Three rods of identical cross-sectional area and made from the same metal, form the sides of an isosceles triangle A B C right angled at B as shown in figure. The point A and B are maintained at temperature T and 2 T respectively, in the steady state. Now, assuming that only heat conduction takes place. The temperature of point C will be

Question

Three rods of identical cross-sectional area and made from the same metal, form the sides of an isosceles triangle A B C right angled at B as shown in figure. The point A and B are maintained at temperature T and 2 T respectively, in the steady state. Now, assuming that only heat conduction takes place. The temperature of point C will be, T 2 + 1, T 2 - 1, 3 T 2 + 1, 3 T ( 2 + 1 )

MARKS App · Accepted Answer

Let T 0 be the temperature of point C and x be the length of rod A B or B C . Then, C A = x 2 + x 2 = 2 x At steady state, the rate of heat flowing from B to C = rate of heat flowing from C to A . So, K A 2 T - T 0 x = K A T 0 - T 2 x 2 2 T - T 0 = T 0 - T By solving, T 0 = 3 T ( 2 + 1 )

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