scholarly journals Second virial coefficient of He4 in the temperature range from 2 to 20 K

1968 ◽  
Vol 72A (2) ◽  
pp. 155 ◽  
Author(s):  
Marjorie E. Boyd ◽  
Sigurd Y. Larsen ◽  
Harmon Plumb
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Temperature Range

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.

COMPRESSIBILITY OF GASES AT HIGH TEMPERATURES: I. METHODS OF MEASUREMENT AND APPARATUS

1949 ◽  
Vol 27b (4) ◽  
pp. 339-352 ◽  
Author(s):  
W. G. Schneider
Keyword(s):  
High Temperatures ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Temperature Range ◽  
Pure Helium ◽  
Methods Of Measurement

Methods and apparatus used for compressibility measurements of gases in the temperature range 0° to 600 °C. are described. A further method which can be used at temperatures above 600 °C. is also described. Data for some measurements with pure helium at 0° and at 600 °C. are given, from which the values (in Amagat units), 0.527 × 10−3 per atm. ± 0.003 × 10−3 and 0.439 × 10−3 per atm. ± 0.005 × 10−3 were obtained for the second virial coefficient at 0° and 600 °C. respectively.

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

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.

Predicting the borderline between the classical and quantum regimes in 4He gas from the second virial coefficient

2014 ◽  
Vol 92 (9) ◽  
pp. 997-1001 ◽  
Author(s):  
H.B. Ghassib ◽  
A.S. Sandouqa ◽  
B.R. Joudeh ◽  
S.M. Mosameh
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Quantum Mechanical ◽  
Interatomic Potentials ◽  
Number Density ◽  
Temperature Range ◽  
Interparticle Potential ◽  
Main Input ◽  
Effective Phase ◽  
Full Quantum

The second Virial coefficient in both classical and quantum regimes of 4He gas is investigated in the temperature range 4.2–10 K. Full quantum mechanical and classical treatments are undertaken to calculate this coefficient. The main input in computing the quantum coefficient is the “effective” phase shifts. These are determined within the framework of the Galitskii–Migdal–Feynman formalism, using two interatomic potentials. The borderline between the classical and quantum regimes is found to depend on the temperature, the number density, and the interparticle potential.

Second Virial Coefficient of the 2cLJ, 3cLJ and 4cLJ Molecules

1994 ◽  
Vol 59 (4) ◽  
pp. 756-767 ◽  
Author(s):  
Tomáš Boublík
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Temperature Range ◽  
Lennard Jones ◽  
Pair Potentials ◽  
Error Bars ◽  
Experimental Values ◽  
The Individual

The second virial coefficient was evaluated for the two-centre, three-centre and four-centre Lennard Jones molecules with the site site distance l ∈ (0,1) at the reduced temperatures Tr = 0.6 - 3.0. The obtained data are correlated by an expression derived originally for the Kihara non-spherical molecules; the same value of the σ-parameter is considered for the both pair potentials whereas εKihara/εncLJ and lKihara / lncLJ vary with the increasing values of lncLJ. Values of the virial coefficient of the individual ncLJ molecules agree within error bars with experimental values in the whole temperature range studied; with only slightly higher deviations also data for the single 2cLJ, 3cLJ and 4cLJ molecules for all the lncLJ values can be correlated.

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.

Sign in / Sign up

Export Citation Format

Share Document