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Standard XII

Physics

Thermal Resistance

Three rods of...

Question

Three rods of the same dimension have thermal conductivities 3K, 2K and K.They are arranged as shown in fig. Given below, with their ends at $100^{\circ}$ C, $50^{\circ}$ C and $20^{\circ}$ C. The temperature of their junction is

60°C

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70°C

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50°C

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35°C

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Solution

The correct option is B
70°C

Let the temperature of junction be $θ$ then

according to following figure.

H = $H_{1} + H_{2}$

$\Rightarrow \frac{3 K \times A \times (100 - θ)}{l} = \frac{2 K A (θ - 50)}{l} + \frac{K A (θ - 20)}{l}$

$\Rightarrow 300 - 3 θ = 3 θ - 120 \Rightarrow θ = 70^{\circ} C$

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