You’re right it doesn’t change the mass, but it does change the volume that mass takes up – which means it changes the *density*. And it’s density not mass that determines whether things float or sink.
Hot air rises because it is less dense than cold air. Like, 1 pound of hot air takes up more space than 1 pound of cold air. That means the hot air is less dense and floats on top of colder air the same way a cork will float on water – because it’s less dense.
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