Heat Capacity and Other Properties of Hexagonal Close-Packed Helium-4

The heat capacity of hcp helium has been measured for six molar volumes from 20.9 to 16.9 ${\mathrm{cm}}^3$ between about 0.3°K and the melting point. The calorimeter, which uses magnetic cooling and thermometry, is described in some detail. The results, expressed as Debye thetas, level off at low temperatures to constant values, ${\theta }_0$. The volume dependence of ${\theta }_0$ gives a Grüneisen constant of 2.60±0.05. The temperature dependence of $\theta$, which is not qualitatively different from that found in other solidified inert gases, is such that $\frac{\theta }{{\theta }_0}$ is a single function of $\frac{T}{\theta }$, irrespective of density. The results have been used with melting-curve data to give the internal energy, entropy, compressibility, and expansion coefficient. The values of the compressibility are in agreement with those obtained from the discontinuity in the heat capacity on melting. Comparison of ${\theta }_0$ with the compressibility and velocity-of-sound data indicates that hcp helium is elastically anisotropic but approximately obeys the Cauchy relations.