A glass bottle contains $5.02 {c m}^{3}$ of mercury which just fills the bottle at $18^{o} C$ . If the temperature of the bottle and mercury is raised to $64^{o} C$ . Determine the volume of mercury which will overflow out of the bottle. The coefficient of cubical expansion of mercury is $180 \times 10^{- 4} /^{o} C$ and the coefficient of linear expansion for glass is $8.4 \times 10^{- 4} /^{o} C$ .

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Solution

Overflow volume of a liquid in a container is given by
$△ V = V_{o} (γ_{L} - γ_{C}) △ T$
here, $V_{o} =$ Initial volume of liquid, $γ_{L} =$ cubical constant of liquid, $γ_{C} =$ cubical constant of container, $△ T =$ change in temperature
According to the question
$△ T = 64 ℃ - 18 ℃ = 56 ℃ γ_{L} = 180 \times 10^{- 4} / ℃ γ_{C} = 8.4 \times 10^{- 4} / ℃ V_{o} = 5.02 {c m}^{3} S o, △ V = 5.02 ((180 - 8.4) \times 10^{- 4}) \times 56 = 5.02 (0.96096) △ V = 4.82 {c m}^{3}$

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