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A glass flask of volume one litre at $0\,^oC$ is filled, level full of mercury at this temperature. The flask and mercury are now heated to $100\,^oC$. How much mercury will spill out, if coefficient of volume expansion of mercury is $1.82 \times 10^{-4}/^oC$ and linear expansion of glass is $0.1 \times 10^{-4}/^oC$ ? ............ $\mathrm{cc}$
$21.2$
$15.2$
$1.52$
$2.12$
Solution
Due to volume expansion of both liquid and vessel, the change in volume of liquid relative to container is given by $\Delta \mathrm{V}=\mathrm{V}_{0}\left[\gamma_{\mathrm{L}}-\gamma_{\mathrm{F}}\right] \Delta \theta$
Given ${V_0} = 100\,\,cc,\,\,{\alpha _g} = 0.1 \times {10^{ – 4}}{\,^o}C$
$\therefore \,{\gamma _g} = 3{\alpha _g} = 3 \times 0.1 \times {10^{ – 4}}\,{\,^o}C = 0.3 \times {10^{ – 4}}\,{\,^o}C$
$\therefore \,\,\Delta V = 1000\left[ {1.82 \times {{10}^{ – 4}} – 0.3 \times {{10}^{ – 4}}} \right] \times 100$
$ = 15.2\,\,cc.$
