A glass flask of volume one liter at 0°C is filled, level full of mercury at this temperature. The flask and mercury are now heated to 100°C. How much mercury will spill out, if coefficient of volume expansion of mercury is $1.82 \times 10^{-4} \, / ^\circ C$ and linear expansion of glass is $0.1 \times 10^{-4} \, / ^\circ C$ respectively
Text Solution
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Due to volume expansion of both liquid and vessel, the change in volume of liquid relative to
container is given by Δ Δ V = $v_0[\gamma_L - \gamma_g]\Delta \theta$
Given V 0 = 1000 cc, α α g = 0.1×10 –4 /°C
$\therefore \gamma_{g} = 3 \alpha_{g} = 3 \times 0.1 \times 10^{-4} / ^{\circ} \mathrm{C} = 0.3 \times 10^{-4} / ^{\circ} \mathrm{C}$
∴ ∴ Δ Δ V = 1000 [1.82 × 10 –4 – 0.3 × 10 –4 ] × 100 =15.2 cc
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