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KCET2013PhysicsThermal Properties of Matter

A solid cylinder of radius R made of a material of thermal conductivity K₁ is surrounded by a cylindrical shell of inner radius R and outer radius 2 R made of a material of thermal conductivity K₂ . The two ends of the combined system are maintained at two different temperatures. Then there is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the s

Options

  1. AK₁+K₂
  2. BK₁ K₂ K₁+K₂
  3. C2 K₁+K₂ 4
  4. DK₁+3 K₂ 4

Correct answer

D. K₁+3 K₂ 4

Step-by-step solution

As there is no loss of heat, and the system is in steady state. array llrl & & Q_ total & =Q₁+Q₂ & & K (4 R² ) d d x & = K₁ R² d d x + K₂ (3 R² ) d d x & & 4 K & =K₁+3 K₂ & & K & = K₁+3 K₂ 4 array

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