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 n_V molecules per unit volume, the magnitude of the difference of the pressure at the top and bottom of the layer is given by dP = A) mgdy. B) mgn_Vdy. C) mgAdy. D) mgn_VAdy. E) mgn_VAPdy.

Question

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The pressure difference, dP, is due to the weight of the air in the layer, which is the product of the mass of air in the layer (m*n_V*dy*A, where m is the average mass per molecule, n_V is the number of molecules per unit volume, dy is the thickness of the layer, and A is the area) and the acceleration due to gravity (g). This simplifies to mgn_Vdy, as A cancels out when considering pressure, which is force per unit area.

When We Consider a Thin Horizontal Layer of the Atmosphere