Thermal conductivity of helium-3 between 3 mK and 300 K

Abstract

Measurements on thermal conductivity of fluid helium-3 in the literature are abundant in the liquid phase, while almost no data are available in the gas phase except some at pressures not higher than 0.1 MPa. A quantum version of the principle of corresponding states is used to predict the thermal conductivity of gaseous helium-3 by using those of helium-4, hydrogen, neon and argon. An empirical equation is developed for the thermal conductivity of both the liquid and gas phases at temperatures from 3 mK to 300 K and pressures up to 20 MPa. Similar to other cryogenic fluids like nitrogen, a sharp peak of the thermal conductivity curve is observed at low pressures.

Thermal resistance network model for thermal conductivity of normal liquid helium-4 and helium-3

“…The Pauli Exclusion Principle causes thermal conductivity (TC) to be proportional to T −2 as the case of electron thermal conductibilities in metals. When the temperature 0.1 K < T < 1 K, the TC firstly decreases to its minimum and then increases with increasing temperature [2]. Above 1 K, the degeneracy effect of Fermi fluids no longer works, and interestingly, the TC of liquid 3 He becomes similar to the TC of He I.…”