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I have done some rough calculations of how long it might take humanity: approx 80,000 years (that's taking Earth's population as 7.5 billion, 11,000 litres a day of breathing, the weight of 1 litre of air at sea level at 1.225 grams, and the total weight of the atmosphere at 5140 trillion tonnes)

Please let me know if my calculations are massively out!

My question for you is admittedly much more complicated to answer - how long would it take all animal species combined to breathe the equivalent sum total weight of the atmosphere? and how long would it take all life combined (also including the weight of air of respiration in plants, fungi, algae, etc)?

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Volume is probably not the best way to think about respiration for most of life on Earth, as it only really applies to animals with lungs (a small proportion of earth's biomass). Instead, it would make more sense to think about rates of respiration in terms of oxygen demands. With that in mind, an average human needs around 0.85 kg of oxygen per day (according to NASA). So, the annual oxygen needs of the human population would found by multiplying 0.85 kg/person/day by 365.25 days/year and 7.5 billion people to get ~2.3e+12 kg of oxygen per year.

For a crude estimate of how long it would take to use up our atmosphere's oxygen at that rate, we could simply divide the total capacity of oxygen in the atmosphere (~1.4e+18 kg) by the annual oxygen demand of the current human population (2.3e+12 kg), to get a rough estimate of 600,000 years for Earth's current population to use up all of Earth's current atmospheric oxygen (note that both calculations require some pretty dubious assumptions, but the problem already seems to start that way if I'm reading it right).

For an even cruder estimate of all life on earth, we can again take the Atmospheric Oxygen capacity (~1.4e+18 kg) and divide by the annual oxygen flux from atmosphere to biosphere (~3.0e+14 kg) to get around ~4700 years. (note that this assumes no flux from the biosphere back into the atmosphere, and also assumes that lithospheric flux is negligible.)

If you want to go further and calculate how long it would take for just animals to use up an atmosphere worth of oxygen, you could start by looking at how Earth's biomass is distributed, and make some more assumptions about the oxygen demand of other animals compared to humans following this same idea that I've used above.

Capacity and Flux estimates came (via wikipedia) from (Walker JC (1980) "The Oxygen Cycle". The Natural Environment and the Biogeochemical Cycles), but there are probably more up-to-date estimates available somewhere. The general idea would be the same.

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  • $\begingroup$ Thankyou for the answer @MikeyC, those numbers from the oxygen cycle wiki page are really interesting too. Our initial figures are closer than they seem... as I was calculating the total amount of air that passes in and out of our lungs, only approx. 5% of which is taken in as oxygen... which should make my number 20 times less than yours, not 10 times less, so I will check that when it comes to doing the math more thoroughly.... $\endgroup$ – Amphibio Jan 12 at 19:01
  • $\begingroup$ I've started towards a way to figure out an answer - 1 litre of CO2 weighs 1.964g at NTP, and the amount of CO2 in one litre of air is about 0.04%. So one litre of NTP air contains 0.0007856g of CO2. $\endgroup$ – Amphibio Jan 13 at 13:42
  • $\begingroup$ An adult tree (yes, very generic!) can take in about 21kg of CO2 per year, or 21,000 grams. 21000 / 0.0007856 = 26731160. So an adult tree must process at least 26 million litres of air a year (and that is assuming it is being 100% efficient, which it won't be... humans take up about 5% of available oxygen that they breathe, not sure what the rate is for stomata...) $\endgroup$ – Amphibio Jan 13 at 13:43
  • $\begingroup$ There are an estimated 3 trillion trees on Earth. 3 trillion x 26 million = 8.1*10^19 litres .... however, I now realise I had the atmosphere in the units of tonnes, not litres... $\endgroup$ – Amphibio Jan 13 at 13:49
  • $\begingroup$ ... So that would be 9.92 x 10^19 grams of air, or 9.92 x 10^13 tonnes of air. Which is about 100 trillion tonnes of air, if I have understood the conversions right $\endgroup$ – Amphibio Jan 13 at 13:59

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