An air bubble of radius 4.5 cm initially at a depth of 12 m below the water surface rises to the sur
Source: JAMB · 2023
An air bubble of radius 4.5 cm initially at a depth of 12 m below the water surface rises to the surface. If the atmospheric pressure is equal to 10.34 m of water, the radius of the bubble just before it reaches the water surface is
Explanation
The temperature is constant, so Boyle’s law applies: P₁V₁ = P₂V₂. Pressures in metres of water: at 12 m depth, P₁ = 10.34 + 12 = 22.34; at the surface, P₂ = 10.34.
V₂/V₁ = 22.34/10.34 = 2.16. Volume depends on r³, so r₂ = 4.5 × (2.16)^(1/3) = 4.5 × 1.293 = 5.82 cm.
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