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 to 10 cm. The phonon mean free path has been associated directly with the effective relaxation length for processes without directional correlation. If V is the group velocity of a phonon wave packet, then the relaxation length formula_31 is defined as: where "t" is the characteristic relaxation time. Since longitudinal waves have a much greater phase velocity than transverse waves, "V" is much greater than "V", and the relaxation length or mean free path of longitudinal phonons will be much greater. Thus, thermal conductivity will be largely determined by the speed of longitudinal phonons. Regarding the dependence of wave velocity