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  4. The ratio of the coefficient of volume expansion of a glass container to that of a viscous liquid kept inside the container is 1: 4. What fraction of the inner volume of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all temperatures ?

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Q. The ratio of the coefficient of volume expansion of a glass container to that of a viscous liquid kept inside the container is $1 : 4$. What fraction of the inner volume of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all temperatures ?

JEE MainJEE Main 2013Thermal Properties of Matter

Solution:

When there is no change in liquid level in vessel then $\gamma'_{real}=\gamma'_{vessel}$
Change in volume in liquid relative to vessel
$\Delta V_{app}=V\gamma_{app}\,\Delta\theta=V\left(\gamma '_{real}-\gamma'_{_{vessel}}\right)$