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According to this video:

When Earth reaches the Komabayashi–Ingersoll limit, it will reach the point where a runaway greenhouse can occur. In the evaporation phase, Earth will end up with an atmospheric pressure of ~273 atm (mostly of evaporated water vapor) and an average surface temperature of 1500°C.

This is really extreme, even worse than Venus. A lot of the water will likely end up in a supercritical state. The crust itself will be so hot that it will melt and become lava. Earth from space will resemble Venus but with whiter clouds (not beige).

My question: How can I estimate/calculate the atmospheric pressure and temperature that will be reached by a given (formally) earth-like planet once it completes the evaporation phase of a runaway greenhouse?

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Pressure

Estimating the atmospheric pressure is easy.

  1. Air pressure is the weight of the column of air.

  2. All the water in the ocean (and lakes and ice sheets etc.) is now atmosphere.

  3. Earth has about 1,400 million cubic kilometers of water, weighing about 1.4E21 kg.

  4. The surface area of Earth is about 510 million square kilometers, or 5.1E14 square meters.

  5. Which gives a pressure of 1.4E21 kg / 5.1E14 m² ≈ 2,750,000 kg/m².

  6. One atmosphere is about 10,332 kg/m².

  7. Which means that a pressure of 2,750,000 kg/m² is about 266 atmospheres. (Plus one atmosphere for the pre-existing air.)

Temperature

Estimating the temperature is very much harder, and I have no idea how to do it. The critical point of water is at 217.75 atmospheres and 647 K or 374 °C; to keep water not-liquid at 267 atmospheres the temperature must obviously be greater than 374 °C, but I do not know of any quick and dirty way to guesstimate how much more.

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  • $\begingroup$ Perhaps the temperature could be estimated through a greenhouse gas calculator and using water vapour as the primary gas? $\endgroup$
    – casualworldbuilder
    Commented Jul 2 at 11:41
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It would not be a remotely simple process and I doubt there is any way of even estimating what you are after short of a detailed and complex computer simulation.

As a starting point, how long did it take the Earth to reach this point? And at what point was photosynthesis on Earth ended? Because once the means of replenishing the oxygen in the atmosphere biologically is lost, hydrogen will start to be to be lost from the upper atmosphere as water dissociates (the oxygen formed will weather oxidisable rocks). By this mechanism over sufficient time a significant portion of Earth’s water could be lost. With sufficient heating (as described) and atmospheric expansion water itself might eventually also be lost to space.

As the amount of energy reaching the Earth increases, the atmosphere itself will expand increasing its volume and reducing its pressure. The higher the water content of the atmosphere the more opportunity for cloud formation at different heights with complex effects on heat retention and radiation. Vast amounts of energy will also be required to boil Earths oceans that will take a great deal of time.

There are many other positive and negative feed back loops that would also need to be factored in. So don't hold your breath.

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  • $\begingroup$ In my earth-like planet scenario, it occurred quickly as the temperature sufficient to kick off the runaway was reached through a resurfacing event (I made another question dealing with that). I didn’t think it mattered that much how quickly things occurred to reach a runaway state (in terms of the end of the evaporation stage atmosphere and temperature). $\endgroup$
    – casualworldbuilder
    Commented Jul 2 at 11:37

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