Question

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 lenses expansion of vessel A is $\alpha$. The coefficient of lenses expansion of the vessel B is

• A. $\frac{\alpha\gamma_1\gamma_2}{\gamma_1+\gamma_2}$
• B. $\frac{\gamma_1 - \gamma_2}{2\alpha}$
• C. $\frac{\gamma_1-\gamma_2+\alpha}{3}$
• D. $\frac{\gamma_1-\gamma_2}{3}+\alpha$

Answer 1

Answer: (D)

$\frac{\gamma_1-\gamma_2}{3}+\alpha$

Answer 2

$\gamma_{real}=\gamma_{app}+\gamma_{vessel};\gamma_{vessle}=3\alpha$ $For\, vessel A=\gamma_{real}=\gamma_1+3\alpha$ $For\, vessel B=\gamma_{real}=\gamma_2+3\alpha_B$ $Hence, \gamma_1+3\alpha=\gamma_2+3\alpha_B$ $\Rightarrow \alpha_B=\frac{\gamma_1 - \gamma_2}{3}+\alpha_1$