Question

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

• A. 21.2 cc
• B. 15.2 cc
• C. 1.52 cc
• D. 2.12 cc

Answer 1

Answer: (B)

Due to volume expansion of both liquid and vessel, the change in volume of liquid relative to container is given by
$\Delta V=V_{0}\left[\gamma_{L}-\gamma_{g}\right] \Delta \theta$
Given $V_{0}=1000\, cc , \alpha_{g}=0.1 \times 10^{-4} /{ }^{\circ} C$
$\therefore \gamma_{g}=3 \alpha_{g}=3 \times 0.1 \times 10^{-4} /{ }^{\circ} C$
$=0.3 \times 10^{-4} /{ }^{\circ} C$
$\therefore \Delta V =1000\left[1.82 \times 10^{-4}-0.3 \times 10^{-4}\right] \times 100$ $=15.2\, cc$