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Thermal Resistance

Two rods of s...

Question

Two rods of same length, area of cross-section and material transfer a given amount of heat in 12s, when they are joined end to end (i.e. in series).But when they are joined in parallel, they will transfer same heat under same conditions in

A

24 s

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B

3 s

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C

48 s

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D

1.5 s

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Solution

The correct option is B
3 s

$Let R = \frac{1}{k A} Case I (series) H_{1} = \frac{T_{1} - T_{2}}{R_{s}} \frac{T_{1} - T_{2}}{2 R} Case II (parallel) H_{2} = \frac{T_{1} - T_{2}}{R_{p}} \frac{T_{1} - T_{2}}{\frac{R}{2}} \Rightarrow 2 H_{1} = \frac{H_{2}}{2} \Rightarrow H_{2} = 4 H_{1} We have, H_{1} t_{1} = H_{2} t_{2} H_{1} (12) = 4 H_{1} t_{2} t_{2} = 3 s .$

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