Thermodynamic Properties of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>. 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 ${\ensuremath{\Theta}}_{0}$, the Debye characteristic temperature at 0 K, and the entropy. ${C}_{V}$ can be represented by the same function of $\frac{T}{{\ensuremath{\Theta}}_{0}}$ 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 ${\ensuremath{\Theta}}_{0}$ obtained in this work and by Ahlers at higher densities can be represented by ${\ensuremath{\Theta}}_{0}=2340{V}^{\ensuremath{-}0.8114}\ifmmode\times\else\texttimes\fi{}{e}^{\ensuremath{-}0.09690V}$.

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