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Q.

A rod CD of thermal resistance 5.0 K/W is joined at the middle of an Identical rod AB as shown in fig. The ends A, B and D are maintained at $100 ° C, 0 ° C$ and $25 ° C$ respectively. Find the heat current in CD.

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a

6.2 W

b

4.0 W

c

2.9 W

d

8.0 W

answer is C.

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Detailed Solution

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The resistance of the rod $α$ length $R_{A C} = R_{C B} = \frac{R_{C D}}{2} = \frac{5}{2} = 2.5 k w$
Question Image
$H_{1} = \frac{T_{C} - T_{D}}{R_{C D}} = \frac{T_{C} - 25}{5} \to (1)$
$H_{2} = \frac{T_{C} - T_{B}}{R_{C B}} = \frac{T_{C} - 0}{2.5} \to (2)$
$∴ H = \frac{T_{A} - T_{C}}{R_{A C}} = \frac{100 - T_{C}}{2.5}$
$H = H_{1} + H_{2}$
$\frac{100 - T_{C}}{2.5} = \frac{T_{C} - 25}{5} + \frac{T_{C} - 0}{2.5}$ on solving
$T_{C} = 45 ° C$
$∴ H_{1} = \frac{45 - 25}{5} = 4.0 w$

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