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Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer

Four identical rods AB , CD , CF and DE are connected as shown in the figure. For each rod, the length, cross-sectional area, and thermal conductivity are l , A , and K respectively. The ends A , E , and F are kept at temperatures T₁ , T₂ , and T₃ respectively. Assuming no heat loss to the atmosphere, determine the temperature at B .

Options

  1. A2 T₁ + 3(T₂ + T₃) 8
  2. B3 T₁ + 2(T₂ + T₃) 7
  3. C3 T₁ + T₂ + T₃ 5
  4. D2 T₁ + T₂ + T₃ 4

Correct answer

B. 3 T₁ + 2(T₂ + T₃) 7

Step-by-step solution

Let the thermal resistance of a rod of length l be R = l KA . The resistances of the given rods are: R_ AB = R R_ CF = R R_ DE = R Since CD is a single rod of length l and B is its midpoint, the lengths of sections CB and BD are l/2 . Therefore, their thermal resistances are: R_ CB = R 2 R_ BD = R 2 Let the temperatures at junctions B, C, and D be T_B , T_C , and T_D respectively. Applying the principle of continuity of heat flow (Kirchhoff's junction law) at junction C: T₃ - T_C R + T_B - T_C R/2 = 0 T₃ - T_C + 2(

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