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Q.

When a liquid, filled in two vessels A and B of equal volumes, is heated, the coefficient of apparent expansions of the liquids are found to be $γ_{1}$ and $γ_{2}$ respectively. If $α_{1}$ be the coefficient of linear expansion of A, then the coefficient of linear expansion of B will be:

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a

$\frac{γ_{2} - γ_{1}}{3} + α_{1}$

b

$\frac{γ_{2} - γ_{1}}{3} - α_{1}$

c

$\frac{γ_{1} - γ_{2}}{3} + α_{1}$

d

$\frac{γ_{1} - γ_{2}}{3} - α_{1}$

answer is C.

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Detailed Solution

$ϑ_{1}^{1} = ϑ_{1} - ϑ_{v e n}$
$ϑ_{2}^{1} = ϑ_{2} - ϑ_{v e n}$
$ϑ_{2}^{1} - ϑ_{1}^{1} = ϑ_{2} - ϑ_{1}$
Linear expansion $α_{1}^{1} = \frac{ϑ_{1}^{1}}{3}$
$α_{2} = \frac{ϑ_{2}^{1}}{3} - α_{1}^{1} + α_{1}$
$α_{2} = \frac{ϑ_{2}^{1} - ϑ_{1}^{1}}{3} + α_{1} \Rightarrow \frac{ϑ_{2} - ϑ_{1}}{3} + α_{1}$

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