I'm stuck on this problem. For part a I'm not sure how to set up the problem. I know that the pressure would vary with an increase in height but I'm not sure how to implement a formula for the varying heights with the quantites given. Would I add dz to each z?

exponential atmosphere. (a) Consider a horizontal slab of air whose thickness (height) is dz. If this slab is at rest, the pressure holding it up from below must balance both the Molecular mass pressure from above and the weight of the slab. Use this fact to find an of air is ~28 g. expression for dP/dz, the variation of pressure with altitude, in terms of the density of air. In setting up the expression, you can let the area of the slab be A. (b) Use the ideal gas law to write the density of air in terms of pressure, tem- perature, and the average mass m of the air molecules. arca = A [P(2 + d=) . A Show that the pressure can be expressed as the differential equation dp mg p, dz KT Mg called the barometric equation. P(=) . A (c) Assuming that the temperature of the atmosphere is independent of height (not a great assumption but not terrible either), solve the barometric equa- tion to obtain the pressure as a function of height: P(z) = P(O)e-mgz/kT Show also that the density obeys a similar equation. (d) Estimate the pressure, in atmospheres, at the following locations: Ogden, Utah (4700 ft or 1430 m above sea level); Leadville, Colorado (10,150 ft, 3090 m); Mt. Whitney, California (14,500 ft, 4420 m); Mt. Everest, Nepal/ Tibet (29,000 ft, 8850 m). (Assume that the pressure at sea level is 1 atm.) (P(0) at sea level z = 0 is 1 atm, and let T = 280 K. Air is ~80% N2 and 20% O2, from which you can estimate the average molecular weight m.) 91'F Mostly sunny ~ msi