Question:  Why does hot air rise?
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Answer:  Consider a small volume in air, we will assume that this volume
contains hot air while the surrounding air is cold.  The forces acting
on this gas are - gravity acting downwards, pressure of gas acting
upwards.  Gravity is same for everything but acceleration caused by pressure
depends on density.  If this volume element is in pressure equilibrium
with the surrounding gas, as it must be as the time taken to reach
pressure eq.  is generally very short, its density must be less than
the surrounding gas.  A less dense gas is accelerated faster and hence
it rises in comparison with the surrounding cold air.  For cold air
the pressure neatly cancels the force due to gravity which gives us the
stable atmosphere.  As this packet of hot air rises, it expands to
maintain pressure equilibrium with its surroundings and cools down.
jasjeet s bagla