An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension 0.095 J m⁻² and density 10³ kg m⁻³. The difference between the pressure inside the bubble and the atmospheric pressure is N m⁻². (Take g=10 m s⁻²)

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2190. Given: R=1.0 mm=10⁻³ m, h=20 cm=0.2 m, T=0.095 J m⁻²=0.095 N m⁻¹, ρ=10³ kg m⁻³, g=10 m s⁻². The bubble sits under a liquid column and has a single liquid-gas surface, so pᵢₙ-p₀=ρ gh+(2T)/R. Column: ρ gh=10³×10×0.2=2000 N m⁻². Curvature: (2T)/R=(2×0.095)/(10⁻³)=190 N m⁻² — a bubble in a liquid takes (2T)/R, not the soap-bubble (4T)/R. pᵢₙ-p₀=2000+190=2190 N m⁻².

An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension 0.095 J m⁻² and density 10³ kg m⁻³. The difference between the pressure inside the bubble and the atmospheric pressure is ______ N m⁻². (Take g=10 m s⁻²)

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