My name is Alexander Fufa

**eV**and here I will explain the following topic:# Wiedemann-Franz Law: How Electrical and Thermal Conductivity Are Related

## Formula

## What do the formula symbols mean?

## Thermal Conductivity

`$$ \kappa $$`Unit

`$$ \frac{ \mathrm{W} }{ \mathrm{m} \, \mathrm{K} } = \frac{ \mathrm{kg} \, \mathrm{m} }{ \mathrm{s}^3 \, \mathrm{K} } $$`

Thermal conductivity is the specific thermal conductivity of the conductor, which depends on the geometry of the conductor (hence "specific"). This tells how capable a conductor is of transporting heat.

## Electrical Conductivity

`$$ \sigma $$`Unit

`$$ \frac{1}{ \mathrm{\Omega} \, \mathrm{m} } = \frac{ \mathrm{s}^3 \, \mathrm{A}^2 }{ \mathrm{m}^3 \, \mathrm{kg} } $$`

Electrical conductivity is the specific electrical conductivity of the conductor, which depends on the geometry of the conductor (hence "specific"). This tells how well a conductor conducts the electric current.

## Lorenz number

`$$ L $$`

Lorenz number is the constant of proportionality between the temperature and the ratio of conductivities. The unit of Lorenz number is \( \mathrm{V}^2 / \mathrm{K}^2 \).

## Temperature

`$$ T $$`Unit

`$$ \mathrm{K} $$`

Absolute temperature of the considered material.

**Explanation**

## Video

The Wiedemann-Franz law is an empirical relationship between the electrical conductivity \( \sigma \) and the thermal conductivity \( \kappa \) of a metal at constant temperature \( T \).

Formula anchor
$$ \begin{align} \frac{\kappa}{\sigma} ~=~ L \, T \end{align} $$

Here \( L \) is the Lorenz number. It is the proportionality constant between the temperature and the ratio of the conductivities. The unit of the Lorenz number is \( \mathrm{V}^2 / \mathrm{K}^2 \).