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Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer

A cylindrical rod with a length of 50 cm and a cross-sectional area of 1 cm ^2 is positioned between a large ice chamber at 0^ C and an evacuated chamber kept at 27^ C , as shown in the figure. Very small portions of the rod extend into the chambers, while the remainder is thermally insulated from the surroundings. The cross section entering the evacuated chamber is blackened, allowing it to completely absorb any inc

Options

  1. A4.5 W m ⁻¹ K ⁻¹
  2. B1.8 W m ⁻¹ K ⁻¹
  3. C0.9 W m ⁻¹ K ⁻¹
  4. D3.6 W m ⁻¹ K ⁻¹

Correct answer

B. 1.8 W m ⁻¹ K ⁻¹

Step-by-step solution

In steady state, the net rate of heat absorbed by the blackened end via radiation equals the rate of heat conducted through the rod. The net rate of heat absorbed by radiation is given by the Stefan-Boltzmann law: P_ rad = A (T₀^4 - T₁^4) where T₀ = 27^ C = 300 K is the temperature of the evacuated chamber, and T₁ = 17^ C = 290 K is the temperature of the blackened end. The rate of heat conduction through the rod is: P_ cond = k A (T₁ - T₂) L where T₂ = 0^ C = 273 K is the temperature of the ice chamber, and L = 50

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