Thermal Conductivity of FluidHe3andHe4at Temperatures between 1.5 and 4.0° K and for Pressures up to 34 atm

Abstract

Measurements of the thermal-conductivity coefficient $\ensuremath{\kappa}$ are reported for liquid ${\mathrm{He}}^{4}$ I between 1.77 and 3.95\ifmmode^\circ\else\textdegree\fi{}K, for fluid ${\mathrm{He}}^{3}$ between 1.5 and 3.95\ifmmode^\circ\else\textdegree\fi{}K, both at pressures up to 34 atm, and for gaseous ${\mathrm{He}}^{3}$ and ${\mathrm{He}}^{4}$ between 1.5 and 3.95\ifmmode^\circ\else\textdegree\fi{}K at \ensuremath{\sim}10 Torr. Special attention is given the liquid-vapor critical region of ${\mathrm{He}}^{3}$ and the $\ensuremath{\lambda}$-transition line of ${\mathrm{He}}^{4}$. Corrections for effects of thermal boundary resistance and convection are discussed for the fixed-separation parallel-plate apparatus used for these experiments. Taking into account these corrections, the over-all accuracy of the data is considered to be better than \ifmmode\pm\else\textpm\fi{}3%, though the precision is better than \ifmmode\pm\else\textpm\fi{}1%. Away from the singular regions ${(\frac{\ensuremath{\partial}\ensuremath{\kappa}}{\ensuremath{\partial}T})}_{P}$ is anomalously positive and increases with pressure for both ${\mathrm{He}}^{3}$ and ${\mathrm{He}}^{4}$. Isobars of $\ensuremath{\kappa}$ for ${\mathrm{He}}^{4}$ I pass through shallow minima and then rise sharply as the $\ensuremath{\lambda}$ line is approached from higher temperature. Isotherms of $\ensuremath{\kappa}$ for ${\mathrm{He}}^{3}$ in the neighborhood of the critical point display distinct cusps. Scaling laws predict that near the $\ensuremath{\lambda}$ temperature ${T}_{\ensuremath{\lambda}}$ the coefficient $\ensuremath{\kappa}$ should be proportional to ${(T\ensuremath{-}{T}_{\ensuremath{\lambda}})}^{\ensuremath{-}\frac{1}{3}}$, and near the critical temperature ${T}_{c}$ it should be proportional to ${|T\ensuremath{-}{T}_{c}|}^{\ensuremath{-}\frac{2}{3}}$; other theories predict $\ensuremath{\kappa}$ to be proportional to ${|T\ensuremath{-}{T}_{c}|}^{\ensuremath{-}\frac{1}{2}}$ near ${T}_{c}$. The experimental data are found to agree qualitatively, but not quantitatively, with these predictions.