You are exactly right.The molecules in hot air are
moving faster than the molecules in cold air.
Because of this, the molecules in hot air tend to
be further apart on average, giving hot air a
lower density. That means, for the same volume of
air, hot air has fewer molecules and so it weighs
less. So since cold air weighs more, it sinks,
driving the hot air up
Basically yes. Our atmosphere, like a body of
water, is a fluid that has a density that is
determined by a balance between gravity and
pressure (plus temperature). Pressure is
generally higher the closer you are to the earth's
surface. If you put a "bubble" of hot air in a
"sea" of cold air, the hot air can have a lower
density but the same pressure as the cold air.
This bubble then floats up until it reaches a
level in the atmosphere where its density matches
that of the surrounding air.
Here is a web
page that discusses how hot air balloons work
which also has some more
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