# Thermal conductivity of metals

1. Oct 28, 2009

### Niles

Hi all

In the following link it says: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thercond.html

"For metals, the thermal conductivity is quite high, and those metals which are the best electrical conductors are also the best thermal conductors. At a given temperature, the thermal and electrical conductivities of metals are proportional, but raising the temperature increases the thermal conductivity while decreasing the electrical conductivity. This behavior is quantified in the Wiedemann-Franz Law:

$$\frac{K}{\sigma}\propto T$$
."

Here K is the thermal conductivity, sigma is the electrical conductivity and T is the temperature.

They say further

"Qualitatively, this relationship is based upon the fact that the heat and electrical transport both involve the free electrons in the metal. The thermal conductivity increases with the average particle velocity since that increases the forward transport of energy."

In my book, the thermal conductivity is given by $K\propto Cv_Fl$, where C is the heat capacity, vF is the Fermi velocity and l is the mean free path.

The Fermi velocity is constant, right? So why is it they say that the thermal conductivity goes up with increasing temperature?

2. Oct 28, 2009

### nasu

The electronic heat capacity C depends on temperature.

3. Oct 28, 2009

### Bob S

Please look at this list of thermal conductivity:
http://en.wikipedia.org/wiki/List_of_thermal_conductivities
and look at aluminum (a good electrical conductor) and then the material just underneath that has a thermal conductivity 5 times higher. It is beryllium oxide, an excellent electrical INSULATOR!!
Bob S.

4. Oct 28, 2009

### nasu

Wiedemann-Franz law applies to electronic conduction only.
Both electrical and thermal conduction coefficients in that ratio are electronic.
There is thermal conduction by lattice too.