Many hours a given tuner works in a year. Another famous example of a Fermi prob
ID: 867987 • Letter: M
Question
Many hours a given tuner works in a year. Another famous example of a Fermi problem is "Caesar's last breath" which estimates that you, right now, are breathing some of the molecules exhaled by Julius Caesar just before he died. Assumptions: 1. The gas molecules from Caesar's last breath are now evenly dispersed in the atmosphere. 2. The atmosphere is 50km thick, has an average temperature of 15 degree C, and an average pressure of 0.20atm. 3. The radius of the Earth is about 6400 km. 4. The volume of a single human breath is roughly 500mL. Perform the following calculation, reporting all answers to two significant figures. Calculate the total volume of the atmosphere. Calculate the total number of gas molecules in the atmosphere. Calculate the number of gas molecules in Caesar's last breath (37 degree C and 1.0 atm). What fraction of all air molecules came from Caesar's last breath? Calculate the total number of gas molecules in the atmosphere. Calculate the number of gas molecules in Caesar's last breath (37 degree C and 1.0 atm). What fraction of all air molecules came from Caesar's last breath? About how many molecules from Caesar's last breath do you inhale each time you breathe?Explanation / Answer
1) The volumen of the atmosphere is the total volume of the earth minus the volume of the portion of the earth that is not the atmosphere.
Vatm = Vtotal - Vno atm
The radius of the earth is 6.400.000 m, and if the atmosphere is 50.000 m thick, the rest of the earth has a radius of 6.350.000. The volume of a sphere is 4/3pi*r3
Vatm = 4/3*pi * [6.400.0003-6.350.0003] = 2.55*1019 m3
Number of molecules:
PV = nRT
n = P*V / RT = (0.20 atm * 2.55*1019 m3) / (0.0000821 atm*m3/mol K * 288 K) = 2.16*1020 moles
Caesar's molecules:
n = (1 atm * 0.5 l) / (0.0821 atm*l/mol K * 310 K) = 0.020 moles
Fraction = 0.020 / 2.16*1020 = 9.26 * 10-23
if 9.26 * 10-23 of the air I breath is from Caesar's breath and I'm in earth, where the average conditions are 20
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