Enrico Fermi was a famous physicist who liked to pose what are now known as Fermi problems in which several assumptions are made in order to make a seemingly impossible estimate. One 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 50 km thick, has an average temperature of 15 °C, and an average pressure of 0.20 atm.
3. The radius of the Earth is about 6400 km.
4. The volume of a single human breath is roughly 500 mL.
Perform the following calculations, 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°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?
5 answers
Wouldn't the volume of the atmosphere+earth = (4/3)*pi*r^3. r would be radius of earth + thickness of atmosphere for total volume. Then determine volume of earth and subtract to obtain volume of the atmosphere.
I calculate that the total volume of Earth + thickness of atmosphere is:
(4/3)*pi*(6450000 m)^3 = 1.124*10^21
I then calculate that the volume of the Earth is:
(4/3)*pi*(6400000 m)^3 = 1.098*10^21
Finally I subtract the volume of Earth from the total volume, which gives me that the volume of the atmosphere is 2.6*10^19