Answer to Question #95501 in Physics for Joy

Question

Make an estimate of the electrical conductivity of Potassium at 0°c if its thermal conductivity has a value of 102.5 W/m/K.

Answer 1

The Wiedemann–Franz law states

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

where $\kappa$ is the thermal conductivity, $\sigma$ is the electrical conductivity, $T$ is the temperature.

The Lorenz constant is equal

$$L=2.44\times 10^{-8}\:\rm W\:\Omega\: K^{-2}$$

Therefore, the electrical conductivity of Potassium at $\rm 0^{\circ}C$

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

$$=\frac{102.5\:\rm W/(m\cdot K)}{2.44\times 10^{-8}\:\rm W\:\Omega\: K^{-2}\times 273\:\rm K}=1.58\times 10^{7}\:\rm S/m$$