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 individual matrix elements are not necessarily reciprocals of one another; for example, "σ" may not be equal to 1/"ρ". This can be seen in the Hall effect, where formula_34 is nonzero. In the Hall effect, due to rotational invariance about the z-axis, formula_35 and formula_36, so the relation between resistivity and conductivity simplifies to: If the electric field is parallel to the applied current, formula_34 and formula_40 are zero. When they are zero, one number, formula_41, is enough to describe the electrical resistivity. It is then written as simply formula_9, and this reduces to the simpler expression. According to elementary