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Three rods of material x and three rods of material y of identical length and cross sectional area are connected as shown in the figure. If the end A is maintained at 60 ∘ C and the junction E at 10 ∘ C , then the temperature of junction C is [Given the thermal conductivity of x is 0.92 W / m . K and that of y is 0.46 W / m . K ]

Options

  1. A10 ∘ C
  2. B20 ∘ C
  3. C30 ∘ C
  4. D40 ∘ C

Correct answer

B. 20 ∘ C

Step-by-step solution

Treating the given network of rods in terms of thermal resistance R x and R y with R x = L A × 0.92 and R y = L A × 0.46 as R = L AK so that if R x = R, R y = 2R x = 2R Now as in this bridge [(P/Q) = (R/S)], so the bridge is balanced, i.e., the temperature at junctions C and D is equal and the rod CD becomes ineffective as no heat will flow through it. Now as the thermal resistance of the bridge between junctions B and E is 1 R BE = 1 R + R + 1 2R + 2R , i.e., R BE = 4 3 R The total resistance of bridge between A a

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