# Water freezing

Is there a formula or method for determining the time it takes for water to freeze from a certain temperature? What parameters would this rely on?

Nathanael
Homework Helper
I imagine it would depend mostly on the temperature it starts from, the temperature it is exposed to (of your freezer or whatever) and probably the surface area (and perhaps what the surface area is exposed to).

I don't know a formula, and there's probably more subtle/complicated things that effect it, but I would guess that the parameters I mentioned would likely be the most important.

russ_watters
Mentor
It can be easy or complicated depending on the provided information.

I'm just wondering generally (as in, a real life application, not textbook problem).
If there hasn't been any work on it, I'll reserve it to study in high school

OmCheeto
Gold Member
Just make sure you don't use distilled water. I had unfrozen water at 10°F the other day.

russ_watters
Mentor
I'm just wondering generally (as in, a real life application, not textbook problem).
If there hasn't been any work on it, I'll reserve it to study in high school
It is safe to say that millions of hours of work have been done on this problem and it is understood exquisitely well -- which doesn't necessarily make it simple, depending on the specific problem.

One example is thermal storage in an air conditioning system. It is cheaper to make "cold" at night due to electricity prices, so large corporations will store "cold" for use during the day. One good way to store it is with ice. So if you have a certain amount of water (often contained in plastic balls), with an anti-freeze solution circulating around it, and a chiller of a certain capacity, it is very easy to calculate how long it will take to freeze all of it.

Say, for example, you have 1 million liters of ice storage capacity and a chiller with an output of 5 MW. If the ice balls start as liquid at 20 C...

Specific heat of water: 1.86 J/g
Latent heat of fusion: 334 J/g

To cool from 20C to 0C takes:
1,000,000 L * 1,000 g/L * 20 C / 5,000,000 J/s * 1 J/g-C= 1.11 hrs

1,000,000 L * 1,000 g/L * 334 J/g / 5,000,000 J/s = 18.5 hrs

sophiecentaur
Gold Member
Is there a formula or method for determining the time it takes for water to freeze from a certain temperature? What parameters would this rely on?
This a bit of a 'How longs a piece of string' question as it can be tackled at all sorts of levels. It's basically a very practical problem - think how you can affect the rate that an ice-cream melts, depending on where you keep it.
Are you planning to dunk your water into an already cold place or are you planning to start with a large mass of water and then try to refrigerate it?
The basic parameters are
Mass of water
Starting temperature
Specific heat capacity of the water
Latent heat of state change
Temperature of the place the water is placed - or the 'cooling power' of your refrigerator

Then there will be details like how good the thermal contact is between the water you want to freeze and the cooler fins etc. The heat transfer would be best if you use forced convection (pumped antifreeze as in russ's description, or circulating air as in your freezer at home). Ice will tend to insulate the inside layers of water and slow things up.
The performance (effective cooling rate or 'Power') of your refrigerator will depend on the ambient temperature and the efficiency (often referred to as Coefficient of Performance)

You will need to specify what you had in mind but I can guarantee you will not have enough information to give a very accurate answer - particularly if you are just talking in terms of a jar of water in a freezer. Give us a clue about your thought experiment.