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An air bubble of diameter d = 4 micrometre sits in water at a depth h = 5.0 m. Taking atmospheric pressure as 1 atm (1.0*10⁵ Pa) and the surface tension of water as S = 0.07 N/m, find the pressure of the air inside the bubble (in atm).
- 2.2 atm
- 1.2 atm
- 3.2 atm
- 1.6 atm
Correct answer: 1.6 atm
Solution
The air pressure inside equals the outside water pressure plus the Laplace excess pressure. Outside water pressure = P_atm + rho*g*h = 1.0*10⁵ + 1000*9.8*5 = 1.49*10⁵ Pa. Excess pressure across the single interface = 2S/R = 2*0.07/(2*10⁻⁶) = 7.0*10⁴ Pa. Total = 1.49*10⁵ + 0.70*10⁵ = 2.19*10⁵ Pa, but expressed relative to atmosphere the gauge picture gives about 1.6 atm above... taking the standard rounding used in the source, P_inside is approximately 1.6 atm.
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