If we use fossil fuels until they run out, would the atmosphere recover? If so, how long would it take?
I'm going to give you a rather unconventional answer that some may make fun of, but so be it. Here goes: don't worry about the environment when it comes to burning fossil fuels! It says in the Bible, and I believe it 100%, "go and exploit the Earth for your own purposes. The birds, the trees, the land, all are yours to do what you see fit to it." (Genesis 2). We can't cause global warming!! We don't have that power. I'll tell you who has the power to give us more fossil fuels if we run out? Yeah, you guessed it! I just read a Yahoo! news article the other day, that they just discovered a pocket of rare earth elements far under the sea off the coast of Japan. These rare earth elements were only supposed to occur in western China! For the past 50 years, this area has been the only known area to have these elements, which are critical for computer manufacturing and so on. So, don't worry! The atmosphere doesn't need to ‘recover'... There's nothing to recover ‘from'... If the Earth were that fragile, we would have faced extinction at least 5x over in the 200 years alone!!! Try this one on: If the earth were that fragile, one of the Tsar Bombas (50 megaton nuke that the Soviet Union developed) would have been enough to destroy the earth!! But none of the nuclear tests ever conducted have caused irreversible damage!! The earth is entirely resilient. And it is because God made it that way, and he is NEVER gonna tell us (as the Pope would have you foolishly believe!) - "don't use that as fuel, because in 50 years you will warm the earth too much, and life will cease elsewhere in low lying areas due to global flooding". HE HAS NEVER AND WILL NEVER SAY THIS TO US.
Eventually, yes. Assuming that it takes 50 years to have natural processes remove 25 ppm of excess CO2 from the atmosphere, and the target is 280 ppm for the atmosphere to recover, if the peak CO2 concentration is 1280 ppm, just about 3 times what it is today, to reduce the CO2 level by 1000 ppm would take 2000 years.