MCQ
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 vessel  $A$  is $\alpha$, the coefficient of linear expansion of vessel $B$ is
  • A
    $\frac{{\alpha {\gamma _1}{\gamma _2}}}{{{\gamma _1} + {\gamma _2}}}$
  • B
    $\frac{{{\gamma _1} - {\gamma _2}}}{{2\alpha }}$
  • C
    $\frac{{{\gamma _1} - {\gamma _2} + \alpha }}{3}$
  • $\frac{{{\gamma _1} - {\gamma _2}}}{3} + \alpha $

Answer

Correct option: D.
$\frac{{{\gamma _1} - {\gamma _2}}}{3} + \alpha $
d
$\gamma_{\text {real}}=\gamma_{\text {app}}+\gamma_{\text {vessel}} ; \gamma_{\text {vessle}}=3 \alpha$

$ForvesselA$ $=\gamma_{\text {real}}=\gamma_{1}+3 \alpha$

$ForvesselB$ $=\gamma_{\text {real}}=\gamma_{2}+3 \alpha_{B}$

Hence, $\gamma_{1}+3 \alpha=\gamma_{2}+3 \alpha_{B}$

$\Rightarrow \alpha_{B}=\frac{\gamma_{1}-\gamma_{2}}{3}+\alpha$

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