The exact fourth and fifth virial coefficients of an inverse-6 potential

1979 ◽  
Vol 57 (12) ◽  
pp. 2194-2195
Author(s):  
Donald S. Hall
Keyword(s):  
Equation Of State ◽  
Cluster Expansion ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients

Numerical values are calculated for all of the four- and five-particle diagrams in the Mayer cluster expansion of the equation of state for an inverse-6 potential. These diagrams are then summed with the appropriate weightings to give accurate values for the fourth and fifth virial coefficients, which are found to be B4 = 0.02820(B2)3 and B5 = −0.0104(B2)4, where B2 is the second virial coefficient.

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.

The Bender Equation of State and Virial Coefficients

2000 ◽  
Vol 65 (9) ◽  
pp. 1464-1470 ◽  
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.

scholarly journals On Using the BMCSL Equation of State to Renormalize the Onsager Theory Approach to Modeling Hard Prolate Spheroidal Liquid Crystal Mixtures

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 846
Author(s):  
Donya Ohadi ◽  
David S. Corti ◽  
Mark J. Uline
Keyword(s):  
Equation Of State ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Pure Component ◽  
Excluded Volume ◽  
Theory Approach ◽  
Prolate Spheroidal ◽  
Empirical Correction ◽  
Prolate Spheroids ◽  
Onsager Theory

Modifications to the traditional Onsager theory for modeling isotropic–nematic phase transitions in hard prolate spheroidal systems are presented. Pure component systems are used to identify the need to update the Lee–Parsons resummation term. The Lee–Parsons resummation term uses the Carnahan–Starling equation of state to approximate higher-order virial coefficients beyond the second virial coefficient employed in Onsager’s original theoretical approach. As more exact ways of calculating the excluded volume of two hard prolate spheroids of a given orientation are used, the division of the excluded volume by eight, which is an empirical correction used in the original Lee–Parsons resummation term, must be replaced by six to yield a better match between the theoretical and simulation results. These modifications are also extended to binary mixtures of hard prolate spheroids using the Boublík–Mansoori–Carnahan–Starling–Leland (BMCSL) equation of state.

The second virial coefficients of mixed polar vapours

1959 ◽  
Vol 249 (1258) ◽  
pp. 414-426 ◽  
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.

The second virial coefficients of mixed organic vapours

1952 ◽  
Vol 210 (1103) ◽  
pp. 557-564 ◽  
Keyword(s):  
Hydrogen Bonding ◽  
Binary Mixtures ◽  
Diethyl Ether ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Corresponding States ◽  
Linear Variation ◽  
Second Virial Coefficients

The second virial coefficients of some binary mixtures of organic vapours have been measured at temperatures between 50 and 120° C. Mixtures of n -hexane with chloroform and of n -hexane with diethyl ether show a linear variation of second virial coefficient with composition. This is shown to be in accordance with prediction from the principle of corresponding states. Mixtures of chloroform with diethyl ether show a linear variation at 120° C, but pronounced curvature at lower temperatures. This is interpreted quantitatively as being due to association by hydrogen bonding with an energy of 6020 cal/mole.

The statistical mechanics of assemblies of axially symmetric molecules - II. Second virial coefficients

1954 ◽  
Vol 221 (1147) ◽  
pp. 508-516 ◽  
Keyword(s):  
Carbon Dioxide ◽  
General Theory ◽  
Force Field ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Intermolecular Potential ◽  
Crystal Data ◽  
Axially Symmetric ◽  
Second Virial Coefficients

A general theory of the second virial coefficient of axially symmetric molecules is developed, the directional part of the intermolecular field being treated as a perturbationon the central-force part. The method is applicable to any type of intermolecular potential, particular models of directional interaction being obtained by suitable choices of parameters. Simple expressions are given for the second virial coefficient due to several types of directional force. The theory is illustrated by some calculations on the force field of carbon dioxide and its relation to the second virial coefficient and crystal data. These indicate that there is strong quadrupole interaction between carbon dioxide molecules.

scholarly journals Determination of Second Virial Coefficient of Gold by a Modified Berthelot Equation of State

2020 ◽  
Vol 1 (4) ◽  
pp. 175-180
Author(s):  
M. Sivakumar ◽  
R. Balasubramanian
Keyword(s):  
Equation Of State ◽  
Critical Point ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Similarity Parameter ◽  
Thermodynamic Similarity ◽  
Van Der Waals Equation ◽  
Wide Range ◽  
Law Of Corresponding States

The present study aims to determine the second virial coefficient of gold over a wide range of temperatures from the boiling point to the critical point. A three - parameter modified Berthelot equation of state has been employed to determine the second virial coefficient of gold. The parameters of the equation of state are determined through the critical - point parameters of gold. The temperature -dependence of the second virial coefficient of gold has been investigated. The obtained results are compared with that of the van der Waals equation of state, Berthelot equation of state, Tsonopoulus correlation, and McGlashan correlation. The results of this work agree well with that of other correlations in the vicinity of the critical point. It is also established that gold obeys the single - parameter law of corresponding states. And, the new parameter introduced in the attractive term of the equation of state is found to be a thermodynamic similarity parameter. Doi: 10.28991/HEF-2020-01-04-02 Full Text: PDF

Measurement of the temperature variation of virial coefficients. I. Application to the second virial coefficient of n-butane

1964 ◽  
Vol 17 (5) ◽  
pp. 501 ◽  
Author(s):  
GA Bottomley ◽  
TH Spurling
Keyword(s):  
Temperature Dependence ◽  
Temperature Variation ◽  
Virial Coefficient ◽  
Small Volume ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Absolute Pressure ◽  
Isothermal Expansion ◽  
Volume Increment

An unconventional apparatus, described in detail, determines, through a measured small volume increment, the temperature dependence of the second virial coefficient of a vapour without the necessity for isothermal expansion. Absolute pressure determinations are avoided by working differentially, vapour against nitrogen reference gas. Results for n-butane at 0-150� agree with established work.

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