The ratio of the coefficient of volume expansion of a glass container to that of a viscous liquid kept…
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 ?
$2: 5$
$1: 4$
$1: 64$
$1: 8$
Solution
When there is no change in liquid level in vessel then $\gamma_{\text {real }}^{\prime}=\gamma^{\prime}$ vessel Change in volume in liquid relative to vessel
$
\Delta \mathrm{V}_{\mathrm{app}}=\mathrm{V} \gamma_{\text {app }}^{\prime} \Delta \theta=\mathrm{V}\left(\gamma_{\text {real }}^{\prime}-\gamma_{\text {vessel }}^{\prime}\right)
$