4He Gas in the Temperature-Range 1 mK–5 K: Thermodynamic Properties from the Quantum Second Virial Coefficient

• Published in: Journal of low temperature physics 2023-10, Vol.213 (1-2), p.28-41
• Main Authors: Joudeh, B. R., Sandouqa, A. S., Al-Obeidat, O. T., Al-Maaitah, A. F., Ghassib, H. B.
• Format: Article
• Language: English
• Subjects: Characterization and Evaluation of Materials; Compressibility; Condensed Matter Physics; Equations of state; Internal energy; Low temperature; Low temperature physics; Magnetic Materials; Magnetism; Physics; Physics and Astronomy; Thermodynamic properties; Thermodynamics; Virial coefficients
• ISSN: 0022-2291; 1573-7357
• DOI: 10.1007/s10909-023-02986-y

The quantum second virial coefficient B q of low-dense 4 He gas is calculated over the temperature range 1 mK–5 K. This is the first step in determining, according to standard expressions, the thermodynamic properties of the system, namely, the virial equation of state, compressibility factor, total internal energy, specific heat capacity, and entropy. These are compared to previous results wherever available. A large negative B q is obtained. It is argued that this is intimately related to the formation of small clusters. Based on the semi-quantitative analysis, the cluster formation is predicted to occur in the present system at a fairly low temperature ~ 0.049 to 2.254 K. It is found that: (1) as the temperature decreases, the second virial coefficient deviates more and more from the classical behavior, thanks to quantum effects; and (2) from the pressure (P)-temperature (T) behavior, it is deduced that P is negative in the T-range 0.04 K