Thermodynamic Properties of Liquid Helium Three. Vapor Pressures below 1°K

Abstract

Vapor pressures of liquid ${\mathrm{He}}^{3}$ have been measured between 0.45\ifmmode^\circ\else\textdegree\fi{} and 1.0\ifmmode^\circ\else\textdegree\fi{}K. Temperatures were measured by the paramagnetic susceptibility of either ferric ammonium or chrome methylamine alum. The salts were calibrated above 1\ifmmode^\circ\else\textdegree\fi{}K against ${\mathrm{He}}^{3}$ vapor pressures using the data of Abraham, Osborne, and Weinstock and the ${\mathrm{He}}^{4}$ temperature scales of Clement ($55E$) and of van Dijk and Durieux ($L55$). The data obtained with the two salts were in good agreement with each other and indicate no preference between the two ${\mathrm{He}}^{4}$ scales.In order to fit the data by a simple equation over the entire temperature range, explicit account had to be taken of the effect on the vapor pressure of the variation of the spin entropy, ${S}_{\ensuremath{\sigma}}$. An equation valid between the critical point and 0\ifmmode^\circ\else\textdegree\fi{}K is $\mathrm{ln}{p}_{\mathrm{mm}}=2.5\mathrm{ln}{T}_{E}+{i}_{0}\ensuremath{-}(\frac{1}{\mathrm{RT}})\ensuremath{\int}{0}^{T}{S}_{\ensuremath{\sigma}}\mathrm{dT}\ensuremath{-}\frac{2.53853}{{T}_{E}}\ensuremath{-}0.20644{T}_{E}+0.07728{{T}_{E}}^{2}\ensuremath{-}0.00919{{T}_{E}}^{3},$ where ${i}_{0}$ is the vapor pressure constant, 5.31733, and the subscript $E$ designates use of the $55E$ scale throughout the calibration and subsequent equation fitting. By this equation the latent heat at absolute zero is 5.044 cal/mole. Between 0.25\ifmmode^\circ\else\textdegree\fi{}K and the critical point, 3.327\ifmmode^\circ\else\textdegree\fi{}K, the entropy integral is fitted by the empirical equation, $(\frac{1}{\mathrm{RT}})\ensuremath{\int}{0}^{T}{S}_{\ensuremath{\sigma}}\mathrm{dT}=0.5020+0.1786\mathrm{ln}T\ensuremath{-}0.00912{T}^{2}$.