Freezing Water at Constant Volume
Most recent answer: 11/14/2014
- 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)
Follow-Up #1: freezing water at constant volume
- 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)