Physics : The bubbles bigger

Assume there is no change of temperature at the bottom and surface of water. The gas inside teh bubble follows Boyle's Law. That is, PV = constant, where P is the pressure of gas inside the bubble nad V is the volume of bubble.

When the bubble is the the bottom of water, the pressure outside is greater than that at surface. The reduction of pressure thus leads to an expansion in volume, as illustrated by the equations below:

Pressure at bottom = P' + pgh
Volume at bottom = V, say
Pressure on surface = P'
Volume on surface = V'

Hence, by Boyle's Law,
(P' + pgh ).V = P'V'
i.e. V' = [(P' + pgh )/P'].V
Clearly, the fraction [(P' + pgh )/P' = (1 + pgh/P') is greater than one. That is, V' > V, the bubble thus expands in volume.