Question

why does the wiedemann franz law always work at high temperatures? why are the scattering processes simular at that range, and what would happen if a electric field is applied

Answer 1

First Part of Question

Why does Wiedemann Franz always work at High temperature?

Wiedmann Franz Law state that the ratio of thermal  and electronic  conductivity directly proportion to the temperature

here k is thermal conductivity, and sigma is electrical conductivity, and L Lorentz No  

at low temperatures T tends to 0 K heat and charge currents are carried by the same quasi- Particles, holes or electrons

At a finite value of temperatures, two mechanisms produce a deviation of the ratio L = k/σT from theoretical value L₀ (1) thermal carriers such as phonon or magnons,(2) Inelastic scattering. As the temperature tends to 0K, inelastic scattering becomes weak and promotes large q scattering values. In the case of metal inelastic scattering vanish entirely as the temperature tends to zero and thermal conductivity also will vanish (k=0). At finite temperature, there is a possibility to the small value of scattering (q), and an electron can be transported without thermal excitation. At higher temperature contribution of phonon to thermal transport play a vital role in a system. above the specific temperature (Debye  temperature), the phonon contribution to thermal transport will be constant, so at above this temperature Lorentz no is constant throughout temperature this is why Weidmann Franz law valid to the high temperature  

The second part of Question

At finite temperature, a small value of q scattering is possible throughout the temperature because phonons dominate the transport mechanism throughout the temperature. This why scattering value (q) will not change throughout the temperature.

The third part of the question

When we apply the electric field on the system ratio of thermal to electrical conductivity will not change, and it is directly proportional to temperature, but proportionality constant will change.

It is the theoretical result here we can see that the ratio of thermal and electrical conductivity is directly proportional to temperature.

It is the result when we apply a constant electric field on the system we can ration of both conductivity will be given the same form and proportional to temperature, but constant of proportionality has a different value.