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 respectively, and "L" is the length of the bar. It is convenient to introduce the thermal-conductivity integral The heat flow rate is then given by If the temperature difference is small "k" can be taken as constant. In that case In this section we will motivate an expression for the thermal conductivity in terms of microscopic parameters. Consider a gas of particles of negligible volume governed hard-core interactions and within a vertical temperature gradient. The upper side is hot and the lower side cold. There is a downward energy flow because the gas atoms, going down, have a higher energy