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I was wondering: If I put three bottles of water next to each other in the fridge, which one is cold first? Does it matter? Is it the one in the middle because it gets refrigerated by the other two?

Thx! :)

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Have you tried the experiment? –  Ted Bunn Aug 20 '11 at 19:44
To give an answer, a number of assumptions have to be made, such as equal quantities of water, distance from the cooling source, separation of the bottles, etc. I think you'll have trouble getting an answer without including such things. But, given what I think you're really trying to ask, the middle one would be insulated by the outer bottles, not refrigerated by it. So, all else being equal, the outer ones would be marginally cooler than the middle one. Other factors (as noted a moment ago) will significantly affect that statement, though. –  Mitchell Aug 20 '11 at 20:10
@Mitchell the outer bottles do technically insulate the inner one, yes. But the outer bottles are hotter than the fridge or the fridge walls. They don't help the inner bottle cool, they work against this. –  AlanSE Aug 20 '11 at 21:04

2 Answers 2

up vote 1 down vote accepted

It depends on where the vent from the cooling system is. For my fridge, this is in the upper left on the back wall. That means that the left one might cool faster in my fridge, as if they were 3 buddies in a house with one standing next to the AC system.

Assuming Perfect Mixing

There is also the chance that the location of the cooling system doesn't matter. There could just be fast mixing of the air in the interior such that this factor doesn't matter, and all the air is approximately the same temperature. This could also be the case if the change in temperature of the air over the heat exchanger was really small. This case is roughly similar to a cooler.

The only path for heat to get in is the walls. Of course the insulation is imperfect and this causes the walls to be slightly higher temperature. Because of the radiative heat balance with the walls, if you assume the air temperature is uniform then the bottles on the outside will cool the slowest. The one on in the middle will get cold fastest will receive less of the wall radiation, but more radiation from the other bottles.

EDIT: I goofed. My argument was that the outer bottles get less cooling due to the wall elevated temperature, but I should have continued to note that the walls won't be enough to compensate for higher T rad from other bottles.

Your thinking here:

Is it the one in the middle because it gets refrigerated by the other two?

is kind of interesting (but wrong). If the 2 outer bottles were not there, the middle bottle would cool much faster in fact. Use of words like "insulate", "refrigerate", and "cool" might get a little difficult in this discussion. One way or the other, the outer bottles don't help cool the inner one, although they cool slower than it does.

EDIT: The outer bottles do insulate the inner bottle. That is correct to say, although I should add that the effect could be mostly through radiative heat transfer. Convection is something you could get into but it's a little trickier. Fewer bottles will probably always cool faster, and this is due to both heat transfer and thermal mass reasons.

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Thank you for your answer! You even answered all the details I forgot to put in my question! ;-) –  Philippe Gerber Aug 20 '11 at 21:40
I think this answer misses something crucial: side bottles start off much warmer than the walls, and while they do shield the centre bottle from the walls they can be expected to radiate more heat towards the centre bottle than they shield. –  Dmytry Aug 20 '11 at 21:44
@Dmytry I should read over my answer better. I couldn't have said it better than your comment. –  AlanSE Aug 20 '11 at 21:55
@Zassounotsukushi yes, convection is very tricky! A pipe around the bottle may result in quicker cooling if it creates funnel effect. I don't think a bottle standing next would make funnel though. –  Dmytry Aug 20 '11 at 22:47

I think in symmetrical case the middle will typically cool down the slowest, unless it is standing right under the cold spot and has the cold air flowing down onto it.

The walls, albeit slightly warmer than the air, are much colder than the bottles, and the middle bottle is receiving radiated heat from 2 bottles standing next to it, whereas side bottle receives radiated heat from one bottle next to them. Furthermore the middle bottle will have restricted airflow on two sides whereas side bottles only on one side.

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