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. The points A and B are maintained at temperatures T and $\sqrt{2} T$ respectively in steady state. Assuming that only heat conduction takes place, if the temperature at point C is $\frac{x T}{\sqrt{2} + 1}$ , then the value of x is ___________.

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answer is 3.

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Detailed Solution

As $T_{B} > T_{A},$ heat flows from B to A through both paths
Rate of heat flow in BC = Rate of heat flow in CA
$∴ \frac{K A (\sqrt{2} T - T_{C})}{l} = \frac{K A (T_{C} - T)}{\sqrt{2} l}$
Solving this we get, $T_{C} = \frac{3 T}{\sqrt{2} + 1}$

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