Why do lakes and rivers only freeze on the surface and not all the way through?

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Why do lakes and rivers only freeze on the surface and not all the way through?

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Normally things get lower density when heated and higher density when cooled. So if you cool a liquid from the top the cold liquid falls down to the bottom pushing up the hotter liquid, so it all keeps the same temperature. This is why ACs are usually mounted high on the wall and heaters are mounted low. But water have the property that the ice is less dense then water and therefore cooling down water to ice makes it float to the top. This is even noticable at temperatures a bit above freezing. So when you cool a lake from the top and the water is almost at freezing the cold water stops falling to the bottom of the lake and just stay on top. The water at the bottom of the lake therefore does not cool down any more. On the surface however the water might freeze into ice and even be cooled far bellow freezing but none of that ends up at the bottom of the lake.

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