Assuming the earth never developed intelligent life capable of actively extracting fossil fuels and burning them back into CO2. Is the amount of carbon locked as as fossil fuels steadily increasing over time or does it reach a steady state at some point? Would it ever be possible that all the CO2 gets captured before the earth gets swallowed up by the sun or is the process of fossil fuels too slow for this to happen?
The events that created fossil fuels is under debate and an open question but that long term capture is a fairly slow and rare event.
But there are a few other issues, one being plant life uses carbon dioxide to make the sugar (glucose) and oxygen gas, once co2 levels dropped enough that conversion process would end. Carbon in fossil fuels is sequestered as sugars and other long chains and not as the lower energy state of co2 which is a gas.
Basically once atmospherically available oxygen and surface water decreased enough to stop life the major methods of carbon sequestration would end.
The far more likely more likely scenario is that co2 becomes far more common, and the balance of sun energy received and radiated changes causing a runaway warming situation. If it got to the stage where sugars “burned” it would get into a runaway situation and very few long carbon chains would exist near the surface.
Remember entropy is all about increases in information and most of that is tending to lower energy states and increased free energy and the lowest energy state is co2. While there is a risk of causing confusion with the mistaken idea that entropy is “disorder”, the second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. What you are asking about would require that it is (ignoring that the earth is not a closed system)
The short answer is that the CO[sub]2[/sub] would never go away completely, because there are other geological processes that release carbon. Most notably, the mantle contains large amounts of carbon that has been there since the formation of the Earth, and some of this carbon is released into the atmosphere by volcanoes and other geological activity.
It also wouldn’t surprise me if, in the absence of clever savannah apes extracting fossil hydrocarbons from the ground, these deposits would get pushed up to the surface via normal geologic processes and eventually oxidize into the atmosphere (either via chemical or biological processes.) But I’m not sure about the timescale on which this would occur.
Intelligent life doesn’t really enter. If there’s animal life, there’ll be atmospheric CO2. That’s in addition to the geologic processes, like volcanism, that also produce CO2.
That’s how clever savannah apes find many fossil hydrocarbon deposits even today:
“Come and listen to a story 'bout a man named Jed,
Poor mountaineer barely kept his family fed.
Then one day he was shooting for some food,
And up through the ground come a bubbling crude”
Oil, that is.
There’s a long term sequestration of CO[sub]2[/sub] in carbonate rocks. We had a thread about this not too long back.
As for fossil fuel buildup, they aren’t accumulating at the rate they were in the Carboniferous. And there have been instances of them burning in the ground. There are several deposits of coal that are currently on fire, although mostly at a low rate. For example, the Buning Mountain in Australia. (There’s another at Centralia, Pennsylvania, but that was a fire started in a mine, so would not be burning without humans.) And I understand there was a large scale burning of coal deposits in the US West some time in the past. Not everywhere in the West, though, or there wouldn’t be any coal in Wyoming.
The Red Canyon #5 mine and the Almy #4 mine near my home town are still burning after explosions in the late 1800’s and I think that the Kemmerer and Hanna mines are still burning too.
In Almy (which is my home town) they are still hot enough to melt any snow that falls on the old entry points during the winter. The low-sulfur coal mined up in the NE of the state are strip mines which would have a different problem.
You can read about the carbon cycle at wikipedia. It involves plants, animals, atmospheric, geologic, and oceanographic processes.
Before humans, CO2 levels fluctuated, but didn’t drop close zero. A graph of the past 400,000 years of CO2 history is available here: Carbon dioxide in Earth's atmosphere - Wikipedia