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 -2 T respectively- In the steady state- the temperature of point C is T c- Assuming that only heat conduction takes place- the ratio T c - T isA- 1-2-2-1B- 3-2-1C- -2-1-3-2-1D- 1-2-1

The correct option is B Refer to Fig. since T_B gt; T_A, heat the flows from B to A and from B to C. In the steady state, rate of flow of heat from B to C ...

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Standard XII

Physics

Conduction Law: Differential Form

Three rods of...

Question

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 the steady state, the temperature of point C is $T_{c}$ . Assuming that only heat conduction takes place, the ratio $\frac{T_{c}}{T}$ is

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Solution

The correct option is B

Refer to Fig. since $T_{B}$ > $T_{A}$ , heat the flows from B to A and from B to C. In the steady state, rate of flow of heat from B to C = rate of flow of heat from C to A, i.e. $\frac{Q_{2}}{t} = \frac{Q_{3}}{t}$ or $\frac{k A (T_{B} - T_{c})}{l} = \frac{k A (T_{c} - T)}{\sqrt{2 l}} (∵ A C = \sqrt{2} B C)$ which gives $\frac{T_{C}}{T} = \frac{3}{\sqrt{2} + 1} (∵ T_{B} = T \sqrt{2})$ which is choice (b).

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