The coefficients of apparent expansion of a liquid when determined using two different vessels $A$ and $B$…
The coefficients of apparent expansion of a liquid when determined using two different vessels $A$ and $B$ are $y_1$ and $y_2$, respectively. If the coefficient of linear expansion of the vessel $A$ is $\alpha$, the coefficient of linear expansion of the vessel $B$ is
$\frac{a \gamma_1 \gamma_2}{\gamma_1+\gamma_2}$
$\frac{\gamma_1-\gamma_2}{2 \alpha}$
$\frac{\gamma_1-\gamma_2+\alpha}{3}$
$\frac{\gamma_1-\gamma_2}{3}+\alpha$
Solution
Coefficient of apparent expansion of liquid for vessel $(A)=\gamma_1$
Coefficient of apparent expansion of liquid for vessel $(B)=\gamma_2$
For vessel $A$
$
\begin{aligned}
& \gamma_{\text {real }}=\gamma_{\text {app }}+\gamma_{\text {vessel }} \\
& \text { For vessel } \quad \gamma_{\text {vessel }}=3 \alpha_A=3 \alpha \\
& \because \quad \gamma_{\text {real }}=\gamma_1+3 \alpha \\
& \text { For vessel } B, \quad \gamma_{\text {real }}=\gamma_2+3 \alpha_B \\
& \therefore \quad \gamma_1+3 \alpha=\gamma_2+3 \alpha_B \\
& \alpha_B=\frac{\gamma_1-\gamma_2+3 \alpha}{3}=\frac{\gamma_1-\gamma_2}{3}+\alpha \\
&
\end{aligned}
$