Heat conduction in helium ii containing some 3helium

Abstract

Synopsis A directed heat current in a reservoir containing a 3He-4He-mixture below the lambda-point drives the 3He towards that part of the reservoir which is artificially kept cold. The quasi-osmotic pressure due to this con- centration gradient must in equilibrium be balanced by a fountain pressure caused by an appropriate temperature gradient. Thus a difference in 3He concentration, X, across the reservoir gives rise to a difference in temper- ature, according to the equation −RTρΔX = f ΔT. This temperature difference is equivalent to a resistance to the heat current, so that He II containing some 3He does not have the virtually infinite heat conductivity of He II containing only 4He. The heat resistances have been measured as a function of the heat current for various concentrations of 3He. It was found to be proportional to the 3He-concentration. By combining the above equation with the diffusion equation D(dX/dz) vnX = 0 one can calculate from the heat resistance and the known 3He-concentration the diffusion constant D. This was found to be independent of 3He-concentration, and, at lower temperatures, in good agreement with the values calculated by applying a gas model to the normal component of He II. The method of this experiment can be used to determine 3He-concentrations down to about 5 × 10−5 with a relative error of less than 5%.