If it was cold enough for the atmosphere to condense, how deep would the ‘liquid air’ be?
Short answer: About 10 meters deep.
Long answer: The total mass of the atmosphere is about 5×1018 kg  with some annual variation due to water vapor. The average density of liquid air is close to 880 kg/m3, between the densities of liquid oxygen and nitrogen, and super close to the density of olive oil. Since the surface area of the earth is about 5×1014 m2, straight forward division tells us that if the atmosphere was condensed to a liquid it would cover the entire earth with a 10 meter thick sea of liquid air.
Think on that for a second. The entire column of atmosphere above you, extending miles (literally all the way to space), would only be 10 meters thick if condensed to a liquid. Liquids are amazingly dense compared to gasses.
Okay, that’s a bit of a stretch. I assumed the density of liquid air to be the density at 1 atmosphere of pressure, because that’s the density of liquid air we can produce on earth (duh! we’re producing it in atmosphere!) – if we truly liquefied the atmosphere, it would only be a pressure of 1 atm at the bottom. At the top there would be no pressure, because there’s no weight on top of it pressing down!
So what happens next? Without the pressure of the atmosphere on top of our liquid air, it would immediately begin to vaporize. If we were somehow able to liquefy the atmosphere, despite the pleas of the laws of thermodynamics not too, it would just boil and reform the atmosphere. Why? Because of the heat of the sun.
But what if it didn’t? What if we teleported the earth far away from the sun, despite the pleas of General Relativity not too? In this case, we’d be less likely to have liquid oxygen and nitrogen and more likely to have solid liquid and nitrogen. The evaporating gas from the liquid carries heat away with it, ultimately freezing what’s left of the liquid air. The atmosphere would strike an equilibrium, depositing some gas onto the ice in the cold winter, and sublimating some ice back into gas in the warm summer season. This is sort of what happens on Mars with CO2 and its polar ice caps.
In reality, the earth has enough gas to make one of the thickest atmospheres in the solar system which makes this process not happen with nitrogen and oxygen, but this annual cycle of temperature dependent deposition and evaporation does happen with one compound in our atmosphere- water. Think on that the next time you see a picture of the poles.
image credit: NASA via Wikimedia Commons
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