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Q.

Heat is flowing through two cylindrical rods of the same material. The diameters of the rods are in the ratio 1 : 2 and the lengths in the ratio 2 : 1. If the temperature difference between the ends is same, then ratio of the rate of flow of heat through them will be

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a

1 : 1

b

1 : 8

c

2 : 1

d

8 : 1

answer is B.

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Detailed Solution

dQdt=KAΔTL=Kπ(D/2)2ΔTL ∴ (dQ/dt)1(dQ/dt)2=KπD1/22ΔT×L2L1×KπD2/22ΔT=D12×L2D22×L1=14×12=18 or       (dQ/dt)1:(dQ/dt)2=1:8
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Heat is flowing through two cylindrical rods of the same material. The diameters of the rods are in the ratio 1 : 2 and the lengths in the ratio 2 : 1. If the temperature difference between the ends is same, then ratio of the rate of flow of heat through them will be