Question

A glass flask of volume one litre at $0{}^{\circ }\text{C}$ is filled, level full of mercury at this temperature. The flask and mercury are now heated to $100{}^{\circ }\text{C}$. Find the amount of mercury that will spill out, if the coefficient of volume expansion of mercury is $1.82\times {10}^{-4}{/}^{\circ }\text{C}$ and the coefficient of linear expansion of glass is $0.1\times {10}^{-4}{/}^{\circ }\text{C}$ respectively.

• A. $21.2\text{cc}$
• B. $15.2\text{cc}$
• C. $1.52\text{cc}$
• D. $2.12\text{cc}$

Answer 1

The correct option is B $15.2\text{cc}$

Given,
Volume of glass flask $V_0=1000\text{cc}$
Volume expansion coefficient of mercury $\left({\gamma }_L\right)=1.82\times {10}^{-4}{/}^{\circ }\text{C}$
Linear expansion coefficient of glass flask $\left(\alpha \right)=0.1\times {10}^{-4}{/}^{\circ }\text{C}$
$\therefore$Volume expansion coefficient of glass flask $\left({\gamma }_g\right)=3\alpha =0.3\times {10}^{-4}{/}^{\circ }\text{C}$
Due to volume expansion of both liquid and vessel, the change in volume of liquid relative to the container is given by
$\Delta V=V_0[{\gamma }_L-{\gamma }_g]\Delta T$
$\therefore \Delta V=1000\times [1.82\times {10}^{-4}-0.3\times {10}^{-4}]\times 100=15.2\text{cc}$
Hence, option (b) is the correct answer.