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JEE MainPhysicsThermal Properties of Matter

Three distinct metal rods of identical length and uniform cross-sectional area are joined together at a common central junction to form a Y-shape. The free ends of the rods are maintained at steady temperatures of 90^ C , 60^ C , and 0^ C . The thermal conductivities of the rods connected to these ends are K , 2K , and 3K , respectively. Assuming no heat loss to the surroundings, the steady-state temperature of the c

Options

  1. A35^ C
  2. B50^ C
  3. C70^ C
  4. D30^ C

Correct answer

A. 35^ C

Step-by-step solution

Let the steady-state temperature of the central junction be T . According to the principle of conservation of energy, the net heat current into the junction must be zero in steady state. H = 0 K A (90 - T) L + 2K A (60 - T) L + 3K A (0 - T) L = 0 Cancelling the common terms K A L : (90 - T) + 2(60 - T) + 3(0 - T) = 0 90 - T + 120 - 2T - 3T = 0 210 - 6T = 0 6T = 210 T = 35^ C Answer: 35^ C

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