scholarly journals Semiclassical Theory for Low Density Properties of Polar Hard D-Sphere Fluid Mixtures

2016 ◽  
Vol 5 ◽  
pp. 48-55
Author(s):  
Shyambhu Kumar ◽  
Ranjit Prasad Yadav
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Virial Coefficient ◽  
Hard Spheres ◽  
Semiclassical Limit ◽  
Second Virial Coefficient ◽  
Low Density ◽  
Fluid Mixtures ◽  
Increase With Increase ◽  
Independent Pair

In the present paper, expansions are obtained for density-independent pair distribution function and second virial coefficient for D-dimensional molecular fluid mixtures of dipolar hard D-spheres in the semiclassical limit. Numerical results for the second virial coefficient are also estimated for binary mixture of (i) hard spheres and dipolar hard spheres and (ii) hard discs and dipolar hard discs. It is found that the quantum effects increase with increase of dipole moment μ2 as well as the concentration x2. The purpose of the present work is to develop a theory for calculating the low density properties of the polar hard D-sphere fluid mixture in the semiclassical limit. We have also developed the theory for estimating the quantum corrections to the density independent pair distribution function (PDF) and second virial coefficient of the polar D-sphere fluid mixtures.Academic Voices Vol.5 2015: 48-55

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 classical and quantum second virial coefficient of low-density 132Xe vapor in the temperature-range 0.1 mK–30 000 K

2019 ◽  
Vol 95 (1) ◽  
pp. 015401 ◽  
Author(s):  
O T Al-Obeidat ◽  
A S Sandouqa ◽  
B R Joudeh ◽  
M M Hawamdeh ◽  
H B Ghassib
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Low Density ◽  
Temperature Range

STICKY SPHERES IN QUANTUM MECHANICS

1994 ◽  
Vol 06 (05a) ◽  
pp. 947-975 ◽  
Author(s):  
M. D. PENROSE ◽  
O. PENROSE ◽  
G. STELL
Keyword(s):  
Quantum Mechanics ◽  
Brownian Motion ◽  
Gaseous Phase ◽  
Virial Coefficient ◽  
Hard Spheres ◽  
Second Virial Coefficient ◽  
Dimensional System ◽  
3 Dimensional ◽  
Fermi Statistics ◽  
Square Well

For a 3-dimensional system of hard spheres of diameter D and mass m with an added attractive square-well two-body interaction of width a and depth ε, let BD, a denote the quantum second virial coefficient. Let BD denote the quantum second virial coefficient for hard spheres of diameter D without the added attractive interaction. We show that in the limit a → 0 at constant α: = ℰma2/(2ħ2) with α < π2/8, [Formula: see text] The result is true equally for Boltzmann, Bose and Fermi statistics. The method of proof uses the mathematics of Brownian motion. For α > π2/8, we argue that the gaseous phase disappears in the limit a → 0, so that the second virial coefficient becomes irrelevant.

Pair distribution function for fluid hard spheres

1969 ◽  
Vol 16 (3) ◽  
pp. 217-223 ◽  
Author(s):  
R.O. Watts ◽  
D. Henderson
Keyword(s):  
Distribution Function ◽  
Pair Distribution Function ◽  
Hard Spheres

Second Virial Coefficient of Low-density Lithium-7 (7Li) Gas in the Temperature Range 1 K40000 K and Beyond

2021 ◽  
Vol 14 (3) ◽  
pp. 239-247
Keyword(s):  
Long Range ◽  
Short Range ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Quantum Mechanical ◽  
Low Density ◽  
Temperature Range ◽  
Repulsive Potentials ◽  
Repulsive Forces ◽  
Good Agreement

Abstract: The second virial coefficient B for low-dense 7Lithium (7Li) gas is calculated over a wide temperature range 1 K40000 K. In the ‘high’-T limit (600 K45000 K), the classical coefficient, Bcl, and the contribution of the first quantum-mechanical correction, Bqc, are computed from standard expressions, using a suitable binary potential. The classical coefficient, Bcl, together with the Boyle temperature, TB, are determined and their values are in good agreement with previous results. In addition, the interface between the classical and quantum regimes is systematically investigated. Furthermore, the calculation of the quantum-mechanical second virial coefficient, Bq, is evaluated using the Beth-Uhlenbeck formula in the temperature range 1 K500 K. A positive value of Bq indicates that the net interaction energy is repulsive, implying that the short-range repulsive forces dominate the long-range attractive forces. However, quite the opposite occurs for negative values of Bq, which are indicative of net attractive interaction. The general behavior of Bq is similar to the potential energy itself, such that the long-range attractive and the short-range repulsive potentials can be deduced from the measurements of Bq. Keywords: Second virial coefficient, Low-density Lithium-7 Gas, Short-range repulsive forces, Long-range attractive forces. PACS: 51.30.+i.

Sign in / Sign up

Export Citation Format

Share Document