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 is reduced, with this behaviour governed by the Knudsen number, defined as formula_27, where formula_28 is the mean free path of gas molecules and formula_29 is the typical gap size of the space filled by the gas. In a granular material formula_29 corresponds to the characteristic size of the gaseous phase in the pores or intergranular spaces. Isotopically pure diamond can have a significantly higher thermal conductivity, increasing from 2,200 W·m·K (for pure natural diamond, 98.9% C) to 3,320 (for 99.9% enriched), possibly 41,000; with 200,000 "predicted" for 99.999% C.) At the atomic level, there are no simple, correct expressions