Question

On heating a liquid of coefficient of cubical expansion $\alpha$ in a container having coefficient of linear expansion $\alpha /3$,the level of liquid in the container will

• A. raise
• B. fall
• C. remain almost stationary
• D. it is difficult to say

Answer 1

The correct option is C remain almost stationary

In case of expansion of volume V of liquid
$V_L=V(1+{\gamma }_L\Delta \theta )=V(1+\alpha \Delta \theta )$
Where $\gamma$ is the coefficient of cubical expansion of liquid while V is the volume of the container

$V_B=V(1+{\gamma }_B\Delta \theta )=V(1+(\frac{\gamma }{3}\left)\Delta \theta \right)=V(1+\alpha \Delta \theta )$
because of volume expansion
${\gamma }_S=3\times \left(linearcoefficientofexpansion\right)$

$3\times \frac{\alpha }{3}=\alpha$

So change in volume of the liquid relative of the container is $V_L-V_S=0$
So the level of liquid in the container will remain almost stationary.