recently I was wondering if there is any specific formula in order to calculate how long it takes for certain liquids to freeze (especially water).

I know this depends on:

  1. the volume of the liquid,
  2. the temperature surrounding the liquid,
  3. the surface of the liquid container,

In order to not make it too complicated let's assume the liquid is surrounded by air and the container has no isolation. This is just out of pure curiosity, so I haven't done any calculations.

  • $\begingroup$ Yes it is possible if you know the thermal coupling from the water to ambient. For example, how many Watts will the water lose per second per degree above ambient? Then there is the complicating factor of parts freezing before other parts, and convection no longer being possible in the frozen parts. Also, right near freezing, the colder water will actually rise. $\endgroup$ – Olin Lathrop Jun 20 '13 at 22:12
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    $\begingroup$ don't forget the temperature of the water as a dependent. For instance, boiling water flash freezes before chilled water $\endgroup$ – Jim Jun 20 '13 at 22:29

Yes, it's possible though usually complicated.

If you have a sphere of water at 0ºC and put it in a freezer at some temperature T that is below zero then the rate of heat flow out from the sphere would be approximately given by Newton's law of cooling. If the cooling rate is slow, and you can make the approximation that the temperature within the water is constant then the heat flow per unit area will be constant while the water is freezing. The time to freeze would be the total latent heat of fusion divided by the heat flow rate per unit area divided by the total surface area.

However even in this simplified situation we don't know the constant of proportionality in Newton's law, and this will depend on the details of the environment e.g. speed of air currents. The best we could do is make conclusions like the freezing time will be proportional to the sphere radius because it's proportional to volume divided by area. We should also find the time is inversely proportional to the temperature difference.

Life gets more complicated when the cooling rate is too fast for us to assume no temperature gradient within the water. For example a skin of ice would form on the outside, and ice is a better insulator than water (because you get convection currents in water). In that case the rate of heat flow (and therefore freezing) would be inversely proportional to the thickness of the skin of ice.

A last complication is that water readily supercools. You can only assume the water will freeze at eactly 0ºC if there's no barrier to nucleation of ice crystals.


yes. you can use newtons law of cooling when the temperature difference between your liquid and surroundings is less than 40 degrees. In case the temperature difference is greater than 40 degrees stefan's law holds good

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    $\begingroup$ This might be a more useful answer if you were to include the formulae you mention. $\endgroup$ – Kyle Kanos Jan 31 '15 at 19:25

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