Question

A glass flask of volume 200cm${}^3$ is completely filled with mercury at ${20}^{0}C$. The amount of mercury that is spilled over when the flask is heated to ${80}^{0}C$ (Coefficient of volume expansion of glass $27\times {10}^{-6/0}C,\gamma$ of mercury $0.18\times {10}^{-3/0}C$)

• A. 2.16cm${}^3$
• B. 0.032cm${}^3$
• C. 1.84cm${}^3$
• D. 2.40cm${}^3$

Answer 1

The correct option is C 1.84cm${}^3$

The increase in volume of the glass flask is

$△V_{glass}={\beta }_{glass}{V}_o△T=(27\times {10}^{-6}{K}^{-1})\left(200{cm}^3\right)(80℃-20℃)=0.324{cm}^3$

The increase in volume of mercury is

$△V_{mercury}={\beta }_{mercury}{V}_o△T=(18\times {10}^{-5}{K}^{-1})\left(200{cm}^3\right)(80℃-20℃)=2.16{cm}^3$

The volume of mercury that overflows is

$△V_{mercury}-△V_{glass}=2.16{cm}^3-0.324{cm}^3=1.84{cm}^3$