A couple of inches of water, expose it to space and repressurize, and the crew would have a ice skating rink.
No, because the water would get sucked out into vacuum along with the air. And because it's a myth that stuff instantly freezes in vacuum. Vacuum is actually a fine insulator (as anyone with a thermos bottle should know firsthand). There's virtually no material medium to conduct or convect heat away, so things lose heat a lot more slowly in vacuum than in air.
According to
the Department of Physics of the University of Illinois at Urbana-Champaign,
T'Girl (a.k.a.
Dracula's Castle) is
correct (notwithstanding a complication discussed below):
You asked about placing water in a vacuum. Liquid water will boil if its vapor pressure is greater than the ambient air pressure. In a vacuum, liquid water will start to boil regardless of what the temperature is. Turning water from a liquid to a vapor takes 540 calories per gram, and this heat is taken from the liquid water, cooling it off. In a vacuum, the water will continue to boil until so much heat has been removed that the remaining water will freeze. This is a very quick way to freeze water.
I'll call this situation
the thought experiment: gravity is on, and the water out of which the rink will freeze is in a tank with only the one planar surface on top exposed to vacuum. The water boils off that surface, until what's left in the tank freezes.
This behavior is confirmed by a NASA experiment, but there is an additional
complication, which is that when the water left in the tank freezes, it flash freezes all at once and suddenly expands. In the NASA experiment (described in a detailed treatment for the International Journal of Mechanical Engineering Education, at
http://www.manchesteruniversitypress.co.uk/uploads/docs/300119.pdf), this sudden freezing of the entire volume of water caused the resulting block of ice to hop out of its pan! So, some system would have to deal with the sudden expansion of the whole rink when it flash freezes. Perhaps having a large enough body of water, under gravity, and in a flexible container would mitigate the popping out effect; if not, I'd suspect the ice rink might fracture when it flash freezes.
As to what happens to that vapor that boils off, based on both observation and theory, it crystallizes. Some links:
So, since gravity is on in the thought experiment, it would make a fine powdery snow onto the skating rink in the vacuum.
All this said, I'm
not convinced that this would be the best way to create a skating rink on the
Enterprise. I'd suggest that allowing the heat to conduct away from the ice through a regulated radiator fin outside the ship (à la what Niven does in the
Ringworld novels to create the polar caps on the maps in the Great Ocean) is a better permanent solution.