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Question
A glass flask has a volume 1 × 10−4 m3. It is filled with a liquid at 30°C. If the temperature of the system is raised to 100°C, how much of the liquid will overflow? (Coefficient of volume expansion of glass is 1.2 × 10−5 (°C)−1 while that of the liquid is 75 × 10−5 (°C)−1).
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Solution
Given: V1 = 1 × 10−4 m3 = 10−4 m3, T1 = 30°C, T2 = 100°C, γglass = 1.2 × 10−5 , `γ_"liquid"` = 75 × 10−5
To find: Volume of liquid that overflows
Formula: `gamma = (V_2 - V_1)/(V_1(T_2 - T_1))`
Calculation: From formula,
Increase in volume = V2 − V1 = γ = V1(T2 − T1)
Increase in volume of glass
= γglass = V1(T2 − T1)
= 1.2 × 10−5 × 10−4 × (100 − 30)
= 1.2 × 70 × 10−9
= 8.4 × 10−8 m3
∴ Increase in volume of glass = 8.4 × 10−8 m3
Increase in volume of liquid -
= `γ_"liquid"`= V1(T2 − T1)
= 75 × 10−5 × 10-4 × (100 − 30)
= 75 × 70 × 10−9
= 5250 × 10−9 m3
∴ Increase in volume of liquid = 5250 × 10−9 m3
∴ Volume of liquid which overflows
= (5250 − 84) × 10−9 m3
= 5166 × 10−9 m3
= 0.5166 × 10−8 m3
∴ Volume of liquid that overflows is 0.5166 × 10−8 m3
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