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It is estimated that the Earth is losing about $5 \times 10^7 kg$ per year. Most of it due to hydrogen loss. I suppose this has an impact on the pressure of the atmosphere in general.

Thus, I am wondering how the pressure at sea level is varying over time from the Earth's birth up to now and how it could go. I.e. which model and equations are involved?

Edit: To clarify I am hinting at that a loss of mass of a gas can lead to a change in pressure at sea level. So I would expect the pressure to diminish over time from now and on.

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    $\begingroup$ I would suspect the oxygen catastrophe once plants evolved would have been a much bigger disruption, given that O2 is about 20% of the atmosphere today and was ~0% before plants... $\endgroup$ – Jon Custer May 23 '19 at 17:30
  • $\begingroup$ is that kg per meter squared or kilometer squared? $\endgroup$ – user207455 May 23 '19 at 17:40
  • $\begingroup$ @Solar Mike it's just kilogram. $\endgroup$ – thermomagnetic condensed boson May 23 '19 at 17:47
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    $\begingroup$ If you go back to the era when the temperature was too hot for the oceans to be liquid, then I think a lot of CO2 that today is dissolved in the oceans was in the atmosphere. Possibly in that era the pressure was orders of magnitude higher, like Venus. Also not sure about volcanic eruptions in the early Earth. They disrupt our atmosphere even today. $\endgroup$ – Ben Crowell May 23 '19 at 18:29
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    $\begingroup$ @thermomagneticcondensedboson - The very, very tiny amount of hydrogen currently in the Earth's atmosphere doesn't last very long. It escapes. It is produced by sunlight-induced electrolysis of the tiny amount of water that manages to reach the stratosphere. The oxygen produced by this electrolysis mostly stays in the atmosphere, the hydrogen mostly escapes. The issue then isn't how much gas the Earth has lost by this process. It's how much water the Earth has lost over time. And it's potentially quite a bit, up to 1/3 of the the oceans' waters by some estimates. $\endgroup$ – David Hammen May 23 '19 at 22:34
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You are right in thinking that atmospheric pressure diminishes over time,but it is impossible to give precise figures for the pressure in any particular geological period except the present. The Earth's primeval atmosphere,as on Mars & Venus,was largely CO2,& the pressure was more than twice what it is today. As you say,H2O has been split in the upper atmosphere & the H2 lost into space along with any residual H2 & He that may have existed 4 billion years ago. A lesser amount of O2 must also have been lost,& some O2 was also absorbed by oxidation of surface elements,notably Fe. A very important amount of CO2 has been extracted by living organisms & buried as fossil fuels & limestone Some CO2 has been returned by volcanoes,but not as much as was extracted.

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