Enrico Fermi (1901-1954) 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. Probably the most famous example is the estimate of the number of piano tuners in Chicago using the approximate population of the city and assumptions about how many households have pianos, how often pianos need tuning, and how many hours a given tuner works in a year. Another famous example of a Fermi problem is \"Caeser\'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 bar. 3. The radius of the Earth is about 6400 km. 4. The volume of a single human breath is roughly 500 mL.

1)Perform the following calculations, reporting all answers to two significant figures. Calculate the total volume of the atmosphere.
2)Calculate the total number of gas molecules in the atmosphere.
3)Calculate the number of gas molecules in Caesar\'s last breath (37 °C and 1.0 bar).
4)What fraction of all air molecules came from Caesar\'s last breath?
5)About how many molecules from Caesar\'s last breath do you inhale each time you breathe?

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PV = nRT

Step 2

The ideal gas law is also known as the general equation of gas refers to the equation of state of a hypothetical ideal gas. It is a good approximation which is used to describe the behavior of many gases under a vast number of conditions.

PV= nRT

P = Pressure of the gas

V= Volume of the gas

n = no of moles of the gas

R = Gas constant

T = Temperature of the gas

Step 3

The relation between number of moles and number of molecules is as follows:

Number of moles = Number of molecules/ Avogadro's number