INVESTIGATION OF THE PERTURBED VIRIAL EQUATIONS WITH ARBITRARY TEMPERATURE-DEPENDENT SECOND AND THIRD VIRIAL COEFFICIENTS

2011 ◽  
Vol 25 (19) ◽  
pp. 2593-2600 ◽  
Author(s):  
JIANXIANG TIAN
Keyword(s):  
Virial Coefficient ◽  
Equations Of State ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Compressibility Factor ◽  
Critical Properties ◽  
Temperature Dependent ◽  
Packing Factor ◽  
Third Virial Coefficient ◽  
Real Fluids

In this paper, the perturbed virial equations of state with temperature-dependent virial coefficients are constructed using the Carnahan–Starling (CS) hard sphere equation as reference. Considering the second virial coefficient, some critical properties are interaction-independent and the critical packing factor is in the range of that of real fluids. But the critical compressibility factor and the liquid–vapor equilibrium properties disagree with experiments. When both the second and the third virial coefficient are considered, the critical properties are interaction-dependent but are out of the range of experimental results of real fluids. As a conclusion, the fourth virial coefficients are required for further consideration.

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.

scholarly journals Predicting second virial coefficients of organic and inorganic compounds using Gaussian process regression

2021 ◽  
Vol 23 (4) ◽  
pp. 2891-2898
Author(s):  
Miruna T. Cretu ◽  
Jesús Pérez-Ríos
Keyword(s):  
Gaussian Process ◽  
Virial Coefficient ◽  
Inorganic Compounds ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Gaussian Process Regression ◽  
Temperature Dependent ◽  
Second Virial Coefficients ◽  
Molecular Features

Intuitive and accessible molecular features are used to predict the temperature-dependent second virial coefficient of organic and inorganic compounds with Gaussian process regression.

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.

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.

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.

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 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.

Fluids of Hard Nonspherical Molecules. II. Monte Carlo Data and Equation of State

2008 ◽  
Vol 73 (4) ◽  
pp. 459-480 ◽  
Author(s):  
Pavel Morávek ◽  
Jiří Kolafa ◽  
Magda Francová
Keyword(s):  
Monte Carlo ◽  
Equations Of State ◽  
Full Range ◽  
Finite Size ◽  
Virial Coefficients ◽  
Compressibility Factor ◽  
Width Ratio ◽  
Monte Carlo Data ◽  
Finite Size Corrections ◽  
Reduced Pressures

New accurate data on the compressibility factor of the hard homonuclear diatomics with a full range of elongations and the hard prolate spherocylinders with length-to-width ratio as high as 9 are presented. The data were obtained by Monte Carlo NpT simulations with finite-size corrections in the range of reduced pressures βp* = 0.5-7.0. New equations of state based on simultaneous correlation of the data with the virial coefficients up to the ninth are presented.

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.

Sign in / Sign up

Export Citation Format

Share Document