Supercooling
 		 Perhaps you have seen videos like this before.  What you are looking at is water cooled well below the freezing point.  Many people consider this to be some strange or exotic behaviour, but its rather ordinary and easy to reproduce.

Without a seminal crystal on which to start crystal growth, the water remains in its liquid form, unable to freeze, and it continues to cool well below its normal freezing point.  Normally a nucleation site, such as a piece of dust or a surface imperfection in the bottle will allow a small number of water molecules to assemble into that initial crystal.  Once this happens, the seed crystal rapidly grows from the supercooled liquid.  At the boundary between water and ice, more energetic molecules in ice are released, and less energetic molecules in the water are taken up by the ice.  As additional heat is removed from the bulk material, additional lower energy molecules are available. In accordance with Le Chatelier's principle this pushes equilibrium towards the ice phase, and the average kinetic energy ( temperature ) rebounds to near zero degrees C.

 This rapid growth seen here is possible because so many water molecules have low enough energy to permanently afix themselves in unocupied lattice sites.  
 		 So the question often asked is what happens from a thermodynamic perspective?  Well temperature is a measure of average kinetic energy.  The key here is average.  When ice forms, the least energetic ( i.e. slowest moving ) liquid molecules more persistently attach themselves to the growing crystals.  This takes the slowest / least energetic molecules out of the liquid phase.  Initially is it very posible that ice crystals themselves are colder than the liquid phase.  ( Similarly the steam from a boiling pot of water is often hotter than the boiling point, as the most energetic molecules escape as steam. )  But this matter quickly resolves itself as the bulk mixture of ice and water achieve thermal equilibrium at / near 0 degrees.

Lets consider freezing where water at 0C freezes to ice at 0C - a simple change of state.  During this state transition, the water sheds 80 calories of heat / gram.  But during supercooling there is no change in state, we just continue to lower the temperature at a rate indicated by the specific heat of the material.  In the case of water, this is near 1 calorie / gram / degree.  ( This actually varies quite considerably with temperature as we shall see.  But for our pusposes we can say 1. )
 
 		 The graph shows how the heat capacity ( from which is directly derived specific heat ) of water varies with temperature.  273K = 0C so for water supercooled to -20C, our 1 calorie / gram / degree assumption is approximately true.  However as we try to super cool water even further, we enter a region where the heat capacity becomes decidedly non-linear.  As we slow down the water molecules, they increasingly form larger clusters as hydrogen bonding plays a larger roll.  At about -35C we see a peak in the heat capacity, and also a great reduction of thermal conductivity.  Something is happening!  This leads to the magic -38C barrier, below which it is impossible to supercool water at ordinary pressures.

If you look at the curve, you can see that the specific heat will increase to more than 1.7 cal / gram / degree C.  So as we approach the magic -38C we will remove 53 calories of heat to supercool the water below 0C.  
 
 		 So back to what is happening.  While the ice is forming, the bottle is essentially a closed system.  There is not a substantial heat flow in or out.  Its an adiabatic system.

The final state of the system is ice in equalibrium with water at 0C.  So nomatter the disposition of the temperature of the ice when it forms, it ends up at 0C, along with the liquid water.  If we were to have "normal" freezing, the amount of water converted to ice would depend on the amount of heat removed from the system after the water was cooled to 0C.  For example, if we have 100g water at 0C, and remove 800 calories of heat, we will arrive at either a mixture of ice and water at 0C where 10g would be ice -or- supercooled water at approximately -8C.  You will note that we do not concern ourselves with the specific heat of ice, same as if we considered this to be a simple state transition at 0C.  Ultimately what matters is the starting and ending point.  So for initial temperatures above -20C, given an initial temperature -X degrees, the fraction of the mass of ice that will result is approximately X / 80.  Even for water supercooled to the limit of -38C, where some 53 calories / gram are removed to achieve that temperature, only 53 / 80 or about 66% of the water is converted to ice.  The implication is that it is not possible for supercooled water to freeze into a solid block of ice.  There will always be a substantial portion as water.
 
 		 And finally, here is what happens when you pour out supercooled water at -21C / -6F.

After this video was shot, I took the resulting slush from the dish and from the bottle, pressed all the water out, yielding a ball of ice at -2.4C.  I then let this ball of ice melt in a beaker. This resulted in 150cc of meltwater at room temperature, meaning 150 grams of ice.  The bottles of water used were 20oz ( 591cc ) bottles.  So we started with 591cc of water of which 150cc were turned to ice during the instant freezing phenomenon.

So does this jive with our theory?  Sure it does, as 150/591 = 25% of the water turned to ice.  In addition, so based on this the initial temperature of the water should be 25% of -80C, so -20C.  And guess what, the initial temperature was -21C on our IR thermometer.  So we have a pretty solid validation of our theory, thankfully backing up simple thermodynamics once again.
 
All Photos Taken and (C)opyright Robert Charles Mahar.
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