When we consider a thin horizontal layer of the atmosphere, of thickness dy, of area A, with pressure P on the bottom, with an average mass m per molecule, and nV molecules per unit volume, the magnitude of the difference of the pressure at the top and bottom of the layer is given by dP =

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The pressure difference dP is due to the weight of the air in the layer. The weight is the force exerted by gravity on the molecules, which is mgnVdy (mass per molecule times gravity times number of molecules per unit volume times thickness).

When We Consider a Thin Horizontal Layer of the Atmosphere