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. The point A and B are maintained at temperatures T and `sqrt(2)` T respectively. In the steady state, the temperature of the point C is `T_c.` Assuming that only heat conduction takes places, `T_c//T` is

Options

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

Answer

B

Explanation

`:. T_(B) gt T_(A)rArr` Heat will flow `B` to `A` via two paths (i) `B` to `A` (ii) and along `BCA` as shown.
Rate of flow of heat in path `BCA` will be same
i.e., `((Q)/(t))_(BC) = (Q/t)_(CA)`

`rArr (K(sqrt(2)T - T_(C))A)/(a) = (k(T_(C)-T)A)/(sqrt(2)a)`
`rArr (T_C)/(T) = (3)/(1+sqrt(2))`.