ChemInform Abstract: THERMODYNAMIC PROPERTIES OF ORGANIC OXYGEN COMPOUNDS PART 32, VAPOUR PRESSURE AND SECOND VIRIAL COEFFICIENT OF PROPANAL

1974 ◽  
Vol 5 (29) ◽  
pp. no-no
Author(s):  
D. AMBROSE ◽  
C. H. S. SPRAKE
Keyword(s):  
Thermodynamic Properties ◽  
Vapour Pressure ◽  
Virial Coefficient ◽  
Second Virial Coefficient

scholarly journals Second virial coefficient for the exponent--spline-Morse-spline-van der Waals potential and its application

2021 ◽  
Author(s):  
E. Somuncu ◽  
B.A. Mamedov
Keyword(s):  
Experimental Data ◽  
Thermal Properties ◽  
Thermodynamic Properties ◽  
Virial Coefficient ◽  
Van Der Waals ◽  
Second Virial Coefficient ◽  
Rare Gases ◽  
Analytical Expression ◽  
Numerical Approaches ◽  
Binomial Function

An analytical expression for the second virial coefficient based on an exponent-spline-Morse-spline-van der Waals (ESMSV) potential is presented here for use in defining the thermodynamic properties of rare gases. Our method is established based on a series expansion of the exponential function, Meijer function, gamma function, binomial function, and hypergeometric function. Numerical approaches have commonly been used for the evaluation of the second virial coefficient with the ESMSV potential in the literature. The general formula obtained here can be applied to estimate the thermal properties of rare gases. Our results for the second virial coefficient based on the ESMSV potential of He-He, He-Ne, He-Ar, and He-Xe rare gases are compared with numerical calculations and experimental data, and it is shown that our analytical expression can be successfully used for other gases.

Thermodynamic properties of spin-polarized 3He gas in the temperature range 1 mK–4 K from the quantum second virial coefficient

2017 ◽  
Vol 31 (28) ◽  
pp. 1750202 ◽  
Author(s):  
A. F. Al-Maaitah ◽  
A. S. Sandouqa ◽  
B. R. Joudeh ◽  
H. B. Ghassib
Keyword(s):  
Thermodynamic Properties ◽  
Low Temperatures ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Matrix Inversion ◽  
Low Energy ◽  
Repulsive Interaction ◽  
Energy Limit ◽  
Temperature Range ◽  
Spin Polarized

The quantum second virial coefficient B[Formula: see text] of 3He[Formula: see text] gas is determined in the temperature range 0.001–4 K from the Beth–Uhlenbeck formula. The corresponding phase shifts are calculated from the Lippmann–Schwinger equation using a highly-accurate matrix-inversion technique. A positive B[Formula: see text] corresponds to an overall repulsive interaction; whereas a negative B[Formula: see text] represents an overall attractive interaction. It is found that in the low-energy limit, B[Formula: see text] tends to increase with increasing spin polarization. The compressibility Z is evaluated as another measure of nonideality of the system. Z becomes most significant at low temperatures and increases with polarization. From the pressure–temperature (P–T) behavior of 3He[Formula: see text] at low T, it is deduced that P decreases with increasing T below 8 mK.

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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