Anna university solved problems

ANNA UNIVERSITY SOLVED PROBLEMS

Problem 2.1

The electrical resistivity of copper at 27 °C is 1.72 × 10^-8 Ωm. Compute its thermal conductivity if the Lorentz number is 2.26 × 10^-8 WΩK^-2. (A.U. April 2014)

Given data

Electrical resistivity ρ = 1.72 × 10^{- 8}Ωm

Temperature T = 27 °C= 27+273 = 300 K

Lorentz number L = 2.26 × 10^-8 WΩK^-2

Solution

We know that Wiedemann - Franz law

K / σ = LT

K = σ LT

K = LT / ρ   σ = 1 / ρ

Substituting the given values, we have

K = 394 Wm^-1K^-1

Problem 2.2

The thermal and electrical conductivities of copper at 20 °C are 390 Wm^-1K^-1 and 5.87 × 10⁷ Ω^-1m^-1 respectively. Calculate Lorentz number. (A.U. May 2012)

Given data

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

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

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

Solution

We know that Lorentz number L = K / σ T

Substituting the given values, we have

L = 2.27 × 10^-8 WΩ K^-2

Success of Classical Free Electron Theory

• It is used to verify Ohm's law.

• It is used to explain electrical and thermal conductivities 3 up as w 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 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 /σ τ 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.