Question

A material which conducts electricity usually also conducts heat.

Why is the conductivity of heat and electricity often related?

Answer 1

The thermal conductivity of this metal is, like electrical conductivity, determined largely by the free electrons. Suppose now that the metal has different temperatures at its ends. The electrons are moving slightly faster at the hot end and slower at the cool end. The faster electrons transmit energy to the cooler, slower ones by colliding with them, and just as for electrical conductivity, the longer the mean free path, the faster the energy can be transmitted, i.e., the greater the thermal conductivity. But the rate is also determined by the very higher the speed, the more rapidly does heat energy flow(i.e., the more rapidly collisions occur). In fact, the thermal conductivity is directly proportional to the product of the mean free path and thermal speed.

Both thermal and electrical conductivity depend in the same way on not just the mean free path, but also on other properties such as electron mass and even the number of free electrons per unit volume. But as we have seen, they depend differently on the thermal speed of the electrons and electrical conductivity is inversely proportional to it and thermal conductivity is directly proportional to it.

Hope you understand.