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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

A

`T/((sqrt2)-1)`

B

`T/((sqrt2)+1)`

C

`(3T)/((sqrt 2)+1)`

D

`T/((sqrt3)(sqrt2 -1))`

Text Solution

Verified by Experts

The correct Answer is:
C

`H_1 = H_2`
`:. (sqrt(2)T -T_C)/((l//KA)) = (T_C-T)/((sqrt(2)l//KA)`
Solving we get,
`T_C = (3T)/((sqrt2) +1)`.
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