Question

Three rods of identical cross–section made of the same material form the three sides of the of an issoceles triangle ABC; right angled at B. The points A and B are maintained at temperature T and √2 T respectively. In steady state temperature of point C is T_C . Assuming that only conduction takes T_c/T is

(1) \(\frac{1}{2(\sqrt{2}-1)}\)

(2) \(\frac{3}{(\sqrt{2}+1)}\)

(3) \(\frac{3}{(\sqrt{2}-1)}\)

(4) \(\frac{1}{(\sqrt{2}+1)}\)

Answer 1

 (2) \(\frac{3}{(\sqrt{2}+1)}\)

In rod AB heat flow from B to A to maintain temperature at end B heat must flow from C to B. Therefore in rod AC heat flows from A to C. The rate of flow of heat in AC and BC must be same. Therefore