Wiedemann-Franz Law

The Wiedemann-Franz Law is one of the fundamental law in physics. It was discovered in the year 1835 and named after German physicists, Gustav Wiedemann and Rudolph Franz. Gustav Wiedemann discovered that thermal conductivity \(\left (\kappa \right )\) and the electrical conductivity \(\left (\sigma \right )\) are approximately have same value at the same temperature for different metals.

In this law:

Thermal Conductivity \(\left (\kappa \right )\) is a degree of capacity of a material to conduct heat.

Electrical Conductivity \(\left (\sigma \right )\) is a degree of capacity of a material to conduct electricity \(\left (\frac{1}{\rho } \right )\).

The law states that the ratio of electronic contribution of the thermal conductivity \(\left (\kappa \right )\) to the electrical conductivity \(\left (\sigma \right )\) of a metal is somewhat equivalent to the temperature \(\left ( T \right )\).

\(\frac{\kappa }{\sigma } = LT\)

Here, the \(L\) is proportionality constant and it is called as the Lorenz number. The \(L\) is equal to:

\(L = \frac{\kappa }{\sigma T} = \frac{\pi ^{2}}{3}\left ( \frac{\kappa _{B}}{e} \right )^{2} = 2.44 \times 10^{-8} \ W\Omega K^{-2}\)

The relationship between the thermal and electrical conductivity is based on the fact that heat and electrical movement involves freely moving electrons in the metal. The thermal conductivity increases the velocity of average particle and also increase in the forward movement of energy. On the other hand, the electrical conductivity decreases the velocity of particle.

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 decreases as both \(\left (\kappa \right )\) and \(\left (\sigma \right )\) increases in the pure metals.