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You have a bottle half with water and half with air. The environment is a vacuum that the bottle is in. The environment does have gravity.

So if we flipped the bottle so that the bottom of the bottle was facing up and the top of the bottle was facing down. If you open the bottle cap to try and remove the water, what would happen?

The aim is to know if the air in the bottle would expand (thus holding the bottles shape) or if the air would remain the same amount and just crunch the bottle; assuming that the water does come out.

My Assumption: I would think the water would not come out the bottle as the air is not able to expand. If you forced the water out the bottle (ie squeeze it out) then I would think that it would scrunch up as to not expand but to continue to occupy the same amount of space for the whole time. (further example at the bottom) When you do this same experiment where there is no vacuum (try this at home) when you tip the water out, there are bubbles that come up and replace the space that the water was occupying

FURTHER EXAMPLE: if we had a bottle that can hold up to 100 units of anything. We have 70 units of water in it and 30 units of air. If you tip the bottle and then open the cap (where outside the bottle has air) you would see that when the water leaks, the bottle holds only 60 units of water, so there will be bubbles that go up into the bottle to occupy the spare 10 units in the bottle. The question is to see what would be replacing that 10 units in the bottle where there is a vacuum outside the bottle.

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  • $\begingroup$ @count_to_10 the use to have gravity is that there is something attempting to get the water out of the bottle. If we did this w/o gravity we cannot be sure what is stopping the water to come out. As for when the water does come out, I'm not sure what would happen; my main focus is on the air in the bottle and if it would expand or crunch the bottle. The reason i think the water would not come out is because i would assume the air could not expand and as there is nothing to replace the space the water would leave if it was to leave the bottle, the water would not be able to leave. $\endgroup$ – Ramboo19 Aug 12 '16 at 13:01
  • $\begingroup$ As @count_to_10 says in his answer, you have a rocket. Go to youtube.com and search for "water bottle rocket" to see what will happen. The only difference in your case is that the environment is a vacuum instead of standard atmosphere. Your rocket will therefore be more efficient because your pressure difference between the inside and outside is higher. $\endgroup$ – James Aug 12 '16 at 18:30
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    $\begingroup$ Re, "air is not able to expand." You might want to re-check that fact. $\endgroup$ – Solomon Slow Aug 12 '16 at 19:28
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If we did this without gravity we cannot be sure what is stopping the water from coming out.

No, the pressure of the water and air would still push it out in vacuum.

You have gravity as a force in your post, so the denser water will be pulled downwards, nearer the cap than the air. It will then get pulled out, and immediately boil, due to the vacuum.

The water would emerge, followed by the air and, because it is at a higher pressure than vacuum, the air would take the handiest way out, through the cap. As the other answers state, there may be a slight very temporary increase in pressure at the neck of the bottle, also, depending on the pressure of the air, some air may cause bubbles in the water as the mixture emerges from the cap.

There is no outside pressure to squash the bottle inwards. This would all happen very fast, in effect the bottle would be like a rocket with all the contents emerging from the cap at relatively high velocities.

 

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If the bottle is filled "half with air" then presumably that air has some pressure. And that air will expand when the bottle is opened (it will try to "match the pressure" of the vacuum), pushing the water out. There will be a pressure difference of $P_{air}+\rho g h - P_{ext}$ - but when $P_{ext}=0$ because there is vacuum environment, there is just the pressure of the air in the bottle plus gravity pushing the water out. But even without gravity the water would come out.

By contrast if you have a bottle with a normal (atmospheric) environment, then there is equal pressure at the mouth of the bottle, and a slightly lower pressure at the surface of the water (lower by $\rho g h$ where $h$ is the height of water in the bottle). This means the air would expand only a little bit - and unless more air bubbles into the bottle, the water flow stops (or the bottle crushes).

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  • $\begingroup$ Agreed. The water would definately come out the bottle regardless if we have gravity or no, as you mentioned. The thing that i am still not sure about is what happens to the air. So when the water leaves the bottle, to the point where there is just enough left in the bottle to stop the air leaking into the vacuum, what happens to the air in the bottle. Does the air expand to take up the remaining space in the bottle, or does the bottle shrink so that the air only takes up the space is originally holds. $\endgroup$ – Ramboo19 Aug 12 '16 at 13:45
  • $\begingroup$ The air expands. There is no pressure to keep it in place. No pressure on the outside of the bottle. Think of the water as a piston, with 1 atm at one side and 0 atm on the other. The piston will expand, and the pressure of the air will drop. Depending on whether the process is adiabatic or isothermal, the amount of the pressure drop will change - but either way, all the water and all the air will escape. $\endgroup$ – Floris Aug 12 '16 at 13:50
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Let's visualize your experiment. You turn the bottle upside down, and open the cap in the surrounding vacuum. Consider an imaginary partition at the mouth of the bottle. There are no molecules below it(the vacuum) and plenty above it(water,air). Entropy of the system will increase, and the stuff inside will be thrown out, assuming the external vacuum is maintained. The water will evaporate as @count_to_10 said and along with the air molecules, will be pushed out. This will NOT be the case, if the surrounding vacuum is a very small region and is not maintained. The initial vapors(+air) that form, will prevent the rest from coming out, and a sort of equilibrium will be reached. Since the air inside is at a much higher pressure, it will push its way out as bubbles, until absolute equilibrium is reached with the surroundings. For a large vacuum, everything will be flushed out as a jet of mist.

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