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delirium happy

Just keep on trying till you run out of cake

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The mass of a fart
peek-a-baa
rho
A few years ago, I was listening to the radio (in the car with my mum on the way to the hospital to have my wisdom teeth removed, as it happens) and they had one of those inane "Strange but true" features that could only exist on the radio or in email forwards.

One of their alleged facts was that on average a fart weighs 5 grams.

This sounded rather dubious to me, so I did a quick calculation. If we assume so and so as the constituent gases of a fart, then use this, this and this as the relative atomic weights, then take that approximation of the ideal gas equation... then we wind up calculating that a 5 gram fart would have a volume somewhere in the region of 4 litres.

Now, it has to be stressed that that was a fairly rough and ready calculation, and I wouldn't put much stock in its accuracy. But as an order of magnitude approximation, it isn't too bad.

I don't know about you, but I've farted in the bath, where the bubbles make it easy to see the volume, and I'm quite, quite sure that even the biggest farts are nowhere even close to 4 litres.

Something is clearly amiss. Either the statement given by the radio was false, or various bits of science that I have learned were false (or both could be wrong, of course). I have absolutely no empirical evidence either way. I have never measured the mass of a fart. Nor, however, have I ever done a chemical analysis of a fart, nor measured relative atomic masses of carbon, hydrogen, oxygen, nitrogen, etc. The closest I've come to empirical evidence is seeing someone else perform demonstrations of Boyle's Law and Charles' Law, both of which are specific cases of the ideal gas law. The only real empirical evidence I have is the volume of the fart, which doesn't tell me which of the two propositions is right, only that they can't both be.

So, given this situation which of the two opposing theories would you be more inclined to believe, and more to the point why?


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Let's assume that a person farts 5g per day on average. I have no clue how accurate that is but it seems reasonable for an order of magnitude calculation.

5g is 1/200 of a kg, so it would take (1.31 * 10^22) * 200 = 2.62 * 10^24 days to fart it all out. Converting that to years give (2.62 * 10^24) / 365 = 7.18 * 10^21 years. Or seven thousand billion billion years.

For comparison, the universe is about 13 billion years old, so to fart out the whole of Pluto would take five hundred billion times as long as the universe has existed. Hopefully that will dissuade your daughter from trying to head out to the Kuiper Belt for a snack.

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