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Question

In the figure shown below, two rods are maintained at the same temperature difference between the ends. As a result, heat is flowing through two rods made of the same material. If the diameters of the rods are in the ratio 1:4 and their lengths are in the ratio 3:2, then find the ratio of the rates of flow of heat through them.


A
1:24
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B
1:8
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C
1:4
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D
1:6
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Solution

The correct option is A 1:24
Given that,
(ΔT)1=(ΔT)2 and k1=k2
Ratio of diameters of rods 1 and 2, (d1d2)=14
Ratio of lengths of rods 1 and 2, (l1l2)=32
We know that,
Rate of flow of heat in rod 1 and 2,
q1=k1A1(T1T2)l1;
q2=k2A2(T1T2)l2
q1q2=(A1A2)×(l2l1)
q1q2=(d1d2)2×(l2l1)=116×23=124

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