a) From the known value of atmospheric pressure at the surface of the Earth, est
ID: 2014799 • Letter: A
Question
a) From the known value of atmospheric pressure at the surface of the Earth, estimate the total number of air molecules in the Earth’s atmosphere. (Hint: Disregard air motion and consider static equilibrium on the atmosphere. The atmosphere presses on the ground and by Newton’s 3rd law there is a reaction force acting on the air. What is balancing this force?)b) During certain seasons, strong winds call Chinooks blow from the west across the eastern slopes of the Rockies and downhill into Denver. Although the winds come from mountains where the temperature is low, the temperature in Denver can climb 20 °C within a few minutes after the Chinook wind arrives. Similar winds occur in the Alps and in Southern California. Explain why the temperature of the Chinook wind rises as it descends the slopes rapidly? (The answer to this is key to solving the numerical part of the problem, if the air moves very quickly then heat transfer into and out of the air can be neglected in the first approximation) Suppose the wind comes from Grays Peak (80 km west of Denver, elevation 4350 m) to Denver (elevation 1630 m) and the atmospheric condition at Grays Peak is -15.0 °C and 5.60 x 10^4 Pa pressure while the conditions in Denver before the wind arrives is 2.0 °C and 8.12 x 10^4 Pa. By how many degrees C will the temperature in Denver rise when the Chinook arrives? (Hint: A detailed discussion of the physics involved in the Chinook winds can be found at http://en.wikipedia.org/wiki/Chinook_wind)
Explanation / Answer
The Surface atmospheric pressure = 1.01 x 10^5 Pa (N/m^2)Surface area = 510,065,600 km^2
Force of gravity at surface per kilogram = 9.81 N / kg
if the system is in static equilibrium on the atmosphere,
mg = PA m = PA/g = 1.01x10^5 N/m^2 * (1kg / 9.81N) * 510,065,600 km^2 * (1000m/km)^2 = 5.2 x 10^18 kg Mass of the atmosphere = 5.2 x 10^18 kg the molar mass of air is 28.96 g/mol the number of moliculesin one gram, n = N/molar mass = 6.02*10^23 molecules/28.96 = 0.2078*10^23 molecules the total molecules, N = 0.2078*10^23 *5.2 x 10^18 *1000 = 1.08*10^44 molecules
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