heat - If I put 3 bottles of water next to each other in the fridge, which one is cold first?

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! :)

Answer

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.