Thermodynamic Properties of hcpHe4

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 °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 Grüneisen equation of state. It is found that the reduced Debye temperature $\frac{\Theta }{{\Theta }_0}$ is not a volume-independent function of the reduced temperature $\frac{T}{{\Theta }_0}$ and that the Grüneisen parameter $\gamma$ is both volume and temperature dependent. It is observed that $\gamma$ and $\frac{\Theta }{{\Theta }_0}$ at a given volume and $\frac{T}{{\Theta }_0}$ 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 $\gamma$ and $\frac{\Theta }{{\Theta }_0}$ are typical for close-packed van der Waals solids in general. The temperature-dependent contributions to other thermodynamic functions are given as well.