| Wiedemann-Franz Law |
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Wiedemann-Franz law states that the ratio of the thermal conductivity ( K ) to the electrical conductivity ( σ ) of a metal is proportional to the temperature ( T ). |
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i.e. K / σ = L x T |
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This law is named after Gustav Wiedemann and Rudolph Franz,
who in 1853 reported that K / σ has approximately the same value
for different metals at the same temperature. The proportionality
of K / σ with temperature was discovered by Ludvig Lorenz in 1872.
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The proportionality constant L, known as the Lorenz number, is
L = K / σ x T = ( π2 / 3 )
x ( kB / e )2
L = 2.44 x 10-8 W Ω K-2
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This relationship is based upon the fact that the heat and electrical
transport both involve the free electrons in the metal. The
thermal conductivity increases with the average particle velocity
since this increases the forward transport of energy. The electrical
conductivity, on the other hand, decreases while particle velocity
increases because the collisions divert the electrons from forward
transport of charge. |
