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Q.

Three rods made of same material and having same cross-section have been joined as shown in fig. Each rod is of same length. The left and right ends are kept at 0°C and 90°C respectively. The temperature of the junction of the three rods will be

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a

60°C

b

45°C

c

20°C

d

30°C

answer is B.

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Detailed Solution

Let the temperature of junction be T. Then
${(\frac{dQ}{dt})}_{1} = {(\frac{dQ}{dt})}_{2} + {(\frac{dQ}{dt})}_{3}$
$∴ \frac{KA (T - 0)}{l} = \frac{KA (90 - T)}{l} + \frac{KA (90 - T)}{l}$
$\Rightarrow T = 180 - 2 T \Rightarrow 3 T = 180 \Rightarrow T = 60^{\circ} C$

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