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I have read at so many places that warmer air moves up as hotter substances expands and as it rises it loses its kinetic energy and it gets converted into its potential energy(gravitational+interatomic) And that's what cause decrease in temperature at higher altitude but there is following confusion I have about this:

I want to know it in terms of pressure like is the pressure of the bottom layer of atmosphere increases as its temperature increases because I think that can lead to its flow from higher pressure to lower pressure?but if that happen then as it starts rising there will be a time where pressure drops and become equal to the layers above it so should stop expanding there? So I am confused that is it due to some sort of force(if yes then please explain) or due to random motion of air particles that warmer air expands and moves up?it should be because of some forces pushing it upwards because bulk flow happens due to pressure gradient otherwise it would be diffusion I think pressure should increases because similar think happens in the case hot air ballons moving upwards

2)why the air above this layer comes down as hot air rises? Is this due to diffusion or bulk flow?

If anyone could explain it in terms of forces (Like we do in Newtonian physics) like by making some sort of force diagrams that would be very intuitive and helpful because the main problem is I am unable to form a consistent picture in my mind to understand it.

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