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Three rods of identical cross-sectional area and made from the same metal form the sides of an isosceles triangle ABC right angled at B . The points A and B are maintained at temperatures T and 2 T , respectively, in the steady-state. Assuming that only heat conduction takes place, the temperature of the point C is

Options

  1. A3 T 2 + 1
  2. BT 2 + 1
  3. CT 3 2 - 1
  4. DT 2 - 1

Correct answer

A. 3 T 2 + 1

Step-by-step solution

As T B > T A , heat flows from B to A through both paths BA and BCA . Rate of heat flow in BC = Rate of heat flow in CA K A 2 T - T c l = KA T c - T 2 l Solving this, we get T c = 3 T 2 + 1

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