Question

A glass flask of volume $200c{m}^3$ is just filled with mercury at $20C$. The amount of mercury that will overflow when the temperature of the system is raised to $100C$ is: ${\gamma }_{glass}=1.2\times {10}^{-5}/C^{\circ },{\gamma }_{mercury}=1.8\times {10}^{-4}/C^{\circ }$

• A. $2.25c{m}^3$
• B. $2.15c{m}^3$
• C. $2.69c{m}^3$
• D. $2.52c{m}^3$

Answer 1

Answer: (C)

$\begin{array}{c}{\gamma }_{glass}=\frac{\Delta V}{V}\\ =1.2\times {10}^{-5}\\ \Delta V_{glass}={\beta }_{glass}{V}_0\Delta T\\ =\left(1.2\times {10}^{-5}\right)\left(200\right)\left(100-20\right)\\ =0.19c{m}^3\\ \Delta V_{mercury}={\beta }_{mercury}{V}_0\Delta T\\ =\left(1.8\times {10}^{-5}\right)\left(200\right)\left(100-20\right)\\ =2.9c{m}^3\\ \Delta V_{mercury}-\Delta V_{glass}=2.9-0.19=2.7\end{array}$

Hence option (B) is correct.