# Wiedemann – Franz Law

## Wiedemann – Franz Law

Wiedemann – Franz Law is the law which relates the thermal conductivity (k) and the electrical conductivity (σ) of a material which consists of somewhat freely moving electrons in it.

Thermal Conductivity (k): It is the degree of capacity of a material to conduct heat.

Electrical Conductivity (σ): It is the degree of capacity of a material to conduct electricity (1/ σ).

In metals, when temperature increases, the velocity of free electrons increases and that leads to an increase in heat transfer and it also increases the collisions between the lattice ions and free electrons. This results in the drop in electrical conductivity.

The law defines the ratio of the electric role of the thermal conductivity of a material to the electrical conductivity of a material is directly relative to the temperature.

k/ σ = LT.

Here, the L is proportionality constant and it is called as the Lorenz number.

L = k/ σT

= (π²/ 3) x (kB/e)² = 2.44 x 10⁻⁸ WΩK⁻².

Where,

L = Lorenz number = 2.44 x 10⁻⁸ WΩK⁻².

T = Temperature.

This law is named after Gustav Wiedemann and Rudolph Franz in 1853 reported that the ratio k/ σ has more or less the similar value for dissimilar metal at the same temperature.

Wiedemann Franz Law Limitations:

1. The value of Lorenz number L is not same for every materials.
2. The law don’t hold true for intermediate temperature.
3. The temperature decrease as both (K) and (σ) increases in the pure metals.