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Q.

An air bubble of radius 1mm is at depth of 8cm below the free surface of a liquid column. If the surface tension and density of the liquid is 0.1N/m and $2000 k g / m^{3}$ respectively, by what amount is the pressure inside the bubble greater than the atmospheric pressure $(g = 10 m s^{- 2})$

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answer is 1800.

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Detailed Solution

$P_{i n} = P_{o u t} + \frac{2 T}{R} P_{i n} = P_{0} + ρ g h + \frac{2 T}{R} P_{i n} - P_{0} = ρ g h + \frac{2 T}{R} \Rightarrow 2 \times 10^{3} \times 10 \times 0.08 + \frac{2 \times 0.1}{10^{- 3}} = 1800 N / m^{2}$

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An air bubble of radius 1mm is at depth of 8cm below the free surface of a liquid column. If the surface tension and density of the liquid is 0.1N/m and 2000kg/m3 respectively, by what amount is the pressure inside the bubble greater than the atmospheric pressure (g=10ms−2)