How long would it take water to freeze in space?

Factual Questions
1

Assume you have a 1 litre water bottle at the distance of Mars. How long (approximately) would it take to freeze?

2

Is the bottle open? Or is it closed?

Do you know about the relationship between water and temperature and pressure?

I think there is a famous law in chemistry called Boyle’s law.

For a fixed amount of an ideal gas kept at a fixed temperature, P [pressure] and V [volume] are inversely proportional (while one increases, the other decreases)

http://en.wikipedia.org/wiki/Boyle%27s_law

Here are some others which may be relevant:

3

Actually it would boil first, pretty damn fast, then freeze.

Prior discussion

And answered by Cecil

4

Am I missing something?
Cecil discusses an open container of water which I know will vapourize.
I am interested in a closed water bottle. I can guess the bottle will bulge as the gases inside expand but I doubt it would break. There would probably not be enough expansion for the water to actually boil especially if the bottle were full.
The bottle receives solar energy which I assume would transmit through.
The problem for me comes with the definition of temperature. Though the light is shining, the bottle is not absorbing, does that mean the temperature is 3K? That’s pretty cold and the bottle would freeze in seconds.

5

Yes, if the container is strong enough (which would not be a big problem – the pressure being contained is about 1 atmosphere), the water would freeze, but not “in seconds” – heat loss would be by radiation from the surface of the container. Fill a vacuum flask with water at about 20 C, then put the vacuum flask into the coldest environment that you can create on earth – say around 1 K. The water inside the flask would not freeze in seconds, because the vacuum around the inner container is a good heat insulator.

6

Go play with this link which gives a rough calculation for the cooling time of a hot sphere. It is a pure cooling calculation and omits the incident light you’re interested in, but idealized it should give you an idea of the time required.

7

Oh, well, all ya had to do was say so…

8

You’re the one missing something. You never specified open or closed. Are Joanie and CookingWithGas supposed to read your mind?

9

[mod note]
Joanie, it’s fine to link to articles on other websites, but please don’t cut & paste big long blocks of text into your SDMB posts. Just give a link with a brief summary of what’s there. Thanks.
(no warning issued)
[/mod note]

10

Water is pretty good at absorbing light outside of visible wavelengths, so your closed bottle will be warmed by the sun. From the blackbody curve for the sun it looks like about half the wattage comes out at wavelengths water absorbs, so you’ll get about half the total power output absorbed by your bottle, or 683 watts/square meter at earth’s orbital radius.
I don’t know if that’s enough to keep your water liquid, however if you paint your bottle black, the water inside should remain liquid anywhere within the sun’s Habitable zone.

11

If you hide your bottle in the shadow of the moon or some such, this calculator for Radiative Cooling of a Hot Sphere begins to be useful.
A 5cm radius sphere of water (Mw = 18, d = 1g/cc) at 293°K, will cool radiatively to 271°K in 700 seconds, about 11.7 minutes.
Water’ll take longer than that to freeze because it has a good size heat of fusion, but I’d guess that 30 minutes would see you with a chunk of ice in your bottle.