A physical paradox
This one should interest scuba divers and physicists alike. I learnt it from a physics lecturer about five years ago.
You have a perfectly rigid jar, which is sealed and filled with a perfectly incompressible liquid. Within the liquid, at the bottom of the jar is a small bubble filled with an ideal gas. Since the gas is less dense than the liquid, it is buoyant and must rise.
However, since the liquid at the bottom of the jar must support the liquid above it, the pressure at the bottom is higher than the pressure at the top. So as the bubble rises, it moves from a region of high pressure to a region of low pressure.
But, the bubble is filled with an ideal gas, so as the pressure on it drops, it must expand.
But, the bubble is confined in an incompressible liquid within a rigid jar, so there is nowhere for it to expand into.
Therefore, the bubble can't expand.
Therefore, the bubble can't rise.
What's gone wrong?