The co-efficient of real expansion $γ_{r}$ of a liquid is 5 times the co-efficient of linear expansion of the material of the container in which the liquid is present. The ratio of the co-efficient of apparent expansion and real expansion of the liquid is:

5 : 2

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1 : 5

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2 : 5

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5 : 1

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Solution

The correct option is D $2 : 5$
$γ_{r} = γ_{a} + γ_{g} = γ_{a} + 3 α_{g}$ .....(1)
$∴ 1 = \frac{γ_{a}}{γ_{r}} + \frac{3 α_{g}}{γ_{r}}$ .....(2)
$γ_{r} = 5 α_{g}$ ....(3) [given]
Substituting $γ_{r}$ from eqn (3) into eqn (2) we get
$\frac{γ_{a}}{γ_{r}} = 1 - \frac{3 α_{g}}{5 α_{g}} = 1 - \frac{3}{5} = \frac{2}{5}$

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