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Old 10-18-2019, 12:38 PM
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Help Me Calculate The Temperature For A 5-Gallon/19-Liter Jug Of Water To Freeze Solid In 12 Hours


My tap water is disgusting, so I buy my water via these 5-gallon (19-liter) refillable jugs. I don't always bring them inside right away, because they're heavy and I'm a pussy, and so they'll oft sit in the back of my car until I need them.

In the winter, this stresses Mrs. Homie out, who insists that they'll freeze solid if the temperature drops below 32F/0C and stays there overnight. I know she's wrong, but I don't know how wrong. By my estimation, 12 hours at or just below freezing means, at most, a thin layer of ice on the surface.

But how long to freeze solid in, say, a 12-hour period? My WAG is that for a 5-gallon/19-liter jug of water to freeze solid in 12 hours, the temperature would have to be in the neighborhood of -20F (-28C) for that period of time. But I could be way off.

Any thoughts?
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Old 10-18-2019, 12:45 PM
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Check this out.
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"The greatest obstacle to discovery is not ignorance -- it is the illusion of knowledge."
--Daniel J Boorstin
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Old 10-18-2019, 12:48 PM
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That article might as well have been written in Japanese. All of that algebra for a man who can barely do simple arithmetic. Please.
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Old 10-18-2019, 01:13 PM
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They used to drop water bottles off at my house and leave them on the front porch if no one was home. I didn't keep track of the temperatures but between 18 and 24 hours, at maybe an average of 27F, they didn't freeze. Those bottles are supposed to be able survive freezing without breaking anyway, if it did freeze you'd just have to wait a little while after you carry it inside.
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Old 10-18-2019, 02:21 PM
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With due respect, That equation is wrong. The author is confused between heat transfer coefficients and specific heat.
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Old 10-18-2019, 02:50 PM
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To even begin working this out, you'd need the starting temperature of the water and probably some insulation characteristic values for the jug.
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Old 10-18-2019, 03:32 PM
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This sounds like a good opportunity for the old adage: "One experiment is worth a thousand expert opinions."
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Old 10-18-2019, 03:39 PM
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And insulation characteristics of the car, too.

And I agree with Tim R. Mortiss: The easiest way to find all of the relevant values would be just to run the experiment anyway.
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Old 10-18-2019, 05:08 PM
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Do you have room in your freezer for one of the jugs? If so, put one in there for 12 hours, then show it to her. It should still be liquid enough to use as a cool pillow while you sleep on the couch.
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Old 10-19-2019, 10:45 AM
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Would the experiment scale up? If OP put 9.5 litres into a jug so that the freeze expansion has lots of room to not burst the jug or overflow into the trunk. Leave it until it freezes, then multiply the time elapsed by 2?
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Old 10-19-2019, 10:47 AM
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Would the experiment scale up? If OP put 9.5 litres into a jug so that the freeze expansion has lots of room to not burst the jug or overflow into the trunk. Leave it until it freezes, then multiply the time elapsed by 2?
Doesn't work. The surface area of the container doesn't scale linearly.
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Old 10-19-2019, 06:27 PM
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It takes 6,7 Megajoules of energy to freeze 20 liters of water.

That means it would take 24 hours to freeze if the cooling power were 75 Watts.

What kind of cooling power do we get with a 20 liter PET bottle sitting out in a few K of freezing temperature? Is it more or less than 75 Watts?

Here is a study on the heat transfer characteristics of PET bottles:

Study on heat transfer coefficients during cooling of PET bottles for food beverages (PDF)

Fluid dynamics is a huge factor in the cooing time.

Can anybody tell from that PDF if the power is easily more than 75 Watts or definitely less? With a quick glance I think it's more. So I think the bottle will EASILY freeze in much less than 24 hours. but maybe someone can read that article more thoroughly and/or has other sources.

Last edited by Frankenstein Monster; 10-19-2019 at 06:29 PM.
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Old 10-19-2019, 06:43 PM
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Correction


Quote:
As expected, air cooling was extremely slow (Ug ~ 10 W/m2 K) but increased 1.5 times in dynamic conditions.
And I realized the surface area of a 20 liter bottle is less than half a square meter.

With five degrees Celsius below zero, 15 W/m2*K and 0.5m2 the power would be half of 75 watts or the freezing time would be 48 hours.

With twenty Celsius below zero the freezing time would be 12 hours.

I think.
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Old 10-19-2019, 11:39 PM
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With no wind blowing 2 to 4 W/m2-K is the typical overall heat transfer coefficient.

However, there is heat conduction from the bottom of the bottle which is probably resting on a cold surface.
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Old 10-20-2019, 12:56 AM
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Quote:
Originally Posted by am77494 View Post
With due respect, That equation is wrong. The author is confused between heat transfer coefficients and specific heat.
You’re absolutely right.

Also, the author uses “such” in an egregiously affected manner. Oof.
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Old 10-20-2019, 09:16 AM
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Originally Posted by TriPolar View Post
Those bottles are supposed to be able survive freezing without breaking anyway, if it did freeze you'd just have to wait a little while after you carry it inside.
If the container is sealed, the expansion of the water as it freezes can be enough to split it open. The worst-case scenario is that the bottle freezes, splits, and then thaws and leaks out all over the car floor through the new hole in the bottle.

Since liquid water takes up about 90% of the volume of the same amount of frozen water, the solution is to fill your bottles less than 90% full just to be on the safe side.
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Old 10-20-2019, 09:24 AM
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Quote:
Originally Posted by MikeS View Post
If the container is sealed, the expansion of the water as it freezes can be enough to split it open. The worst-case scenario is that the bottle freezes, splits, and then thaws and leaks out all over the car floor through the new hole in the bottle.

Since liquid water takes up about 90% of the volume of the same amount of frozen water, the solution is to fill your bottles less than 90% full just to be on the safe side.
I don't know if the OP is filling his own bottles, that can be done at some places. The ones filled at the factory look like they have enough space for expansion if they freeze. Most bottled liquids are that way to prevent freezing in storage and shipment.

Last edited by TriPolar; 10-20-2019 at 09:24 AM.
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