The thermodynamics of a free Bose gas with effective temperature scale [Formula: see text] and hard-sphere Bose gas with the [Formula: see text] scale are studied. [Formula: see text] arises as the temperature experienced by a single particle in a quantum gas with 2-body harmonic oscillator interaction V osc , which at low temperatures is expected to simulate, almost correctly, the attractive part of the interatomic potential V He between 4 He atoms. The repulsive part of V He is simulated by a hard-sphere (HS) potential. The thermodynamics of this system of HS bosons, with the [Formula: see text] temperature scale (HSET), and particle mass and density equal to those of 4 He , is investigated, first, by the Bogoliubov–Huang method and next by an improved version of this method, which describes He II in terms of dressed bosons and takes approximate account of those terms of the 2-body repulsion which are linear in the zero-momentum Bose operators a0, [Formula: see text] (originally rejected by Bogoliubov). Theoretical heat capacity CV(T) exhibits good agreement, below 1.9 K, with the experimental heat capacity graph observed in 4 He at saturated vapour pressure. The phase transition to the He II phase, occurs in the HSET at Tλ = 2.17 K, and is accompanied, in the modified HSET version, by a singularity of CV(T). The fraction of atoms in the momentum condensate at 0 K equals 8.86% and agrees with other theoretical estimates for He II. The fraction of normal fluid falls to 8.37% at 0 K which exceeds the value 0% found in He II.
