Three rods of identical area of cross-section and made from the same metal from the sides of an isosceles triangle. ABC, right angled at B. The points A and B are maintained at temperatures T and `sqrt 2T` respectively. In the steady state the temperature of the point C is `T_(C)`.
Assuming that only heat conduction takes place , `T_(C) / T` is equal to

Options

A. `1 / (sqrt2+1)`
B. `3 / (sqrt2 + 1)`
C. `1 / (2(2sqrt2 - 1)`
D. `1 / (sqrt3(sqrt2 -1)`

Answer

B

Explanation

`therefore` `(T_(B) gt T_(A) rArr` Heat will flow B to A via two paths (i) B to A
(ii) 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(2T) -T_(C))A/(a) = (K(T_(C)-T)A)/(sqrt(2a) rArr (T_(c))/T = (3)/(1+sqrt(2))`