Question
A glass flask of volume $250 \mathrm{~cm}^3$ is just filled with mercury at $20^{\circ} \mathrm{C}$. How much mercury overflows when the temperature of the system is raised to $100^{\circ} \mathrm{C}$ ? The coefficient of volume expansion of glass is $12 \times 10^{-6}\left({ }^{\circ} \mathrm{C}\right)^{-1}$ and that of mercury is $18 \times 10^{-5}\left({ }^{\circ} \mathrm{C}\right)^{-1}$.

Answer

The increase in the volume of the flask is, $(\Delta\text{V})_\text{f}=\text{V}\gamma\ \Delta\text{t}=250\times12\times10^{-6}\times80$ $=0.24\text{cm}^3$ The increase in the volume of mercury is, $(\Delta\text{V})_\text{m}=250\times18\times10^{-5}\times80$ $3.6\text{cm}^{3}$ Therefore, the volume of mercury overflowing is, $3.6 - 0.24 = 3.36cm^3$

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