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.

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.

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 use of gas-liquid chromatography to determine activity coefficients and second virial coefficients of mixtures II. Experimental studies on hydrocarbon solutes

1966 ◽  
Vol 295 (1442) ◽  
pp. 271-287 ◽  
Keyword(s):  
High Pressure ◽  
Equation Of State ◽  
Activity Coefficients ◽  
Virial Coefficients ◽  
Injection System ◽  
Gas Liquid Chromatography ◽  
Molal Volume ◽  
Carrier Gas ◽  
Second Virial Coefficients ◽  
Experimental Values

This paper describes apparatus of a new design for measuring accurately gas-liquid retention volumes in packed columns under carrier gas pressures up to 25 atm. It includes a high pressure soap-film flowmeter, a high pressure vapour phase sample injection system and a pressure control system at the column outlet which enables a flame-ionization detector to be operated at atmospheric pressure. Results are reported for a series of hydrocarbon solutes in three different stationary liquids (squalane, dinonylphthalate and n -hexadecane), with nitrogen, hydrogen and argon as carrier gases. Solute activity coefficients at infinite dilution in the stationary liquids, and second virial coefficients ( B 12 ) for the solute + carrier gas mixtures have been obtained by analysing the retention volume data by the procedure established in part I. The activity coefficients are compared with values obtained from static vapour pressure measurements made by two widely different methods, and the agreement is satisfactory in both cases. The second virial coefficients ( B 12 ) are compared with those values predicted by the principle of corresponding states via the reduced equation of state of McGlashan & Potter (1962). The B 12 values given by using the ‘geometric mean’ combining rule for the mixed critical temperature in the reduced equation of state differ from our experimental values by as much as 75 cm 3 /mole. Using the combining rule of Hudson & McCoubrey (1960) or that of Munn (1961), both of which take account of differences in molal volume and ionization potential between the two components, however, gives B 12 values which agree with our experimental values.

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.

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.

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.

Corresponding states in mixtures of slightly imperfect gases

1951 ◽  
Vol 206 (1087) ◽  
pp. 448-463 ◽  
Keyword(s):  
Virial Coefficients ◽  
Corresponding States ◽  
Gaseous Mixtures ◽  
Second Virial Coefficients ◽  
Experimental Values

The principle of corresponding states, in a form that makes no reference to any particular equation, is extended to apply to mixtures. The principle, thus extended, is used to calculate the second virial coefficients. of gaseous mixtures. The values so calculated agree with the experimental values nearly always to within 1cm. 3 /mole and often much better.

Correlation of second virial coefficients of polar gases by redlich-kwong equation of state

AIChE Journal ◽  
1980 ◽  
Vol 26 (5) ◽  
pp. 858-862 ◽  
Author(s):  
Bojan D. Djordjević ◽  
Andjelka N. Mihajlov-Duduković ◽  
Aleksandar Z. Tasić
Keyword(s):  
Equation Of State ◽  
Virial Coefficients ◽  
Second Virial Coefficients

A modification of the Redlich-Kwong-Soave equation of state and the determination of its parameters on the basis of saturated vapour pressures and second virial coefficients of pure substances

1989 ◽  
Vol 54 (6) ◽  
pp. 1446-1463 ◽  
Author(s):  
Petr Voňka ◽  
Pavel Dittrich ◽  
Josef P. Novák
Keyword(s):  
Equation Of State ◽  
Virial Coefficients ◽  
Effective Algorithm ◽  
Liquid Equilibrium ◽  
Second Virial Coefficients ◽  
Saturated Vapour ◽  
Pure Substances ◽  
Better Than ◽  
Wagner Equation

The temperature dependence of parameter a = a(Tr) of the Redlich-Kwong-Soave equation of state was modified. To calculate the corresponding individual parameters, an effective algorithm applying the Newton method was proposed. The parameters were determined for 60 substances, and the new modification correlates saturated vapour pressures from the values of pr = 0.001 to pr = 1.0 with the accuracy which is usually better than 0.2% and is comparable with that attained in terms of the Wagner equation. The modification proposed is utilized above all when applying the equation of state to the calculation of vapour-liquid equilibrium.

Sign in / Sign up

Export Citation Format

Share Document