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

The quantum second virial coefficient B_q of low-dense ⁴He 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 < T < 0.17 K. In the negative-P regime, the system becomes unstable.