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Well, maybe not individual atoms. But, since atoms move through the liquid relatively freely, small regions of hot and cold water will randomly appear in the water. Hotter regions will rise and cooler regions will sink. This doesn’t change the question . Yes, but there will always be faster and slower atoms. It’s a rule of nature. http://www.algebralab.org/practice/practice.aspx?file=Reading_DistributionOfKineticEnergies.xml

Hello, I have an interesting question about water natural convection without an external heat source. Say we have a high tower filled with water. The tower walls don't allow any heat to escape or enter the system. There is a constant gravitational force present in a system (g-force). At the beginning the water is all at the same temperature. The water naturally contains faster and hotter atoms and slower and cooler atoms. Because of the buoyancy forces the hotter atoms will have a tendency to rise and cooler atoms will have a tendency to sink. Is it correct to say that after some time the water at the top of a tower will become hotter than the water at the bottom of a tower? Or the heat transfer will cancel out this effect?