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 inside the conductor. Conductivity is the inverse (reciprocal) of resistivity. Here, it is given by: For example, rubber is a material with large "ρ" and small "σ"—because even a very large electric field in rubber makes almost no current flow through it. On the other hand, copper is a material with small "ρ" and large "σ"—because even a small electric field pulls a lot of current through it. As shown below, this expression simplifies to a single number when the electric field and current density are constant in the material. When the resistivity of a material has a directional component,