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  4. Three rods of identical cross-sectional area made from the same metal form the sides of an isosceles triangle A B C right angled at B. The points A and B are maintained at temperatures T and √2 T respectively in the steady state. Assuming that only heat conduction takes place, temperature of point C will be

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Q. Three rods of identical cross-sectional area made from the same metal form the sides of an isosceles triangle $A B C$ right angled at $B$. The points $A$ and $B$ are maintained at temperatures $T$ and $\sqrt{2} T$ respectively in the steady state. Assuming that only heat conduction takes place, temperature of point $C$ will bePhysics Question Image

Thermal Properties of Matter

Solution:

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As $T_{B} >T_{A}$,
heat flows from $B$ to $A$ through both paths $B A$ and $B C A$.
Rate of heat flow in $B C=$ Rate of heat flow in $C A$
$\therefore \frac{K A\left(\sqrt{2} T-T_{C}\right)}{L}=\frac{K A\left(T_{C}-T\right)}{\sqrt{2} L}$
Solving this, we get $T_{C}=\frac{3 T}{\sqrt{2}+1}$