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The coefficient of apparent expansion of a 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
$\gamma_{\text {real }}=\gamma_{\text {app }}+\gamma_{\text {vessel }}$
for $\mathrm{A} \rightarrow \quad \gamma_{\mathrm{real}}=\gamma_{1}+3 \alpha$
for $B \rightarrow \gamma_{\text {real }}=\gamma_{2}+3 \alpha_{\mathrm{B}}$
$\alpha_{B}=\frac{\gamma_{1}-\gamma_{2}}{3}+\alpha$
