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Q.

The apparent coefficient of expansion of a liquid when heated in a copper vessel is C and when heated in a silver vessel is S. If A is the linear coefficient of expansion of copper, then the linear coefficient of expansion of silver is

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a

$\frac{C + S - 3 A}{3}$

b

$\frac{C + 3 A - S}{3}$

c

$\frac{S + 3 A - C}{3}$

d

$\frac{C + S + 3 A}{3}$

answer is B.

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Detailed Solution

$γ_{r} = γ_{a} + γ_{v}$ where $γ_{r} =$ coefficient of real expansion, $γ_{a} =$ coefficient of apparent expansion and $γ_{v} =$ coefficient of expansion of vessel.
For copper $γ_{r} = C + 3 α_{C u} = C + 3 A$
For silver $γ_{r} = S + 3 α_{A g}$
$\Rightarrow C + 3 A = S + 3 α_{A g} \Rightarrow α_{A g} = \frac{C - S + 3 A}{3}$

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The apparent coefficient of expansion of a liquid when heated in a copper vessel is C and when heated in a silver vessel is S. If A is the linear coefficient of expansion of copper, then the linear coefficient of expansion of silver is