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Q.

The ratio of the coefficient of volume expansion of a glass container to that of a viscous liquid kept inside the container is 1:4. What fraction of the inner volume of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all temperatures?

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a

1:4

b

2:5

c

1:64

d

1:8

answer is B.

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Detailed Solution

${ΔV}_{c} = {ΔV}_{l} \Rightarrow V_{c} γ_{c} ΔT = V_{l} {ΔTγ}_{l} \Rightarrow \frac{V_{l}}{V_{c}} = \frac{γ_{c}}{γ_{l}} = \frac{1}{4}$

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The ratio of the coefficient of volume expansion of a glass container to that of a viscous liquid kept inside the container is 1:4. What fraction of the inner volume of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all temperatures?