Question

Coefficient of linear expansion of a vessel completely filled with $\text{Hg}$ is $1\times {10}^{-4}{/}^{\circ }\text{C}$. If there is no overflow of $\text{Hg}$ on heating the vessel, then coefficient of cubical expansion of $\text{Hg}$ is

• A. $3\times {10}^{-4}{/}^{\circ }\text{C}$
• B. $>3\times {10}^{-4}{/}^{\circ }\text{C}$
• C. $\le 3\times {10}^{-4}{/}^{\circ }\text{C}$
• D. Data is insufficient.

Answer 1

The correct option is C $\le 3\times {10}^{-4}{/}^{\circ }\text{C}$

Given that,
There is no overflow of $\text{Hg}$ on heating the vessel.
$\Rightarrow$ Expansion in volume of $\text{Hg}$ $\le$ Expansion in volume of container.
Since Volume expansion coefficient of vessel $\gamma =3\alpha$ [$\alpha$ given],
i.e, volume expansion coefficient of $Hg\le 3\alpha$ for no overflow.
From the data given in the question, $\alpha =1\times {10}^{-4}{/}^{\circ }\text{C}$
$\therefore {\gamma }_{Hg}\le 3\times (1\times {10}^{-4}){/}^{\circ }\text{C}$
Or
${\gamma }_{Hg}\le 3\times {10}^{-4}{/}^{\circ }\text{C}$
Hence, option (c) is the correct answer.