Would it be possible to freeze water by Charles' law?

[Spreadsheet]

Say I have a container that is surrounded by a vacuum. Now, I have a handle, and when I pull this handle, the volume inside the container increases but the mass stays the same. The container is full of air, and there is an ice cube tray inside. I lift the handle and lock it in place. Would it be possible to have such a container that would allow the ice cubes to eventually freeze and then you could take them out?

 

[JaredJames]

Say I have a container that is surrounded by a vacuum. Now, I have a handle, and when I pull this handle, the volume inside the container increases but the mass stays the same. The container is full of air, and there is an ice cube tray inside. I lift the handle and lock it in place. Would it be possible to have such a container that would allow the ice cubes to eventually freeze and then you could take them out?

If the volume could expand infinitely, you'd still not have a perfect vacuum - there'd still be some particles in there bumping around.

Now, for the purpose of this question, let's assume we could attain a perfect vacuum - this means that no matter how much more we expand the box the pressure won't get lower than a perfect vacuum and as such the temperature won't change due to it - and no matter how much you expand the box, you can never get a temperature below absolute zero - this is where you get space in the "shade" from the sun being 2.7K (-271^oC).

This leaves only radiation loses from the liquid inside.

So the question now becomes - "does water freeze in a vacuum?".

Assuming that net in through radiation < net out from radiation, then yes, eventually the water would freeze as it equalises with the surrounding temperature (specifically when it drops below the freezing point).

At least that's my take on it.

 

[Fish4Fun]

I think the biggest problem you will run into is the water boiling, not freezing. As you reduce the pressure, the boiling point and the freezing point both drop.

I don't mean to hi-jack your thread, but these two questions might extend your thought experiment:

What happens if you release a gallon of 25C water into deep space? Does the very low pressure cause the water to first "boil", and then at some period of time later after the water has lost sufficient heat, cause the water vapor to "freeze"?

If you were to collect frozen water vapor in deep space and "bring the frozen water vapor into a 1ATM, 25C cabin", what would the temperature of the ice be in the cabin?

Fish

 

[JaredJames]

As you reduce the pressure, the boiling point and the freezing point both drop.

That's something I was curious about. I wasn't sure if the freezing point dropped or not.

 

[S_Happens]

I think the biggest problem you will run into is the water boiling, not freezing. As you reduce the pressure, the boiling point and the freezing point both drop.

Although your first statement is true, the phase diagram for water doesn't agree with you about the freezing point dropping with pressure. It's very small, but it does in fact increase with a decrease in pressure, which is what you'd expect considering that solid water is less dense than liquid water.

 

[Fish4Fun]

S_Happens,

Perhaps I am looking @ the wrong phase diagram for water?

http://bhs.smuhsd.org/science-dept/marcan/apchemistry/cool_phase_changes_diagram.html

As you state, down to 4.58 torr, the decreasing pressure slightly increases the freezing point; however, below 4.58 torr (0.089 PSI), the freezing point drops steadily. The OP states a vacuum, the ranges being:

Low Vacuum 760 to 25 Torr
Medium Vacuum 25 to .001 Torr
High Vacuum .001 to 10^-9 Torr
Ultra-High Vacuum 10^-9 to 10^-12 Torr

For a portion of the medium vacuum range, the freezing point of water decreases as the pressure drops. For ALL of the low vacuum range the freezing point increases (as you stated). I was honestly extending the thought exercise to Outer Space, where the vacuum ranges from 10^-6 Torr and lower (High Vacuum), hence my assertion; though my assumption of Outer Space has NOTHING to do with the OP.

