Breathing Room

Last night I attended my very first Jiu Jitsu class and so have raised my Batman training to the next level. I'll tell you all about it tomorrow. But tonight, let's answer yesterday's non- Superhero Fermi Problem (we'll use this answer for the next, and second from last Fermi problem).

The atmosphere pushes down on you (you might not have the weight of the world on your shoulders but you definately have the heavens weighing down on you). That pressure is measured in atmospheres (atm). The pressure of the atmosphere is normally 1atm (duh). In useful units 1 atm = 10^5 N/m^2. Where's that pressure come from? All the air molecules over head weigh down on you. Since the pressure is force per area, above every 1 meter squared there is a force (or weight) of 10^5N and remembering Force=Weight=mg where we round gravity to 10m/s^2. So the mass of the particles above 1 meter squared is 10^4kg.

We already used the area of the earth in the buses Fermi question and we use it again here: surface area of earth =5*10^{14} m^2. We know the mass of atmosphere above every square meter AND we know the total number of square meters that make up the surface of the planet. Therefore, we estimate the total mass of the atmoshere to be 10^4 kg/m^2 *   5*10^{14} m^2 = 5 * 10^{18}kg of air in the atmosphere!

BUT

Air isn't pure oxygen, O_2. The percent of the atmosphere that is O_2 definitely isn't 100%and it's not 1%. So we could guess 10% but I think that it's fairly common knowledge that air is 20% O_2 so let's use that number.

5 * 10^{18}kg * 20/100 = 10^{18}kg of oxygen. That's alot of elephants - or subway trains for that matter of oxygen. Wikipedia says that the atmosphere is really 5 quadrillion tons. A ton is 1000 kg and a quadrillion is 10^15 so we were only off by a factor of 5. Once again, we're pretty darn close.