The coefficient of linear expansion of a vess | vedclass

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Question

(C) Let $\alpha$ be the coefficient of linear expansion of the vessel. Given $\alpha = 1 	imes 10^{-5} /^{\circ} C$.The coefficient of cubical expans

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$\leq 3 	imes 10^{-5} /^{\circ} C$

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(C) Let $\alpha$ be the coefficient of linear expansion of the vessel. Given $\alpha = 1 	imes 10^{-5} /^{\circ} C$.The coefficient of cubical expansion of the vessel is $\gamma_{	ext{vessel}} = 3\alpha = 3 	imes 1 	imes 10^{-5} /^{\circ} C = 3 	imes 10^{-5} /^{\circ} C$.Let $\gamma_{	ext{Hg}}$ be the coefficient of cubical expansion of $Hg$.For no overflow to occur when the vessel is heated,the expansion of the $Hg$ must be less than or equal to the expansion of the vessel's volume.Therefore,$\gamma_{	ext{Hg}} \leq \gamma_{	ext{vessel}}$.Substituting the value,we get $\gamma_{	ext{Hg}} \leq 3 	imes 10^{-5} /^{\circ} C$.

The coefficient of linear expansion of a vessel completely filled with $Hg$ is $1 \times 10^{-5} /^{\circ} C$. If there is no overflow of $Hg$ on heating the vessel,then the coefficient of cubical expansion of $Hg$ is:

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