Fish

 

[Fish4Fun]

S_Happens,

Perhaps I am looking @ the wrong phase diagram for water?

http://bhs.smuhsd.org/science-dept/marcan/apchemistry/cool_phase_changes_diagram.html

As you state, down to 4.58 torr, the decreasing pressure slightly increases the freezing point; however, below 4.58 torr (0.089 PSI), the freezing point drops steadily. The OP states a vacuum, the ranges being:

Low Vacuum 760 to 25 Torr
Medium Vacuum 25 to .001 Torr
High Vacuum .001 to 10^-9 Torr
Ultra-High Vacuum 10^-9 to 10^-12 Torr

For a portion of the medium vacuum range, the freezing point of water decreases as the pressure drops. For ALL of the low vacuum range the freezing point increases (as you stated). I was honestly extending the thought exercise to Outer Space, where the vacuum ranges from 10^-6 Torr and lower (High Vacuum), hence my assertion; though my assumption of Outer Space has NOTHING to do with the OP.

Fish

 

[Spreadsheet]

The container is not going to be a perfect vacuum. I imagine that it would be low pressure, cold air. Could the water freeze when that happens? Could you get it to the point where you can essentially "match" the temperature and pressure to just the right amount so that the water would freeze?

 

[Subductionzon]

Yes, you can freeze water by exposing it to a vacuum. It happened around the ISS all the time when certain "fluids" were vented into space. Now they recycle, but I remember reading in the past how ice could block the vents at times.

I don't think that the icecube tray idea would be too practical. When exposed to a low enough pressure water can exist as a solid or as a gas, but not as a liquid. As the pressure drops the water will start to boil, using its own heat to turn the liquid water into a gas. The heat it takes to boil water is much higher than the heat released when the water freezes so more of it will end up as ice than will end up as gas.

 

[S_Happens]

S_Happens,

Perhaps I am looking @ the wrong phase diagram for water?

http://bhs.smuhsd.org/science-dept/marcan/apchemistry/cool_phase_changes_diagram.html

As you state, down to 4.58 torr, the decreasing pressure slightly increases the freezing point; however, below 4.58 torr (0.089 PSI), the freezing point drops steadily. The OP states a vacuum, the ranges being:

Low Vacuum 760 to 25 Torr
Medium Vacuum 25 to .001 Torr
High Vacuum .001 to 10^-9 Torr
Ultra-High Vacuum 10^-9 to 10^-12 Torr

For a portion of the medium vacuum range, the freezing point of water decreases as the pressure drops. For ALL of the low vacuum range the freezing point increases (as you stated). I was honestly extending the thought exercise to Outer Space, where the vacuum ranges from 10^-6 Torr and lower (High Vacuum), hence my assertion; though my assumption of Outer Space has NOTHING to do with the OP.

Fish

No, we're looking at the same one. Just like you said, we were each looking at different ranges without specifying.

 

[Redbelly98]

Yes, it looks like this is possible. At least in theory.

The trick is to cool the air by letting it expand, to below the freezing point of water, while staying above the vapor pressure of water.

Let's try a thermodynamic calculation of the temperature change in air, for a reasonable pressure change from 1 atm to 4.58 Torr (the triple point pressure of water). That would insure solid ice, not vapor, for temperatures below 0 C.

Air is 99% diatomic molecules, so we can say

P V^5/3 = constant​

for adiabatic expansion of the air. And V ~ T/P for an ideal gas, so

P (T/P)^5/3 = T^5/3 / P^2/3 = constant
​

or

T / P^2/5 = constant​

So we can say

T₁ / P₁^2/5 = T₂ / P₂^2/5​

Starting from T₁=20 C or 293 K, P₁= 1 atm or 760 Torr, and P₂ = 4.6 Torr, we end up with a temperature

T₂ = T₁*(P₂ / P₂)^2/5
= 293K * (4.6/760)^2/5
= 293K * 0.13
= 38 K​

The air does not actually get this cold, since it will continue to draw heat from the water. This should suffice to freeze the water, though it depends on the relative amounts of water and air present.

EDIT:
Just to be really sure the water does not boil off, take the pressure down to 76 Torr, well above the vapor pressure of water at 20 C (that would be 17 Torr or so). I still calculate a cooled air temperature of 117K after expansion, enough to freeze an appropriate amount of water.