Three rods of identical cross-sectional area and made from the same metal form the sides of an isosceles triangle ABC right angled at B as shown in the figure. The points A and B are maintained at temperature T and `(sqrt2)T` respectively in the steady state. Assuming that only heat conduction takes place, temperature of point C will be

Options

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

Answer

A

Explanation

As `T_BgtT_A`, heat flows from B to A through both paths BA and BCA.
Rate of heat flow in `BC=` Rate of heat flow in CA
`=(KA(sqrt(2)T-T_C))/(l)=(KA(T_C-T))/(sqrt(2)l)`