Rising bubble

A small spherical gas bubble of diameter d=4 μmd=4~\mu \mbox{m} forms at the bottom of a pond. When the bubble rises to the surface its diameter is n=1.1n=1.1 times bigger. What is the depth in meters of the pond?

Details and assumptions

The atmospheric pressure is pA=105 Pap_{A}=10^{5}~\mbox{Pa}, the acceleration of gravity is g=9.8 m/s2g=9.8~\text{m}/{\text{s}^{2}} and water's surface tension and density are σ=73×103 N/m\sigma=73\times 10^{-3}~\text{N}/\text{m} and ρ=1×103 kg/m3\rho=1\times 10^{3}~\text{kg}/\text{m}^3, respectively. The gas expansion is assumed to be isothermal.

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