(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 p_{0}.

(c) If p_{0} = 1.03×10_{5} N m^{–2}, ρ_{0} = 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.