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Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer

Seven rods A , B , C , D , E , F and G are connected as depicted in the figure. Every rod possesses an identical cross-sectional area A and length l . The thermal conductivities of the respective rods are K_A = K_C = K₀ , K_B = K_D = 2K₀ , K_E = 3K₀ , K_F = 4K₀ and K_G = 5K₀ . The rod E is maintained at a steady temperature T₁ , while the rod G is maintained at a steady temperature T₂ ( T₂ > T₁ ). Determine the unifo

Options

  1. A3T₁ + 2T₂ 5
  2. BT₁ + 2T₂ 3
  3. C2T₁ + T₂ 3
  4. DT₁ + T₂ 2

Correct answer

B. T₁ + 2T₂ 3

Step-by-step solution

Let the thermal resistance of rod A be R_A = l K₀ A = R₀ . The thermal resistances of the other relevant rods are: R_C = l K₀ A = R₀ R_B = l 2K₀ A = R₀ 2 R_D = l 2K₀ A = R₀ 2 Since rod E is maintained at a steady temperature T₁ and rod G is maintained at a steady temperature T₂ , the junctions of A and C with E are at temperature T₁ , and the junctions of B and D with G are at temperature T₂ . Let the temperature of the upper junction (between A, B, and F) be T_x and the lower junction (between C, D, and F) be T_y

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