"Heat rises" or "warm air rises" is a widely used phrase (and widely accepted phenomenon).
Does hot air really rise? Or is it simply displaced by colder (denser) air pulled down by gravity?
Answer
The mechanism responsible for the rising of hot air is flotation: Hot air is less dense than cold air and hence air pressure will exert an upwards force, in the same way air rises in water. Now if cold air was magically unaffected by gravity, then it would not be able to exert pressure on the hot air and thus it would not rise.
The statement that "heat rises", by the way, is not universally true. Look at water. Here, it is the cold water that is less dense than warm water (at least in the temperature regime of importance to freezing). In winter, when water gets colder, the cold water raises to the top and eventually will freeze, while the water below remains liquid for the moment.
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