Consider a sufficiently rigid and sealed container completely filled with liquid (e.g. water), pressurized at 1 bar, at constant temperature. Inside the container there is a buoy partially filled with gas (e.g. air) and with lower part opened. Both buoy and container are cylindrical in shape.
It is assumed that absolute pressure at the top is $100000 \ \mathrm{Pa}$ and at the bottom it is $100000 + \rho g h \ \mathrm{Pa}$
What happens when the buoy is pushed downwards?
Let's first examine what would happen if the container's top was open to the atmosphere:
- As the hydrostatic pressure increases with depth, the gas would be compressed and the liquid level inside the buoy would raise.
- Gas pressure would equal the "head" pressure at the surface between gas and liquid
- Liquid level at the top would be lowered a little
Now let's go back to completely sealed case:
- Liquid level inside the buoy cannot raise because this would create a vacuum elsewhere in the container?
- If the liquid level inside the buoy would raise it would mean it's density in the whole container has decreased?
- If the liquid level stays same then the gas experiences increased pressure at the interface (due to hydrostatic pressure) so we end up with gas with higher pressure but same volume (which is against Boyle's Law or requires gas temperature increase)?
I'm really confused here and unable to fix that out. So, what really happens?