Internal energy of a grand canonical ensemble of a mixture of helium isotopes with duo-fermion spin degeneracy

Abstract

We have considered a system consisting of a mixture of helium isotopes 3He-4He interacting weakly in pairs. The partition function of the system with duo-spin and varying number of bosons and fermions is developed to bring out the superfluid properties of the system. The study focused on a Grand Canonical ensemble of 3He - 4He isotopes whose superfluid properties have been determined by distinctively singling out the duo spin component. The internal energy was established algebraically, analyzed and found out to be increasing with temperature. For high temperatures, internal energy remains constant due to particle saturation.