Thermal Rayleigh Disk Measurements in Liquid Helium II

Abstract

The torque exerted by heat flow on a disk suspended in liquid helium II has been measured and shown to agree with theoretical values. As reported earlier by P. M. Morse and one of the authors, such a disk constitutes a direct mechanical detector of the internal fluid convection currents associated with heat current in helium II. Thus the device is capable of detecting second sound mechanically, whereas ordinary microphones (either pressure or velocity type) do not respond. Furthermore it provides a direct measure of second sound intensity in terms of fundamental quantities, such as kinetic energy density and the geometry. The agreement between observed torque on the disk and predictions based on the two-fluid theory lend further credence to the internal consistency of that hypothesis. Behavior within various temperature ranges, between 1.2°K and the $\lambda$-point, strongly implies that both the normal fluid and superfluid components exert their respective contributions to torque on the disk, as if each fluid individually obeyed the classical König formula. That the disk recognizes the net torque exerted by both fluids in a manner conforming to this extension of the original classical hydrodynamics indicates that Bernoulli type forces (and the resultant couples) are associated with each separate fluid component, and with the heat current as a whole. The resultant generalized Bernoulli relationship earlier reported by Morse and one of the authors to hold near the $\lambda$-point has now been verified throughout the entire liquid helium II temperature range down to 1.2°K. In view of the generalized form of this principle it would appear that for the majority of classical hydrodynamical devices and experiments there exists the thermal counterpart in liquid helium II. In the present investigation, calculations are based on the numerical values of heat content $\mathrm{TS}$ measured for helium II by Kapitza in total flow experiments (through semi-permeable apertures). The present correlations concern alternatively observing by mechanical means the heat current in internal counterflow (no total flow). Employed as a calorimeter the thermal Rayleigh disk yields values of specific heat $c_v$ for liquid helium II in conformity with values obtained earlier by other investigators using customary methods.