Wiedemann–Franz law
The Wiedemann Franzsche law also Wiedemann - Franz law is an empirical law, which describes the relationship between thermal conductivity and electrical conductivity in a metal to be almost proportional to the temperature T, independent of the considered metal:
The proportionality constant in the range (or ) is called the Lorenz number.
History
The law was named after Heinrich Gustav Wiedemann and Rudolf Franz. These had 1853 first found that the ratio for all metals at the same temperature is approximately equal. Ludvig Lorenz then finally realized in 1872, the linearity of this relationship for temperature resistant.
The first theoretical explanation of the law was made in 1900 by Paul Drude, who was named after him with the Drude model for the Lorenz number the value
Calculated, the Boltzmann's constant and the electron charge indicated. This value differs by incorrect assumptions in the Drude model by a factor of two from the experimentally determined values , represents the connection but already qualitatively correct dar. With around 1933 by Arnold Sommerfeld enhanced Drude -Sommerfeld theory is the Lorenz number finally quantitatively confirmed:
Importance
The Wiedemann - Franzsche law testifies to the fact that in metals the charge carriers are also carriers of thermal energy. It applies to (compared to the Debye temperature ) very low and very high temperatures. Deviations arise at intermediate temperatures between about 10 K and 200 K by ballistic heat conduction. In addition, the Wiedemann - Franzsche law does not account for contributions of lattice vibrations ( phonons) for heat conduction since, although they transport heat, but no charge.
In the graph of the reciprocal of the electrical conductivity, the resistivity and the thermal conductivity of copper is applied as a red and green lines. The product of two quantities, the blue line is dependent on the temperature. After division by the temperature gives the Lorenz number, light blue line. At 300 C it is 2.31 × 10-8 K-2 and V2 increases to 900 K of less than 5 % to 2.41 × 10-8 K V2 -2.