Lennard-Jones Fluid

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.

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

1971 ◽  
Vol 24 (12) ◽  
pp. 2449 ◽  
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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