Direct measurements of the constant-volume heat capacity of solid parahydrogen from 22.79 to 16.19cm3/mole and the resulting equation of state

Abstract

The constant-volume heat capacity of solid parahydrogen ($p-{\mathrm{H}}_2$) has been measured directly from below 4 K to the melting line for six molar volumes (22.787 to 16.19 ${\mathrm{cm}}^3$/mole). These data have been analyzed using the Mie-Grüneisen equation of state (EOS) to give the volume and temperature dependence of the Grüneisen parameter and the EOS for $p-{\mathrm{H}}_2$, as well as the volume dependence of the quadrupole-quadrupole interaction parameter for orthohydrogen impurities. Good agreement is found with earlier 4-K high-pressure compression data, and reasonable agreement with direct strain-gauge measurements of $P(V,T)\mathrm{}$. The thermodynamic properties for solid $p-{\mathrm{H}}_2$ at $P=0\mathrm{}$ are obtained by extrapolation to larger molar volumes, with the $T=0\mathrm{}$, $P=0\mathrm{}$ equilibrium volume given as 23.234 (±0.05) ${\mathrm{cm}}^3$/mole and the triple-point volume of the solid as 23.48 (±0.05) ${\mathrm{cm}}^3$/mole. The rather large temperature dependence of the Grüneisen parameter which results from a comparison with high-pressure melting-line data is discussed in terms of an explicit temperature dependence of the lattice vibration spectrum. No indications were found for phase transitions in solid $p-{\mathrm{H}}_2$, nor for premelting anomalies.