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

Answer

B

Explanation

(b) Heat flow from B to A, A to C and C toB(for steady
state condition, `DeltaQ//Deltat` is same)
Where `(DeltaQ)/(Deltat)=(kA DeltaT)/l`
For sides AC and CB `((DeltaT)/(sqrt2a))_(AC)`
`=(DeltaT/a)_(CB)`
`rArr(T-T_c)/(sqrt2a)=(T_C-sqrt2T)/a rArr T-T_c=sqrt2T_c-2T`
`rArr 3T=T_c(sqrt2+1) rArr (T_c)/T=3/(sqrt2+1)`