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Three rods of identical cross-sectional ...

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 as shown in the figure. The points A and B are maintained at temperature T and `(sqrt2)T` respectively in the steady state. Assuming that only heat conduction takes place, temperature of point C will be

Text Solution

Verified by Experts

As `T_(B)gtT_(A)`,
heat flows from B to A through both paths
Rate of heat flow in BC = Rate of heat flow in CA
`therefore(KA(sqrt2T-T_(C)))/l=(KA(T_(C)-T))/(sqrt2l)`
Solving this we get, `T_(C)=(3T)/(sqrt2+1)`
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