Air, the element of the gassy stuff all around us. Air has one of the strongest Nymphs in my oppinion, but I've wondered a while now about one thing:
Can you calculate about how much of earths atmosphere consists of farts?
Let me try to do this question as much justice as xkcd's whatif would.
A little bit of research suggests that an average human breathes in about 10-20 liters of air per minute across all activities. Of course, you don't fart all the air you breathe in, so let's assume that we fart a percentage of that back out and rest comes out as exhalation. Let's assume that the ratio is 0.1% of all air breathed in. This gives us .01-.02 liters of fart per minute per person. Therefore, for the average person, they'll fart ~7900 liters per year.
Wikianswers tells me that Earth's effective atmosphere is 4.2 billion cubic kilometers of air. That would translate to 4.2*10
21 liters of air.
Then we have to worry about our population. Let's just play with nice round numbers. In other words, billions. Wiki tells me that the world population hit 1 billion around 1804, then 2 around 1927, 3 in 1959, 4 in 1974, 5 in 1987, 6 in 1999, and 7 in 2012. For each billion people, we get 7.9 trillion liters of air per year.
This brings us to the next point: It's not possible that only unfarted air gets farted. Of course, as the amount of farted air increases, the chance that someone has breathed it in (and refarted it) increases. Therefore we need to consider the ratio of farted air to unfarted air:
percent of newly farted air=(7.9 trillion liters*(1-%farted from last year)/total air)
Therefore, we have the model for checking out farted air:
% farted total=(7.9 trillion liters*(1-%farted from last year)/totalair)+%farted from last year
I.E.
X
t+1=(7.9*10
12*(1-X
t)/(4.2*10
21))+X
tI'd calculate it for you but I'm bad with wolfram alpha.
Let's estimate it instead.
The total number of billions of people we need to calculate for is (1927-1804)*1+(1959-1927)*2+(1974-1959)*3+(1987-1974)*4+(1999-1987)*5+(2012-1999)*6+(2014-2012)*7. This is 436.
(436*7.9 trillion)/4.2 sextillion~0.8*10
-6. Let's say it's 1*10
-6 or .0001% of our atmosphere being farts. I guess unstable gas isn't all that common.