Formula: Wiedemann-Franz Law Thermal Conductivity Electrical Conductivity Lorenz number Temperature
$$\frac{\kappa}{\sigma} ~=~ L \, T$$
$$\kappa ~=~ \sigma \, L \, T$$
$$\sigma ~=~ \frac{\kappa}{L \, T}$$
$$L ~=~ \frac{\kappa}{\sigma \, T}$$
$$T ~=~ \frac{\kappa}{\sigma \, L}$$
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.