My name is Alexander FufaeV and here I write about:
Wiedemann-Franz Law: How Electrical and Thermal Conductivity Are Related
Important Formula
$$\frac{\kappa}{\sigma} ~=~ L \, T$$
$$\kappa ~=~ \sigma \, L \, T$$
$$\sigma ~=~ \frac{\kappa}{L \, T}$$
$$L ~=~ \frac{\kappa}{\sigma \, T}$$
$$T ~=~ \frac{\kappa}{\sigma \, L}$$
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.
The Wiedemann-Franz law is an empirical relationship between the electrical conductivity \( \sigma \) and the thermal conductivity \( \kappa \) of a metal at constant temperature \( T \).
$$ \begin{align} \frac{\kappa}{\sigma} ~=~ L \, T \end{align} $$
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 \( \mathrm{V}^2 / \mathrm{K}^2 \).