Q: 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 points A and B are maintained at temperature T and (√2)T respectively. In the steady state, the temperature of the point C is Tc. Assuming that only heat conduction takes place, Tc/T is

(a) $\large \frac{1}{2(\sqrt{2}-1)}$

(b) $\large \frac{3}{(\sqrt{2}+1)}$

(c) $\large \frac{1}{ \sqrt{3}(\sqrt{2}-1)}$

(d) $\large \frac{1}{(\sqrt{2}+1)}$

Ans: (b)

Sol: Heat Current , $\large I \propto \frac{\Delta T}{l} $

$\large I_{BC} = I_{CA} $

$\large \frac{\sqrt{2}T-T_c}{a} = \frac{T_c – T}{\sqrt{2}a} $

$\large 3 T = T_c (\sqrt{2} + 1)$

$\large \frac{T_c}{T} = \frac{3}{\sqrt{2} + 1}$