Theory of Bosehyphen;Einstein Fluids, Statistical Mechanical Treatment of the Thermodynamic Properties of Liquid Helium

摘要

A formal development of the difference in thermodynamic properties of a Bosehyphen;Einstein and a hypothetical Boltzmann system is presented. The treatment is valid for any thermodynamic phase of the two systems, including the liquid phase to which it is intended to apply. The formal equations show the change in activity of the liquidhyphen;gas and crystalhyphen;liquid transitions for the two systems. A transition, which we identify with the lambda transition in liquid helium is predicted. By reasonable choice of a reduced mass parameter the lambda line can be correctly located. The nature of the lambda transition is related to the behavior at its singularity, of a series, thenth coefficient of which is a defined integral of functions of coordinates ofnmolecules. The simplest assumption which can be made to permit integration does not lead to the correct order of the transition.