Anna University Solved Problems [Lorentz number]

ANNA UNIVERSITY SOLVED PROBLEMS

Problem 2.1

The electrical resistivity of copper at 27 °C is 1.72 × 10-8 Ω m. Compute its thermal conductivity if the Lorentz number is 2.26 × 10-8 W Ω K-2. 

Given data

Electrical resistivity ρ = 1.72 × 10-8 Ω m

Temperature T = 27°C = 27 + 273 = 300 K

Lorentz number L = 2.26 × 10-8 W Ω K-2

Solution

We know that Wiedemann - Franz law

Substituting the given values, we have

Problem 2.2

The thermal and electrical conductivities of copper at 20°C are 390 Wm-1K-1 respectively. Calculate Lorentz number.

Given data

Thermal conductivity of copper K = 390 Wm-1K-1

Electrical conductivity of copper σ = 5.87 × 107Ω-1 m-1

Temperature T = 20°C = (20 +273) = 293 K

Solution

We know that Lorentz number L = K / σT

Substituting the given values, we have

Success of Classical Free Electron Theory

• It is used to verify Ohm's law.

• It is used to explain electrical and thermal conductivities of metals.

• It is used to derive Wiedemann-Franz law.

• It is used to explain the optical properties of metals.

Failures of Classical Free Electron (CFE) Theory

• Classical theory states that all the free electrons absorb the supplied energy. But, the quantum theory states that only a few electrons absorb the supplied energy.

• The electrical conductivity of semiconductors and insulators cannot be explained by this theory.

• The photo-electric effect, Compton effect and black body radiation cannot be explained on the basis of classical free electron theory.

• According to the classical free electron theory, the ratio K /σT is constant at all temperatures. But, it is found that it is not constant at low temperature.

• According to this theory, the value of specific heat capacity of a metal is 4.5R. But, the experimental value is given by 3R. (Here R is the universal gas constant.)

• The susceptibility of paramagnetic material is inversely proportional to temperature. But, the experimental result shows that paramagnetism of metal is independent of temperature. Moreover, ferro-magnetism cannot be explained by this theory.