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Byju's Answer

Standard XI

Statistics

Slope

Three rods of...

Question

Three rods of identical cross-sectional area and 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 $C$ is

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Solution

The correct option is A

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 $C A$

$\frac{K A (\sqrt{2} T - T_{c})}{l}$ = $\frac{K A (T_{c} - T)}{\sqrt{2} l}$

Solving this, we get $T_{c}$ = $\frac{3 T}{\sqrt{2} + 1}$

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The correct option is A As TB > TA, 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(√2T−Tc)l = KA(Tc−T)√2l Solving this, we get Tc = 3T√2+1