Physics for Information Science: Unit I: Electrical Properties of Materials
Wiedemann - Franz Law and Lorentz Number
Value, Theory, Law, Proof, Formula
Law: The ratio between the thermal conductivity and electrical conductivity of a metal is directly proportional to the absolute temperature of the metal.
WIEDEMANN - FRANZ LAW
AND LORENTZ NUMBER
Law:
The ratio between the thermal conductivity and electrical conductivity of a
metal is directly proportional to the absolute temperature of the metal.
where
L is a constant called as Lorentz number whose value is
2.44
× 10-8 W Ω K-2 (Quantum mechanical value)
at temperature T = 293 K.
Proof:
(i) By Classical theory
We
know electrical conductivity (from classical theory)
Thermal conductivity
(from classical theory)
……(1)
We
know kinetic energy of an electron 
Substituting this in equation (1) we can write
(or)
(or)
where
Substituting
the value of Boltzmann constant KB = 1.38 × 10-23 JK-1
charge
of electron e = 1.6021 x 10-19 Joules, we get
L=1.12
× 10- 8 W Ω Κ-2
It
is found that the classical value of Lorentz number, is only one half of the
experimental value (i.e.,) 2.44 × 10-8 W Ω K-2.
This
Discrepancy in the experimental and theoretical value of 'L' is the failure of
classical theory. This discrepancy can be rectified by quantum theory.
(ii) By Quantum theory
In
quantum theory the mass of the electron (m) is replaced by the effective mass
m*.
The
electrical conductivity 
Rearranging
the expression for thermal conductivity and substituting the electronic specific
heat, the thermal conductivity can be written as
(or)
(or)
where
Substituting
the values for Boltzmann constant (KB) and the charge of the
electron e we get
Lorentz
number L=2.44 × 10-8 W Ω K-2
Thus
quantum theory verifies Wiedeman-franz law and has good agreement with the
experimental value of Lorentz number.
Physics for Information Science: Unit I: Electrical Properties of Materials : Tag: : Value, Theory, Law, Proof, Formula - Wiedemann - Franz Law and Lorentz Number
Physics for Information Science: Unit I: Electrical Properties of Materials
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Physics for Information Science
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