Thermodynamic Properties of hcp<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>

Precision heat-capacity measurements at constant volumes for hcp ${\mathrm{He}}^{4}$ are presented for molar volumes between 13.7 and 20.8 ${\mathrm{cm}}^{3}$ and for temperatures between 1.3 \ifmmode^\circ\else\textdegree\fi{}K and the melting temperature. These data are used to calculate the deviations of the equation of state for hcp ${\mathrm{He}}^{4}$ from the Gr\"uneisen equation of state. It is found that the reduced Debye temperature $\frac{\ensuremath{\Theta}}{{\ensuremath{\Theta}}_{0}}$ is not a volume-independent function of the reduced temperature $\frac{T}{{\ensuremath{\Theta}}_{0}}$ and that the Gr\"uneisen parameter $\ensuremath{\gamma}$ is both volume and temperature dependent. It is observed that $\ensuremath{\gamma}$ and $\frac{\ensuremath{\Theta}}{{\ensuremath{\Theta}}_{0}}$ at a given volume and $\frac{T}{{\ensuremath{\Theta}}_{0}}$ are the same for hcp ${\mathrm{He}}^{4}$ and hcp ${\mathrm{He}}^{3}$, and it is suggested that the observed volume and temperature dependence of $\ensuremath{\gamma}$ and $\frac{\ensuremath{\Theta}}{{\ensuremath{\Theta}}_{0}}$ are typical for close-packed van der Waals solids in general. The temperature-dependent contributions to other thermodynamic functions are given as well.

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