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

For the same ideal gas composition and temperature, $\rho =pM/(RT)$, hence $\Delta \rho /{\rho }_0=\Delta p/p_0=10^{-5}$. The bubble volume is $V=4\pi r^3/3=4.189\times 10^{-3}{\mathrm{m}}^3$. The gas's mass in excess of displaced ambient air isThis 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.