
How much air did Julius Caesar breathe in his lifetime?
Fact:
He was killed at the age of 56 (Et tu Brute?).
Fact:
On average, a human being uses between 1 and 2 m^{3} of air per hour.
A part of the exhaled air will be reinhaled, so let's say it is 1 m^{3}/hour.
Conclusion:
In a 56 year lifetime that is 56 x 365.25 x 24
= ca. 500000 m^{3}.
What fraction of the Earth's atmosphere is that?
Fact:
The Earth's circumference is 40000 km,
so its surface is 40000^{2}/pi = ca. 5 x 10^{8} km^{2}.
Fact:
The air pressure at ground level is 1 kg/cm^{2}
and the density of air at ground level is 1.3 kg/m^{3}.
Conclusion:
The air column above 1 cm^{2}
is 1/1.3 kg = ca. 0.77 m^{3} effectively,
and 0.77 m^{3}/(1 cm^{2}) = 7700 m,
so the effective thickness of the atmosphere is 7.7 km.
This leads to a total effective atmosphere volume
of 7.7 x 5 x 10^{8}
= 3.85 x 10^{9} km^{3}
= 3.85 x 10^{18} m^{3}.
Thus, the fraction of the atmosphere breathed by Julius Caesar
is 5 x 10^{5} /(3.85 x 10^{18})
= 1.3 x 10^{13},
so about every 1.3 in 10,000,000,000,000 molecules of the Earth's atmosphere
have been inhaled and exhaled by Julius Caesar.
The Oxygen component of the air is an essential part of biological cycles,
but the 80% Nitrogen is chemically inert, so let's reduce this result
to 10^{13} = 1 in 10,000,000,000,000.
What does this mean?
Since the weather is a very turbulent global phenomenon
(it takes only a week for a Caribian hurricane to become a European depression),
all of Julius Caesar's exhaled air has been mixed with the atmosphere very
homogeneously in the more than 2000 years that passed since he died.
Your own lungs contain ca. 3 to 4 litres of air right now,
let's calculate with 4 litres.
That is (using Avogadro's law: 6 x 10^{23} molecules
is ca. 25 litres at room temperature)
a total of 6 x 10^{23} x 4/25
= ca. 10^{23} molecules.
Combining these results leads to the following conclusion:
