Re:It will fall down (Score 1)

You're still missing the point. At the same pressure, a litre of hot air does have less mass than a litre of cold air. Hot air rises because it is less dense than cold air, because the particles bounce off each other more energetically. So yes, heating unconfined air does make a given volume lighter. The relationship between the particles average speed (be careful here, you said velocity) and the Earth's escape velocity is such a smaller effect as to be negligible.