Second virial coefficient as a corresponding states temperature variable for pure fluids: a universal saturation curve

1985 ◽  
Vol 24 (2) ◽  
pp. 262-265 ◽  
Author(s):  
Barbara A. Hacker ◽  
Carol K. Hall
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Corresponding States ◽  
Saturation Curve ◽  
Pure Fluids ◽  
Temperature Variable

The quantum second virial coefficient of 3He at low density in the temperature range 0.005–10 K

2017 ◽  
Vol 95 (12) ◽  
pp. 1208-1214 ◽  
Author(s):  
O.T. Al-Obeidat ◽  
A.S. Sandouqa ◽  
B.R. Joudeh ◽  
H.B. Ghassib ◽  
M.M. Hawamdeh
Keyword(s):  
First Principles ◽  
Virial Coefficient ◽  
Scattering Length ◽  
Second Virial Coefficient ◽  
Repulsive Interaction ◽  
Saturation Curve ◽  
Low Density ◽  
S Wave ◽  
Temperature Range ◽  
The Many

The quantum second virial coefficient Bq for 3He is calculated from first principles at low density in the temperature range 0.005–10 K. By “first principles”, it is meant that the many-body phase shifts are first determined within the Galitskii–Migdal–Feynman formalism; they are then plugged into the Beth–Uhlenbeck formula for Bq. A positive Bq corresponds to an overall repulsive interaction; a negative Bq represents an overall attractive interaction. The s-wave scattering length a0 is calculated quite accurately as a function of the temperature T. The effect of the (low-density) medium on Bq is studied. Bq is then used to determine the volume of 3He at the saturation curve. The compressibility is evaluated as a measure of the non-ideality of the system.

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.

Extended law of corresponding states: square-well oblates

2021 ◽  
Author(s):  
Miguel Gómez de Santiago ◽  
Peter Gurin ◽  
Szabolcs Varga ◽  
Gerardo Odriozola
Keyword(s):  
Short Range ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Corresponding States ◽  
Pair Potentials ◽  
Single Master Curve ◽  
Law Of Corresponding States ◽  
Square Well ◽  
Reduced Density ◽  
Reduced Temperature

Abstract The vapour-liquid coexistence collapse in the reduced temperature, Tr=T/Tc, reduced density, ρr= ρ/ρc, plane is known as a principle of corresponding states, and Noro and Frenkel have extended it for pair potentials of variable range. Here, we provide a theoretical basis supporting this extension and show that it can also be applied to short-range pair potentials where both repulsive and attractive parts can be anisotropic. We observe that the binodals of oblate hard ellipsoids for a given aspect ratio (κ=1/3) with varying short-range square-well interactions collapse into a single master curve in the Δ B*2--ρr plane, where Δ B*2= (B2(T)-B*2(Tc))/v0, B2 is the second virial coefficient, and v0 is the volume of the hard body. This finding is confirmed by both REMC simulation and second virial perturbation theory for varying square-well shells, mimicking uniform, equator, and pole attractions. Our simulation results reveal that the extended law of corresponding states is not related to the local structure of the fluid.

Interpretation of Preferential Adsorption Using Random Phase Approximation Theory

1995 ◽  
Vol 60 (10) ◽  
pp. 1641-1652 ◽  
Author(s):  
Henri C. Benoît ◽  
Claude Strazielle
Keyword(s):  
Approximation Theory ◽  
Random Phase Approximation ◽  
Virial Coefficient ◽  
Random Phase ◽  
Second Virial Coefficient ◽  
Solvent Mixture ◽  
Gyration Radius ◽  
Thermodynamic Quantities ◽  
Phase Approximation ◽  
Preferential Adsorption

It has been shown that in light scattering experiments with polymers replacement of a solvent by a solvent mixture causes problems due to preferential adsorption of one of the solvents. The present paper extends this theory to be applicable to any angle of observation and any concentration by using the random phase approximation theory proposed by de Gennes. The corresponding formulas provide expressions for molecular weight, gyration radius, and the second virial coefficient, which enables measurements of these quantities provided enough information on molecular and thermodynamic quantities is available.

Scattering of anyons with hard-disk repulsion and the second virial coefficient

1991 ◽  
Vol 44 (19) ◽  
pp. 10731-10735 ◽  
Author(s):  
Akira Suzuki ◽  
M. K. Srivastava ◽  
R. K. Bhaduri ◽  
J. Law
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Hard Disk

GENERAL FORMULA FOR THE SECOND VIRIAL COEFFICIENT

1961 ◽  
Vol 39 (11) ◽  
pp. 1563-1572 ◽  
Author(s):  
J. Van Kranendonk
Keyword(s):  
Phase Shift ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Resolvent Operators ◽  
Simple Derivation ◽  
Scattering Phase ◽  
Scattering Phase Shifts ◽  
Quantization Volume ◽  
Mechanical Expression ◽  
The Waves

A simple derivation is given of the quantum mechanical expression for the second virial coefficient in terms of the scattering phase shifts. The derivation does not require the introduction of a quantization volume and is based on the identity R(z)−R0(z) = R0(z)H1R(z), where R0(z) and R(z) are the resolvent operators corresponding to the unperturbed and total Hamiltonians H0 and H0 + H1 respectively. The derivation is valid in particular for a gas of excitons in a crystal for which the shape of the waves describing the relative motion of two excitons is not spherical, and, in general, varies with varying energy. The validity of the phase shift formula is demonstrated explicitly for this case by considering a quantization volume with a boundary the shape of which varies with the energy in such a way that for each energy the boundary is a surface of constant phase. The density of states prescribed by the phase shift formula is shown to result if the enclosed volume is required to be the same for all energies.

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