Thermodynamic Properties of $$^{4}$$ 4 He Gas in the Temperature Range 4.2–10 K

Abstract

The thermodynamic properties of \(^{4}\)He gas are investigated in the temperature-range 4.2–10 K, with special emphasis on the second virial coefficient in both the classical and quantum regimes. The main input in computing the quantum coefficient is the ‘effective’ phase shifts. These are calculated within the framework of the Galitskii–Migdal–Feynman (GMF) formalism, using the HFDHE2 and Sposito potentials. The virial equation of state is constructed. Extensive calculations are carried out for the pressure–volume–temperature (P–V–T) behavior, as well as chemical potential, and nonideality of the system. The following results are obtained. First, the validity of the GMF formalism for the present system is demonstrated beyond any doubt. Second, the boiling point (phase-transition point) of \(^{4}\)He gas is determined from the P–V behavior using the virial equation of state, its value being closest than all previous results to the experimental value. Third, the chemical potential \(\upmu \) is evaluated from the quantum second virial coefficient. It is found that \(\upmu \) increases (becomes less negative) as the temperature decreases or the number density n increases. Further, \(\upmu \) shows no sensitivity to the differences between the potentials used up to n = 10\(^{27}\) m\(^{-3}\). Finally, the compressibility Z is computed and discussed as a measure of the nonideality of the system.