Sarthaks Test
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(a) Pressure decreases as one ascends the atmosphere. If the density of air is ρ, what is the change in pressure dp over a differential height dh?

(b) Considering the pressure p to be proportional to the density, find the pressure p at a height h if the pressure on the surface of the earth is p0

(c) If p0 = 1.03×105 N m–2, ρ0 = 1.29 kg m–3 and g = 9.8 m s–2, at what height will the pressure drop to (1/10) the value at the surface of the earth? 

(d) This model of the atmosphere works for relatively small distances. Identify the underlying assumption that limits the model.

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(a) Consider a horizontal parcel of air with cross section A and height dh. Let the pressure on the top surface and bottom surface be p and p+dp. If the parcel is in equilibrium, then the net upward force must be balanced by the weight.

(b) Let the density of air on the earth’s surface be ro , then

(d) The assumption p  r is valid only for the isothermal case which is only valid for small distances.

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