Experimental Thermal Conductivity of Two Dilute Solutions of<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>3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>in Superfluid<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>

Measurements are presented of the thermal conductivity at saturated vapor pressure of 1.3 and 5.0% dilute solutions of ${\mathrm{He}}^{3}$ in superfluid ${\mathrm{He}}^{4}$ over the approximate temperature range 0.035-0.5\ifmmode^\circ\else\textdegree\fi{}K and of pure superfluid ${\mathrm{He}}^{4}$ over the temperature range 0.04-0.16\ifmmode^\circ\else\textdegree\fi{}K. Heat transport is primarily by ${\mathrm{He}}^{4}$ phonons whose paths are limited by the ${\mathrm{He}}_{3}$-quasiparticle-${\mathrm{He}}^{4}$-phonon interaction and by boundary scattering, in qualitative agreement with a theory of thermal conduction in dilute solutions by Baym and Ebner. There is, however, quantitative disagreement with their calculation of the thermal conductivity for the above solutions.

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