# DoITPoMS

Thermal conduction metals

Metals typically have a relatively high concentration of free conduction electrons, and these can transfer heat as they move through the lattice. Phonon-based conduction also occurs, but the effect is swamped by that of electronic conduction.

The following simulation shows how electrons can conduct heat by colliding with the nuclei and transferring thermal energy. Click the “source” button to apply a heat source to one side of the sample. The graph will show the thermal gradient within the sample, and you can also apply a heat sink to the opposite side of the sample using the “sink” button.

## Wiedemann-Franz law

Since the dominant method of conduction is the same in metals for thermal and electrical conduction (i.e. electrons!), it makes sense that there is a relationship between the two conductivities.

The Wiedemann-Franz law states that the ratio of thermal conductivity to the electrical conductivity of a metal is proportional to its temperature.

$LT = \frac{\kappa }{\sigma }$

Where L the proportionality constant (also known as the Lorenz number), is:

$L = \frac{\kappa }{{\sigma T}} = 2.45 \times {10^{ - 8}}W\Omega {K^{ - 2}}$

The law can be explained by the fact that free electrons in the metal are involved in the mechanisms in both heat and electrical transport. The thermal conductivity increases with the average electron velocity since this increases the forward transport of energy. However, the electrical conductivity decreases with an increase in particle velocity because the collisions divert the electrons from forward transport of charge.