0.04% Is a Lot of Molecules
An evergreen in the denial crowd is that CO2 is only a very small part of the atmosphere so how could it make a difference.
ADDED: In the comments Mark B points out that
The silliness is that it is precisely because CO2 is a very small part of atmosphere that humans are able to meaningfully change it's concentration. For example we are depleting O2 at the same rate as we are adding CO2, but the change is a negligible percentage of the normal content so only the most pedantic would dwell on it. That is, we've changed the CO2 concentration by about 45% and the O2 concentration by about 0.06%.The short answer is that the atmosphere is very big. Eli has a nice BOE (back of the envelope, not quite a Fermi problem but Eli would be quite pleased if others thought it in the neighborhood of same) answer
| "... the estimation of rough but quantitative answers to unexpected questions about many aspects of the natural world. The method was the common and frequently amusing practice of Enrico Fermi, perhaps the most widely creative physicist of our times. Fermi delighted to think up and at once to discuss and to answer questions which drew upon deep understanding of the world, upon everyday experience, and upon the ability to make rough approximations, inspired guesses, and statistical estimates from very little data." |
It starts by estimating the number of molecules in a m3 of air. Well a Bunny who knew Loschmidt's number 2.7 x 1019 cm-3 or 2.7 x 1025 m-3 (which is the same thing since 1 m3 is 106 cm3 ) could start there or you could rearrange the ideal gas law
pV = nRT to n/V = p/RTSince 1 atm is 101, 325 N/m², the gas constant R is 8.314 J K-1mol-1 and 0 C is 273 K
n/V = 101 325 N/m² /(8.314 J K-1mol-1 x 273.15 K) = 44.64 mol m-3 which is a little surprising, since the average weight of a molecule of air is ~ 29 g or 0.029 kg so a cubic meter would weigh 1.3 kg but that is another direction. In any case since there are 6.02 x 1023 molecules per mole that gives us Loschmidt's number again, in case a bunny has forgotten it or 2.69 x 1025 m-3.
If 400 ppm or 0.04% of that is CO2 there are 1.07 x 10 21 CO2 molecule in a cubic meter. A useful estimate of the average distance between CO2 molecules is the inverse of the cube root. of the number density. That is 4.5 x 10-8 m.
So how does that compare to the wavelength of light at which CO2 absorbs light in the IR. Hmm, that's about 14 microns. A micron is a millionth of a meter, So how many CO2molecules are there along one wavelength of IR light where it is capable of absorbing.
About 300.
That's enough
POSTED BY ELIRABETT AT 10:37 PM
Florifulgurator said...My answer to that evergreen: "Put 250 microgram of LSD in 250g of unchlorinated water. That's 1ppm LSD. You sure will swallow that glass of water. Report back what you have seen."
8/6/17 7:07 AM
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