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Q.

Two hollow spheres of different materials, one with double the radius and one-fourth wall thickness of the other, are filled with ice. If the times taken for complete melting of ice in the larger to the smaller one are in the ratio of 25:16, then their corresponding thermal conductivities are in the ratio

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a

4:5

b

5:4

c

8:25

d

25:8

answer is C.

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Detailed Solution

ΔQΔt=KAΔTΔx ⇒ ΔQ=KAΔTΔxΔtAssuming the thickness of the spheres to be small, we haveFor smaller sphere:(rate of heat flow) (time) - (volume of ice melted) (ρL) i.e., K14πr2Δθd⋅16=43πr3ρL ……..(i)For larger sphere:K24π(2r)2Δθd/4⋅25=4π3(2r)3ρL ……..(ii)Dividing Eq. (ii) by Eq. (i), K2/K1=8/25

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