# Q & A: thermodynamics of supercooled water

Q:
If you do the sums, supercooled water, even at -20 deg C, will only freeze around 15% of the water. I have seen videos of supercooled water poured from a bottle instantly turning to a mound of slush. It certainly seems that more than 15% (at most) of the water has turned to ice. Is it possible that the molecules in the supercooled water are taking on some of the order eventually to be seen in the ice. This would be sen as an apparent increase in the specific heat as the water cools below zero and a reduction in the latent heat, because the water would already have some of the order of the ice crystal. With a reduced latent heat, a greater proportion of the ice would then be able to freeze once nucleation begins.
- John Hobson (age 61)
Devizes, Wiltshire, UK
A:

That's a brilliant question!

(For those who want to follow our earlier discussion of the supercooling effect, see .)

I get ~23% ice for a first crude calculation of fraction that could freeze starting with -20°C supercooled water, just using the standard latent heat and the standard heat capacity. So that's a little higher even without getting into your idea about the increased heat capacity.

Fortunately, the thermodynamic properties of supercooled water have been measured, including the constant-pressure (Cp) and constant volume (Cv) heat capacities. (See e.g. Figure 5 in  .)  Cp does show an increase of the sort you were thinking about, but it isn't all that big- around 20% for supercooling to about -30°C, and of course less in the range up to 0°C. So that doesn't increse the fraction of ice that can form by a lot. Since any real experiment is done in a cold bottle, you can count some of the bottle heat capacity too, which helps also to increase the frozen fraction a little. When you're done allowing for all these factors, maybe about 30% of the water could turn to ice- and more if the water was a little more supercooled.

So I think the bottom line is that although that was a great idea and does describe a real effect, the main effect is just that slush can have a smaller fraction of ice than you would guess by eye.

Mike W.

(published on 04/02/2014)