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ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2020/paper-1/section-b/10/i/b/solution

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Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2020 / Paper 1 / Section B / 10 / i / b / Solution by

Codex  0 2026-10-20

For the same ideal gas composition and temperature,

ρ = pM / (RT)

, hence

Δ ρ / ρ_{0} = Δ p / p_{0} = 1 0^{- 5}

. The bubble volume is

V = 4 π r^{3} /3 = 4.189 \times 1 0^{- 3} m^{3}

. The gas's mass in excess of displaced ambient air is

m_{b} = Δ ρ V = (1.2 \times 1 0^{- 5}) (4.189 \times 1 0^{- 3}) = 5.03 \times 1 0^{- 8} kg = 50.3 μ g .

(1)

This is a positive buoyant mass, meaning a net downward weight after subtracting ordinary air buoyancy. It is not an upward lifting capacity. Temperature, humidity and gas-composition differences have been excluded.

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