The three rods of same meterial and crosssectional area from the sides of a triangle `ABC` The points `A,B` and `C` are maintained at temperature `T T sqrt2` and `(3T)/((sqrt2 +1))` respectively Assuming that only heat conducting takes place the system is in steady state, find the angle at `B` The temperature difference per unit length along `SB` and `CA` is equal
.

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `90^(@)`

Answer

D

Explanation

`T_(B) gt T_(A)` heat will flow from `B` to `A` and from `C` to `B` to remain in steady state. The conduction formula is `(DeltaQ)/(DeltaT) = (KA)/(L) DeltaT`
`(T_(C))/(T_(A))=(3)/(sqrt2+T_(A))` and `T_(A)-T_(c) =sqrt2 (T_(C) - T_(A)sqrt2)`
`(T_(A)-T_(c))/(Lsqrt2)=((T_(c)-T_(A)sqrt2))/(L) = (T_(C)-T_(B))/(L)`
from this we can find that `L_(CB) = L, L_(AC) = L sqrt2`
and for which `L_(AB) = L :. haTB = 90^(@)` .