> After that time, the way we look at it, it's at the same point in experiment as if we have just put the colder water in. So we seem to still be missing something.
Unless there is very substantial mixing, the container of hot water will never be at the same state as the container of cooler water.
We did this in high school, with 3 open-topped 10L buckets, one with 25C water, one with 95C water and no mixing, and one with 95C water sitting on a magnetic mixer. They were not in a freezer, but outside at ~-25C.
The freezing order was 95C unmixed, 25C, 95C mixed. We also had a few temperature probes in the 95C unmixed bucket, and found that about halfway through, the temperature of the water in the middle about 1/3rd of the way from bottom was sitting at 0C, while the temperature of the water at middle at the top was still >70C.
Our final findings were that:
1. The buckets cool mainly by evaporation, which is only happening at the top, and which is much faster for hotter water
2. Water of different temperature stratas can be surprisingly stable even in a small container
3. In the unmixed bucket a stable, slow flow of water down the sides and up the middle forms. New hot water emerges from the middle, gets cooled and pulled to the sides, and then pulled down to the bottom. This circular flow is probably caused by the fact that water at the sides get initially cooled a bit and so it sort of biases the flow.
But now there's people saying it still works with closed-top containers, so I dunno. My physics teacher clearly did this every year and knew what was going to happen. The class came up with those findings after some very specific questions by him.