Thermal conductivity electrons. In this case the mean velocity is the Fermi velocity which is temperature independent. The mean free path is determined by the impurities and the crystal imperfections which are temperature independent as well. So the only temperature-dependent quantity is the heat capacity "c", which, in this case, is proportional to "T". So with "k" a constant. For pure metals such as copper, silver, etc. "l" is large, so the thermal conductivity is high. At higher temperatures the mean free path is limited by the phonons, so the thermal conductivity tends to decrease with temperature. In alloys the density of
Thermal conductivity the molar volume. More rigorously, the mean free path of a molecule in a gas is given by formula_77 where "σ" is the collision cross section. So The heat capacity per particle "c" and the cross section "σ" both are temperature independent so the temperature dependence of "k" is determined by the "T" dependence of "v". For a monatomic gas, with atomic mass "M", "v" is given by formula_79 So This expression also shows why gases with a low mass (hydrogen, helium) have a high thermal conductivity. For metals at low temperatures the heat is carried mainly by the free