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 Time variation due to phonon decay is described with a relaxation time ("τ") approximation which states that the more the phonon number deviates from its equilibrium value, the more its time variation increases. At steady state conditions and local thermal equilibrium are assumed we get the following equation Using the relaxation time approximation for the Boltzmann equation and assuming steady-state conditions, the phonon thermal conductivity "λ" can be determined. The temperature dependence for "λ" originates from the variety of processes, whose significance for "λ" depends on the temperature range of interest. Mean free path is one factor that determines the