Thermodynamic Properties ofHe4. The hcp Phase at Low Densities

Improved apparatus has been developed for measurement of the constant-volume heat capacity $C_V$ of condensed phases at low temperatures. The high-pressure calorimeter is closed by a remotely operated valve at the calorimeter and several problems associated with the usual blocked-capillary technique are thus eliminated. The heat capacity of hcp ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ has been measured from approximately 0.35 K to the temperature of the transition to a mixed phase and for molar volumes $V$ between 20.5 and 21. 0 ${\mathrm{cm}}^3$/mole. The data permit reliable extrapolations to 0 K to determine ${\Theta }_0$, the Debye characteristic temperature at 0 K, and the entropy. $C_V$ can be represented by the same function of $\frac{T}{{\Theta }_0}$ for all molar volumes in the range studied. The data are in good agreement with Ahlers's recent measurements in the limited region of overlap, but the temperature dependence of $C_V$ at low temperatures and densities is different from that deduced by Ahlers by extrapolation from higher temperatures and densities. The values of ${\Theta }_0$ obtained in this work and by Ahlers at higher densities can be represented by ${\Theta }_0=2340\mathrm{}{V}^{-0.8114\mathrm{}}\times e^{-0.09690V}$.