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
Electrical resistivity and conductivity equations can be worked out by hand, but for very accurate answers in complex cases, computer methods like finite element analysis may be required. In some applications where the weight of an item is very important, resistivity density products are more important than absolute low resistivity – it is often possible to make the conductor thicker to make up for a higher resistivity; and then a low resistivity density product material (or equivalently a high conductivity to density ratio) is desirable. For example, for long distance overhead power lines, aluminium is frequently used rather than copper (Cu) because it is