Freezing Water at Constant Volume

My son and I were working on a school lesson regarding errosion, specifically the power of water and freezing to break down rocks such as limestone or granite. When water freezes, it expands and can apply pressure between surfaces to cause and increase fractures. Suddenly, I had a thought. What if you could freeze water inside a container that had no space for the water to expand within. For example, suppose you had a solid steel sphere several inches thick, with a container in the center that was completely full of pure water and then you slowly cooled the sphere with liquid nitrogen until the water frozed inside the core. Questions 1. Would the water freeze into a solid? 2. If desolved impurities were also present, what would happen to them? 3. Would the frozen water remain a liquid or a solid? 4. If the water in the core was removed (by cutting the sphere open), would the water rever to a liquid or remain a solid? (I recall that when hydrogen is cooled to absolute zero, it remains a solid, in theory anyway. That is why I asked this question.)
- gerad dickinson (age 60)
austin,texas

1. Your steel sphere keeps the water at almost constant volume as it cools. Since water expands when it freezes at constant pressure, as ice starts to form it squeezes on the liquid. That increase the pressure and lowers the freezing point. Then with more cooling, a little more ice forms, the pressure goes up more, and the freezing point drops a little lower. So instead of all the water freezing at 0°C, the amount of frozen water increases gradually. I calculate, from the expansion of water on freezing (about 8.3%) and the compressibility of ice (about 1.2*10^-10
Pa^-1) that if all the water froze the pressure would go up to about 10⁹ Pa. Even at high pressures water forms some sort of solid ice below -20°C, as you can see on the phase diagram of water. ()  So at around that temperature, all the water will freeze. In order to fit well with the container I think it will freeze into a combination of two different forms of ice, with different volumes. In practice, the steel will expand some allowing all the water to freeze at somewhat higher temperature, and possibly preventing the ice from having to go into the other forms..

2. Dissolved impurities should almost all be pushed out of the ice into the liquid. When there's no liquid left, the impurities should be left as separate little parts, e.g. salt crystals. The same thing happens whenever you freeze ice slowly.

3. See (1) above.

4. If the ice is allowed to expand freely, it goes to a state with a lower potential energy (at a given temperature) than the compressed state. The extra energy goes into heating up the ice. I did a rough calculation that indicates the heat would be enough to get heat the ice by a few °C, not quite enough to start to melt it.

If you're interested I can try to figure out the effect of the compressibility of the steel and do the calculation of (4) more carefully.

Mike W.

(published on 11/14/2014)

This is a fascinating question that's captured my imagination for many years. We finally published the answer to this question, derived using classical thermodynamics. The article is open-access and free to download: "Freezing water at constant volume and under confinement" https://www.nature.com/articles/s42005-020-0303-9
- Wenhao Sun (age 31)
Ann Arbor, MI

Thanks, I'm glad you sent us this link!

https://www.nature.com/articles/s42005-020-0303-9

https://www.nature.com/articles/s42005-020-0303-9

Mike W.

(published on 02/21/2020)