Dumb physics question

[SNOWBALL]

In an Edward Norton movie called "the score", a safecracker pumps an imprenetrable safe full of water, and freezes the water, which cracks the safe. Assuming the safe was strong enough, would the water just not freeze?

[Silent A]

The water would freeze. The extra pressure would only aid the process (although not by much).

I'm just trying to remember how they froze the water.

[SNOWBALL]

[ QUOTE ]
The water would freeze. The extra pressure would only aid the process (although not by much).

I'm just trying to remember how they froze the water.

[/ QUOTE ]

ok, so it would freeze but not expand? Or would it expand regardless of how strong the safe is?

[Schweitzer]

As the water cools it would freeze and tend to expand. The safe, if strong enough, would exert enough pressure on the water to keep it from expanding. Basically the pressure on the water would increase as the water froze but the water would not expand.
All things will contract under enough pressure or expand when pressure is removed. For example, a bag of chips will expand until it pops open if brought to high altitudes due to reduced air pressure. Ice will have an equilibrium volume dependent on the external pressure acting on it. If the pressure is increased, its equilibrium volume will decrease.

[Silent A]

The water would "try" to expand. As it did, it would exert immense pressure/stress on the steel safe. This in turn would exert a pressure force back on the water/ice. In general, increasing pressure makes freezing "easier" as the molecules are pushed closer together making it easier for them to crystallize into ice (basically, the water will be able to freeze at a temperature slightly higher than 0 deg C - but not much - and so it takes a little less energy to freeze).

Also, the ice would expand a bit because the safe will always deform a little under the stress. However, the ice wouldn't expand nearly as much if it were free. This difference in expansion (between actual in the safe and normal in the open) results in an extremely high pressure inside the safe.

Imagine you had filled a 1 m3 (or 250 gallon, if you prefer) safe with ice/water. Now try to imagine how hard it would be to put another 0.1 m3 (or 25 gallons) in it. The force required to do this is the same as would be created by freezing a safe full of water.

[Neuge]

[ QUOTE ]
In general, increasing pressure makes freezing "easier" as the molecules are pushed closer together making it easier for them to crystallize into ice (basically, the water will be able to freeze at a temperature slightly higher than 0 deg C - but not much - and so it takes a little less energy to freeze).

[/ QUOTE ]
This is true for most every substance, but not water. Increased pressure actually lowers the freezing point.

[Neuge]

I think this is an interesting question and I don't know the answer. I'd suspect the answer is yes, the water would just not freeze, but think it would take an incredibly strong safe. I'll think about it and see if I can come up with some reasoning.

[Silent A]

[ QUOTE ]
I think this is an interesting question and I don't know the answer. I'd suspect the answer is yes, the water would just not freeze, but think it would take an incredibly strong safe. I'll think about it and see if I can come up with some reasoning.

[/ QUOTE ]

Since the freezing point of water drops with pressure, the question becomes does it drop fast enough that the water won't freeze. Heres' a hhase diagram of water ...



"E" marks average conditions on Earth (V is for Venus, M for Mars).

It shows that above approx 10,000 atmospheres, the ice will freeze at any temperature (but with a different crystalline structure than common ice). Either that or you'd have to cool it to below -20 deg C. The thing is, in these regions ice is denser than liquid water. Which means the pressures should never get this high. Only in the region labeled "Ih, Ic" does ice have a lower density than water (0.92 g cm-3).

The answer, I think, is that the water won't freeze completely. Or, you could end up with a mixture of two types of ice crystals. It's most likely that this would occur on the boundary between Ih (density 0.92) and II/III (density 1.17 and 1.14) in the figure below (a close up of the above):



So we're looking at 200 MPa of pressure and about -20 deg C.

[Neuge]

[ QUOTE ]
The answer, I think, is that the water won't freeze completely. Or, you could end up with a mixture of two types of ice crystals. It's most likely that this would occur on the boundary between Ih (density 0.92) and II/III (density 1.17 and 1.14) in the figure below (a close up of the above):



So we're looking at 200 MPa of pressure and about -20 deg C.

[/ QUOTE ]
Yes, this is what I was looking for. I couldn't seem to find to solid phase diagram and phase densities for ice and had no idea of the critical point behavior.

You're right, if you keep decreasing the temperature, the pressure would increase without any freezing* until the critical point is reached at liquid/Ih/III. If the temperature is decreased further we'll end up with a Ih/III mixture at temp and pressure along that equilibrium line until we hit the Ih/II/III critical point. Further decreases in temperature would be a mixture of Ih/II at temp and pressure along that critical line**.

So basically, we need a safe that can withstand at least 200 MPa of mechanical stress and it's immune from this type of cracking technique. At that strength the water would just freeze.

* There may be minimal freezing, I'm not sure what the density function for liquid water looks like along that equilibrium line.
** It may not be an equilibrium Ih/II mixture. It would depend on the mole fractions of Ih and III produced in the first phase transition and the phase transition enthalpies of Ih->II and III->II. EDIT: This would also depend on the phase change density changes between Ih->II and III->II as well.

[Silent A]

For those of you who don't think in MPa very well, that's about 2000 Atmospheres or 30,000 psi.