Three rods of identical cross-sectional area and made from the same metal, from the sides of an isosceles triangle ABC right angled at B, as shown in Fig .7(CF).23. The points A and B are maintained at temperature T and `sqrt(2)T` respectively in the steady. Assuming that only heat conduction takes place, temperature of point C will be

Options

A. `(T)/(sqrt(2) +1)`
B. `(T)/(sqrt(2) -1)`
C. `(3T)/(sqrt(2) +1)`
D. `(sqrt(3)T)/(sqrt(2) +1)`

Answer

C

Explanation

Let `T_(0)` be the temperature of point C and x be the length of rod AB or BC . Then
`CA =sqrt(x^(2) + x^(2)) = sqrt(2)x`
At steady state, the rate of heat flowing from B to C = rate of heat flowing from C to A.
`:. (KA(sqrt(2)T - T_(0)))/(x) = (KA(T_(0) - T))/(sqrt(2)x)`
or `sqrt(2) (sqrt(2)T- T_(0)) = T_(0) - T`
On solving, `T_(0) = (3T)/((sqrt(2) + 1))`