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Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer

A hollow metallic sphere of radius 20 cm encloses a concentric metallic sphere of radius 5 cm . The region between the two spheres is filled with a nonmetallic material. The inner and outer spheres are maintained at temperatures of 50^ C and 10^ C respectively, and it is observed that 100 J of heat travels from the inner sphere to the outer sphere per second. Determine the thermal conductivity of the material between

Options

  1. A150 W m ⁻¹^ C ⁻¹
  2. B25 8 W m ⁻¹^ C ⁻¹
  3. C75 4 W m ⁻¹^ C ⁻¹
  4. D75 8 W m ⁻¹^ C ⁻¹

Correct answer

D. 75 8 W m ⁻¹^ C ⁻¹

Step-by-step solution

The rate of heat flow through a spherical shell of inner radius r₁ and outer radius r₂ is given by H = 4 K r₁ r₂ (T₁ - T₂) r₂ - r₁ where K is the thermal conductivity of the material. Given: H = 100 W r₁ = 5 cm = 0.05 m r₂ = 20 cm = 0.20 m T₁ = 50^ C T₂ = 10^ C Substituting the values into the formula: 100 = 4 K (0.05)(0.20)(50 - 10) 0.20 - 0.05 100 = 4 K (0.01)(40) 0.15 100 = 1.6 K 0.15 K = 100 0.15 1.6 K = 15 1.6 = 150 16 = 75 8 W m ⁻¹^ C ⁻¹

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