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Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer

Two rods with identical geometrical dimensions are placed between two heat baths maintained at 100^ C and 0^ C , as shown in the figure. The temperature at their junction is 70^ C . Determine the new junction temperature if the two rods are interchanged.

Options

  1. A30^ C
  2. B40^ C
  3. C70^ C
  4. D50^ C

Correct answer

A. 30^ C

Step-by-step solution

Let R₁ and R₂ be the thermal resistances of the two rods. In the initial arrangement, the heat current through both rods is the same. Therefore, 100 - 70 R₁ = 70 - 0 R₂ 30 R₁ = 70 R₂ R₁ R₂ = 3 7 When the rods are interchanged, let the new junction temperature be T . The heat current remains the same through both rods in the new series combination: 100 - T R₂ = T - 0 R₁ 100 - T T = R₂ R₁ Substituting R₂ R₁ = 7 3 , we get: 100 - T T = 7 3 300 - 3T = 7T 10T = 300 T = 30^ C

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