The Specific Heat of Liquid Helium at Temperatures between 0.6 and 1.6 K

The measurement of lattice specific heats at low temperatures using a heat switch

The accuracy of the measurement of small specific heats at low temperatures is often limited by the difficulty of achieving adequate thermal insulation of the specimen, especially when exchange gas has been used to cool it down. The paper describes a make-and-break contact which makes possible a degree of thermal insulation an order of magnitude higher than is usually obtained. This ‘heat switch’ has been used to measure the specific heats of three substances with a simple lattice structure. It has been verified that the temperature varia­tion of the specific heats of potassium chloride and grey tin is very close to a T 3 relation at temperatures below about θ D /60. The specific heat of graphite is more complex because of the anisotrophy of the lattice.

Heat transfer in liquid helium below 1°K

The thermal conductivity of liquid helium has been measured between 0.2 and 1.0° K. Below 0.6° K the heat flow is exactly proportional to the temperature gradient and the thermal conductivity is proportional to the specific heat and the diameter of the specimen. Thus the sole mechanism of heat transfer appears to be by phonons which are scattered only at the boundaries of the specimen. These results are in satisfactory accord with previous theoretical discussions and with measurements of the propagation of heat pulses in the liquid. The experiment also afforded the opportunity of making subsidiary measurements of the thermal resistance of the boundary between a metal and liquid helium. Besides being of practical importance, the results show that some modification is called for in the existing theoretical treatments.

Ultrasonic measurements in liquid helium

Measurements have been made of the velocity and absorption of ordinary sound in liquid helium at frequencies of 2, 6 and 12 Mc/s, over the temperature range from the normal boiling-point down to 0-85° K. The accuracy of the velocity measurements has been increased above that reported in an earlier paper, and the temperature and frequency ranges of those measurements have been extended. Particular attention has been paid to the attenuation in the neighbourhood of the A-point and in the very low temperature region. The attenuation is found to be very high near the A-point and at low temperatures, and is proportional to w2 between 1-2°K and the A-point. At lower temperatures a change in the frequency dependence is observed, indicating the presence of a relaxation effect. The significance of these results is discussed in relation to a recent theory of Khalatnikov.

The thermal conductivity of solid helium

The thermal conductivities of crystals of solid helium at densities between 0⋅194 and 0⋅218 g/cm 3 have been measured at liquid-helium temperatures. In order to interpret the results, the specific heat of solid helium at these densities has been measured from 0⋅6 to 1⋅4° K. The range of densities employed is sufficient to allow the observation of Debye characteristic temperatures varying by 40 %, and of thermal conductivities varying by factors of over 10. It is shown that the conductivity measurements are in accord with the ‘umklapp’ type of thermal resistance derived by Peierls (1929, 1935). Further work was restricted by the difficulty of obtaining good single crystals in narrow tubes, but measurements of the conductivity at one density were obtained down to 0⋅3° K. In this region the conductivity is limited by boundary scattering and is higher than that observed by other authors for liquid helium II at similar temperatures.