# Joan of Arc Heavy Breathing 8/2/19

By Richard Bleil

Joan of Arc was born around 1412 and fought alongside the French in the hundred-year war in support of the yet uncrowned King Charles Vii, claiming she received visions from archangel Michael, Sint Margaret and Saint Catherine of Alexandria instructing her to do so. Her heroism and leadership during the war continue to be lauded to this day. When captured by the Burgundian Faction (a group of French nobles allied with the English) at Compiegne on May 23, 1430 and subsequently handed over to the English. After a trial, she was burned at the stake on 30 May, 1931 for her “crimes”. She was canonized as a saint herself by the Catholic Church in 1920.

Well at least it didn’t take very long.

And you are breathing the same air as she did, despite her short nineteen-year life. In fact, in every breathe you take, you breathe in 54 million molecules exhaled by Joan of Arc. Yup, 54 MILLION molecules exhaled by Joan of Arc WITH EACH BREATH!!! Here is the calculation.

First, a quick lesson in scientific notation. Scientific notation is a shorthand way to write exceptionally large (or small) numbers. Thanks to calculators in the ‘70’s, it’s often written as an “E” notation, which I shall adapt here. So if we have 5,233, as an example, we can write this as 5.233E3. By convention, the decimal point always goes after the first non-zero whole number (engineering notation says go right before it, but we use the scientific notation here). The number after the E means “move the decimal point this many places to the right”. Now, in a case like this, scientific notation doesn’t help much, but if we were talking about, say, 6.3 billion, which written out would be 6,300,000,000. In scientific notation, it would simply be 6.3E9. Notice that we don’t put the zeros. As you move the decimal point nine places to the right, any “missing” numbers are automatically assumed to be zero.

Now, on with the calculation. I’m going to calculate the volume of the earth without the atmosphere first, then with the atmosphere. The difference between the two will be the volume of the air. So, the radius of the earth is 6.371E6 m, or 6.371E8 cm. The volume for the volume of a sphere is V=4(pi)r^3/3, so the volume of the earth is 1.083E27 cubic centimeters.

The height of the atmosphere is 12 km, which is 1.2E4 m, or 1.2E7 cm. Thus, the radius of the earth WITH the atmosphere is 6.49E8 cm. Using the same calculation as before, the volume of the earth plus the atmosphere is 1.15E27 cm^3. The difference, (1.15E27-1.08E27=)7.0x10E25 cm^3, is the volume of the atmosphere.

Isn’t this fun?

Now, we know the volume of air surrounding the earth. Using the average density of air, we can convert this to the mass of air surrounding the earth, which will eventually lead to moles, and then the number of molecules of air. The average density of air is 1.3 g/L, or 1.3E-3 g/mL (the negative sign in front of the three means that you move the decimal place three places to the left, rather than right). We need mL, because 1 mL equals one cubic centimeter, so this gives us the same units as above, or 1.3E-3 g/cm^3. By multiplying the average density of air by the volume of the atmosphere, we discover that the mass of air is 9.1E22 g of air. This, by the way, is 2.0E20 pounds, or 1.0E17 TONS of air. This is 100,000,000,000,000,000 tons, or one thousand trillion tons of air. Right there, resting on your shoulders.

Okay, so far so good. Now, let’s find out the volume of air that Joan of Arc breathed in her lifetime. Each breathe a human takes is approximately 500 cm^3 (500 mL). The total volume of a lung is significantly larger (about ten times larger) but remember there is air left in the lungs with each breathe. Using the average density of air, that means that each breath is approximately

A human breathes about 15 times minute. So, one year is 365.25 (accounting for leap years) days, or 5.3E5 minutes. In nineteen years, then, Joan of Arc took approximately 7.9 million breathes, for a total volume of 3.9E9 cm^3 of air.

Now, if we take the ratio of the volume of air that she breathed and the volume of air on the earth, we see that she breathed approximately 5.6E-19% of the earth’s air (the negative number in front of the 19 means you move the decimal nineteen places to the LEFT).

Doesn’t seem like much, does it?

But, at this percentage, that means that for each breathe that YOU take, 2.8E-12 cm^3 is the same air that she breathed. Now, let’s figure out how many molecules that is. First we find moles, then we can use Avogadro’s number to find out how many molecules that is.

Using the same density of air, we see that the mass of each breathe we take is 2.6E-15 g of each breathe we take has been exhaled by Joan of Arc. The average formula mass of air is 29 g/mol, so dividing the mass by the average formula mass, and we breathe in 9.0E-17 moles of air once exhaled by Joan of Arc.

Eesh, this is becoming less and less impressive. But remember, there are 6.0E23 molecules for each mole of anything, so this amounts to 5.4E7, or 54,000,000 molecules.

Yes, you breathe 54 MILLION molecules of air that was once exhaled by Joan of Arc WITH EACH BREATHE YOU TAKE!!!!!!!

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