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I read that we are facing the very real possibility of Earth's average temperature rising by more that 2 degrees Celsius by the end of the century.

As I understand our planet is constantly loosing its atmosphere and oceans to space but at a very microscopic and thus safe levels. Will Global warming lead to accelerated evaporation converting Earth into a dead waterless desert in the observable future?

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    $\begingroup$ I'm sure somebody more expert will come along with a detailed answer, but the short answer is "no". We can be confident of this because the Earth has been hotter in the past (before humans emerged) and it retained its atmosphere and oceans. $\endgroup$ – Semidiurnal Simon Aug 31 '18 at 10:54
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    $\begingroup$ Research someone could do: for any given temperature, find out what quantity of water/air has enough kinetic energy to reach escape velocity, and what percentage are also going in the right direction (the faster the particle, the less vertically it has to travel to escape the Earth's atmosphere). Unfortunately, I'm not interested enough in this problem to do that because I agree with @SemidiurnalSimon and also believe the necessary temperature would mean the oceans would be full of scalding hot water and we'd probably all be dead. $\endgroup$ – Barry Carter Sep 1 '18 at 18:13
  • $\begingroup$ All I can tell you is that there are predictions that oceans will evaporate in about a billion years or so when the sun is hotter, but I assume you are talking about man-made global warming. I guess the question would be whether human neglect could tip the scales into a positive feedback system that would turn our planet into a "Venus". My guess is that mankind would be set back to the stone age (metaphorically speaking) and natural processes would bring the Earth into equilibrium before it would get hot enough to lose oceans. $\endgroup$ – Jack R. Woods Sep 10 '18 at 18:11
  • $\begingroup$ So global warming causes sea levels to rise and evaporate ? $\endgroup$ – blacksmith37 Sep 22 '18 at 15:48
  • $\begingroup$ @blacksmith37 That's two parallel processes happening simultaneously. $\endgroup$ – Denis Kulagin Sep 22 '18 at 15:52
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We know that terrestrial hydrogen reaches space because ultraviolet images reveal a halo of hydrogen atoms surrounding the Earth (Fig. 2). Some of these atoms are escaping while the rest are trapped. The temperature at Earth’s exobase is typically around 1000 K, although it varies as the Sun’s ultraviolet output cycles up and down every 11 years or so. At 1000 K, hydrogen atoms have an average speed of 5 km/sec, which is below Earth’s escape velocity of 10.8 km/sec at the exobase. Yet hydrogen atoms still manage to escape because many move faster than average. This loss of particles from the energetic tail of the speed distribution is called “Jeans’ escape” after James Jeans (from the University of Cambridge), who described it mathematically in the early twentieth century.

The escape of planetary atmospheres Catling & Zahnle, Scientific American,2009 1

The exobase is the lower boundary of the exosphere.

enter image description here

I guess that two degrees increase in surface temperature would not make much difference to the $~1000K$ at the exobase.

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Volume of all oceans = 1.33E9 km^3.

Molar volume of water = 1.802E-14 km^3/mol

Moles of water in the oceans = (1.33E9 km^3)*(1mol/1.802E-14 km^3) = 7.38E22 mol.

Enthalpy of vaporization of water = 40.65 kJ/mol

Energy required to turn all of the oceans from liquid to gas = (40650 J/mol)*(7.38E22) = 3E27 joules.

How much energy is that? It's a lot. According to www.wolframalpha.com it is equal to as much energy as the sun produces in eight seconds.

And that is only the amount of energy required to convert the liquid water into gas. It doesn't take into account the amount of energy required to heat the liquid up to 100C or the gas to escape velocity temperatures.

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    $\begingroup$ (Or to put it to Earth values... looks like we take in about 21.6 MJ * 510.1 trillion * 365 = 4E24 J of energy per year from the sun as a whole. So that's on towards 1000 years to boil off the oceans... even if every bit of solar energy went to boiling them. [And then a couple °C holdover is only a tiny amount (< 1%) of Earth's temperature, when in the absolute Kelvin scale required for such calculations)]. Now that's not to say it's not a ton of energy, just puts the scale of Earth's systems in scope.) $\endgroup$ – JeopardyTempest Sep 20 '18 at 23:08

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