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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

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

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

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

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

answer is C.

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Detailed Solution

$\begin{array}{l} γ_{r} = γ_{a} + γ_{g} \\ γ_{S} + 3 α_{s} = γ_{C} + 3 α_{c} \\ \Rightarrow S + 3 α_{s} = C + 3 A \\ \Rightarrow α_{s} = \frac{C + 3 A - S}{3} \end{array}$

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