Thermodynamic Correlation of the Entropy of Bose–Einstein Condensation Transition to the Lambda Points of Superfluids

Abstract

In this work, the authors show an apparent connection in the behaviors of superfluid Helium in its two stable isotopes, where the lambda transition to superfluidity is seen to correspond to a theoretical Bose–Einstein condensation temperature of the ideal parts of the two isotopes. A statistical model for the physical and thermodynamic behaviors is developed based on their known properties, where the equations of the partition function, entropy, and specific heat are constructed in such a way where one term applies to the ideal part of the fluid and the second to its interacting part. The calculated temperatures for the formation of a theoretical Bose–Einstein condensation in the ideal parts of both isotopes almost completely matches their lambda transition temperatures. The models of the two isotopes are very different due to the fermionic nature of Helium-3, for which the model is formed based on the Bardeen–Cooper–Schrieffer (BCS) theory of Cooper pairs of fermions. Using this formulation, the Bose–Einstein condensation temperature for the pairs of Helium-3 atoms is calculated, as opposed to the condensation temperature for Helium-4, which is directly derived from the bosonic atoms, leading to its much lower value than Helium-4.