Let’s do the math
5.25.08 by DeusThe radius of the planet Earth is roughly 6371 km, and the troposphere extends an average of 12km above the surface. From that follows that we have [(4/3)π*63833]-[(4/3)π*63713], or 1,083,206,916,846 cubic kilometers, of atmosphere. 21 percent of that is oxygen, so there are about 227,473,452,538 cubic kilometers of O2 that we have available for breathing. Now, if the oxygen were increased by just three percent, or 32,496,207,505 cubic kilometers, the atmosphere would ignite if you lit a match. Conversely, if you subtact a few percent from those 227,473,452,538 km3 of O2, replacing it with something like CO2 or all the other stuff released by us into the atmosphere, or perhaps dropping a few nukes into the South American rainforests, there won’t be enough to sustain human life.
Feel free to check my math.
92 Comments
Interesting post, but I have a couple problems with your math and science:
1) You have computed the volume of the atmosphere, a meaningless number for your purposes due to the differences in density throughout it. To find a more meaningful number requires some rudimentary calculus. The number of moles of gas in the atmosphere can be calculated with a formula derived from the formula n = PV/RT. The formula (Integral(0,Vt)(P(V)dV))/(RT) where P(V) is an equation for pressure in terms of volume and Vt is the total volume of the atmosphere will give the total number if moles. P(h) = Ps * e^((-gMh)/(RT)) where h is height, Ps is pressure at sea level, g is earth’s gravitational constant, and M is the molar mass of air. V(h) = (4pi/3)((h + Re)^3 - (Re)^3) where Re is the radius of earth. This equation can be rearranged as follows:
V/(4pi/3) = (h + Re)^3 - Re^3
V/(4pi/3) + Re^3)^(1/3) = h + Re
h = (V/(4pi/3) + Re^3)^(1/3) - Re
Thus combining the two equations yields P(V) = Ps * e^((-gM((V/(4pi/3) + Re^3)^(1/3) - Re))/(RT)). This can be integrated (if you feel like it - I don’t) and plugged into the equation to get a much more accurate idea of the amount of air in the atmosphere.
2) The air can’t catch fire. Fire requires a) an oxidizer, and b) a fuel. Oxygen is the oxidizer. There is no fuel (nitrogen, argon, water, and carbon dioxide, the four other largest components of the atmosphere, are non-flammable).
I do think this is a very interesting topic of research/conversation!
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