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The coefficient of apparent expansion of liquid when determined using two different vessels $A$ and $B$ are $\gamma _1$ and $\gamma _2$ respectively. If the coefficient of linear expansion of the vessel $A$ is $\alpha $, then coefficient of linear expansion of $B$
$\frac{{\alpha {\gamma _1}{\gamma _2}}}{{{\gamma _1} + {\gamma _2}}}$
$\frac{{{\gamma _1} - {\gamma _2}}}{{2\alpha }}$
$\frac{{{\gamma _1} - {\gamma _2} + \alpha }}{3}$
$\frac{{{\gamma _1} - {\gamma _2}}}{3} + \alpha $
Solution
$\gamma _{real} = \gamma _{apparent} + \gamma _{vessel}$
For $A: \gamma_{\text {real }}=\gamma_{1}+3 \alpha \quad\left(\because \alpha_{A}=\alpha\right)$
For $\mathrm{B}: \gamma_{\text {real }}=\gamma_{2}+3 \alpha_{\mathrm{B}}$
$\Rightarrow \gamma_{1}+3 \alpha=\gamma_{2}+3 \alpha_{\mathrm{B}}$
$\alpha_{\mathrm{B}}=\frac{\gamma_{1}-\gamma_{2}}{3}+\alpha$
