Question

Now, assume that the atmosphere, instead of being isothermal, is adiabatic, which means that pressure everywhere is proportional to Tn/(1-1), where the adiabatic coefficient γ is about 1.4 dT (a) Figure out what dz is, in terms of T, γ, m, k, and g, as well as P and TO, the pressure and the temperature on the ground. (b) In mountaneering, there is a rule of thumb that the temperature drops by about 1°C for every 100 meters you go up a mountain. Compare this rule of thumb with your answer to part (a) (c) Solve the differential equation in (a) to compute the temperature at airplane cruis- ing altitude (about 11km for jet airplanes). Assume a reasonable ground-level temperature. (d) The adiabatic assumption (which implies that P T) is physically a statement that, as air raises from the ground to higher altitudes, it does not exchange heat with its surroundings. It's a good assumption because air is an excellent insulator: any heat ex change is too slow to make a large difference in temperature. However, there is another piece of physics in play: air contains water vapour and, as it moves up and cools, the water vapour will condense (turn into liquid water). Given this effect, is the real temperature at the altitude of 11km higher or lower than your answer to part (c)?

Answer 1