Q. 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 $\alpha,$ the coefficient of linear 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) $\frac{\gamma_{1} - \gamma_{2}}{3} + \alpha$
Explanation
(d) $\gamma_{real} = \gamma_{app} + \gamma_{vessel};\gamma_{vessel} = 3\alpha$
For vessel $'A^{'} \Rightarrow \gamma_{real} = \gamma_{1} + 3\alpha$
For vessel $'B^{'} \Rightarrow \gamma_{real} = \gamma_{2} + 3\alpha_{B}$
$Hence,\ \gamma_{1} + 3\alpha = \gamma_{2} + 3\alpha_{B} \Rightarrow \alpha_{B} = \frac{\gamma_{1} - \gamma_{2}}{3} + \alpha$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.