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Imagine that we had a space station with a relatively large hangar, and we allowed a ball of water to accumulate that had a 10 meter diameter and a water temperature of 20C. While the hangar is pressurized, someone decides to use a (closed loop) rebreather tank to sit in the middle of the sphere and breathe, so they're not dying and they're not exhaling any air into the water (just to keep things simpler).

Someone cycles the airlock and the sphere is now floating in the middle of the hangar in a hard vacuum.

What would happen to the water, and what would happen to the person inside? Would the sphere of water maintain enough pressure on the person that they would be fine, would the water boil off so quickly that it wouldn't be useful for long, or would the water freeze? I see several options, and this is a question I've wondered about for awhile, but I haven't been able to solve it.

coder543
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It boils, then the vapor freezes.

It doesn't directly freeze because water is great at holding heat, and the only way to dissipate heat in vacuum is radiation, no convection. However there is no constraint on pressure, and as we know low pressure makes water boil. The process of boiling acts to carry away heat and separates the water into a fine mist which then freezes into flakes.

It's sort of a matter of surface area versus volume, heat loss happens through the surface area but the whole volume is affected by the pressure so it's effects are stronger.

Aganju
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ArtisticPhoenix
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It is a perennial but pernicious myth that liquid water would flash into vapor in space if the pressure were suddenly released. Even though the free energy difference (between water and ultra-tenuous vapor) would favor vaporization, evaporation is very endothermic. The water must acquire the heat of vaporization (over 500 cal/g) from the environment, and/or it must cool off. Heat delivery in space is especially slow because the only sources are sunlight and IR radiation from the Earth below, or in your scenario, the space station.

As for the unhappy fate of Astronaut Aqualung in the middle of your ball of water, the depressurization of the hangar would almost immediately result in depressurization of his environment as well. Since the rebreather is not designed to maintain pressure, he would die of anoxia long before he was encased in ice, which would ultimately sublime, leaving his cadaver to freeze dry. (The very thought makes my blood boil, but only figuratively.)

Bert Barrois
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What Would Happen To The Water?
The water in the sphere will experience a vapor pressure that corresponds to its temperature, according to the Antoine equation, https://en.wikipedia.org/wiki/Antoine_equation. As long as there is atmospheric pressure on the water, the sphere will maintain its "static" condition. However, as soon as the sphere experiences vacuum, there will no longer be any ambient pressure on the sphere, and the vapor pressure of the water inside the sphere will immediately cause boiling. The pressure inside the sphere, due to the vapor pressure of the water in the sphere, leads to a net outward force on each small piece of the sphere, and the sphere immediately becomes filled with small steam bubbles and starts expanding outward as a result.

Temperature Inside The Sphere
The heat necessary to cause boiling of the water in the sphere comes from the water itself, so the temperature of the water in the sphere immediately starts dropping upon exposure to vacuum conditions. The rate of boiling is proportional to the difference in temperature between the water in the sphere and the "equilibrium" temperature dictated by the Antoine equation at vacuum conditions (slightly lower than 0 deg. C). This means that the boiling rate will logarithmically decline as boiling continues and the temperature keeps dropping. This process will continue, and assuming that full vacuum conditions are maintained, a portion of the water that remains, in the form of droplets, will freeze. The resulting ice will then slowly sublime, and eventually will completely evaporate, with the sublimation rate depending on radiant heat transfer from the environment.

Pressure On The Person
The person in the sphere initially experiences the ambient pressure produced by the air in the air lock. Assuming that the person is in a micro-gravity environment, there will be no significant contribution to the pressure experienced by that person due to the amount of water surrounding him or her, as static pressure of water is given by the formula $P=\rho g h$, where $g$ approaches zero. This leads to an unfortunate effect for the person on the re-breather. That person must necessarily breathe oxygen at the ambient pressure, meaning that as vacuum conditions occur, the person will be getting no oxygen. In addition, that person has a core temperature of 98.6 deg F, which is substantially above the "equilibrium" temperature dictated by the Antoine equation, meaning that the person's blood will very quickly generate steam bubbles, and any dissolved gasses will come out of solution. Obviously, this condition is fatal.

David White
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My best guess:

The water will start to boil uniformly. In the interior the boiling is retarded because the expansion is hindered. After slightly more than half of the volume of water has transformed into bubbles, the remaining liquid freezes. This happens first near the surface. As the liquid inside continues to expand water will violently escape through holes and cracks, turning into ice mist. A Swiss cheese like structure of ice, possible flying apart into many pieces, remains that slowly sublimates.

my2cts
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