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 the electronic thermal conductivity when the electrochemical potential gradient inside the sample is zero, as a starting point. As next step the transport coefficients are written as following where formula_56 and "a" the Bohr radius. The dimensionless integrals "I" are defined as where "s"("x") is the dimensionless transport distribution function. The integrals "I" are the moments of the function where "x" is the energy of carriers. By substituting the previous formulas for the transport coefficient to the equation for "λ" we get the following equation From the previous equation we see that "λ" to be zero the bracketed term