There are some resource questions posed by the book and film The Martian:
In the movie, they show some high-tech buildings on Mars … the lead character spends more than a year bouncing around those, yet his oxygen supply never seems to be a problem. Is this a realistic view of $O_2$ management? Is there a real-life system that could be operated like this?
Okay, first things first: You can take as much oxygen as you're willing to pay for. One liter of LO2 at 1.41kg converts to 810 liters of oxygen at 1 bar, so space isn't that much of a problem; the weight is - but you only need it for the trip, because you can manufacture as much as you desire on Mars from the atmosphere.
Now that means question 2 only matters during the trip, and currently the numbers for that aren't too good: about 30% if you have the CO2 separated from air already. But again, that's for the trip. On Mars we have all the CO2 we'd ever wish for, so we can be as wasteful as we wish, providing we keep our energy demands in check.
So now for question 3, where things are getting interesting. The paper on electrolysis of CO2 gives us some numbers to work with:
With 2V of power supply, drawing 0.3A of current, processing 10cm^3 of CO2 at atmospheric pressure, heated to 950C, per minute, they were able to obtain about 1.5cm^3 of pure oxygen per minute.
0.3A * 2V is 0.6 Watt. That's energy demand for 1.5cc/min of O2 from 10cc of CO2 at 1 bar.
Human needs 550 liters of pure oxygen per 24h. That's 380cc/minute.
To obtain 380cc of oxygen per minute we must scale up both power consumption and CO2 intake. 152 Watt, and 2533cc of CO2.
152W looks very promising. The electrolysis really doesn't cost us all that much. There are two problems left though.
First, the CO2 on Mars is not at 1 bar, but at 0.006 bar. And then, its temperature rarely rises above 0C.
So we're scaling our intake up again. 2533cc/0.006 is 0.42 m^3. That volume of martian atmosphere must be processed each minute - but that's still a pretty reasonable intake. But we need to pressurize it to 1 bar, not only to improve electrolysis efficiency but primarily because we must pump that oxygen into the habitat!
Using some figures from Compressed air energy storage Wikipedia page, I found compressing 1m^3 of gas per minute, by 1 bar (from ~0, more precisely 0.006, to 1 bar) takes about 7.16KW. If we match it with our required 0.43m^3, we're obtaining almost precisely 3KW. Add another 1KW of losses on pumping efficiency (1/3 is a reasonable estimate), for 4KW and here's our primary energy cost, totally dwarfing the 152W of electrolysis. The good news though is that most of that energy will appear as heat in the newly compressed CO2. I don't know how much you will heat 2.5 liter of CO2 at atmospheric pressure if you apply 4KW for a minute to it, but with lousy heat capacity of gasses, I can only assume that's a lot. Somebody correct me if I'm wrong here, but our 950C temperature problem seems to be solved.
That way, in a little over 4 kilowatt, we have oxygen for one human indefinitely. It's not cheap but it's definitely doable with solar panels and we're getting a lot of free heat for habitat heating, as the discarded heated CO2+CO mix can be used to heat up the hab before being depressurized and released back into the atmosphere.
It is possible we could do much better by working at 0.006bar with the electrolysis and pressurizing only the produced O2, but I didn't find any studies of efficiency of that process in such low pressure, so what I presented is what I know.
Now, for the last question: Is this a realistic view of O2 management? Yes, it is. The produced oxygen can be liquified for storage, transport and use on the return trip or as oxidizer for launch. It's just a matter of enough energy input - the device in the article worked for 253 hours and didn't show any signs of wear - it seems that the pump might be more vulnerable than the electrolytic separator, but compressing gas by 1 bar, at less than 1m^3 per minute is not really such a heavy task for a compressor; building one that can last years is an engineering challenge, but definitely not an impossible one.
Is there a real-life system that could be operated like this? - yes, with 1.5cc/minute oxygen output. Definitely not sufficient for Mars survival, but definitely possible for upscaling. Since The Martian takes place in 2035, we can safely assume reliable, efficient systems of required throughput will be made by then.
Edit: When I said a lot, I still underestimated the actual heat. The machinery will definitely require some very serious cooling.
Our CO2 will get very hot; its specific heat changes with temperature but at some 7000K it's around 1.5 kJ/kg K. At 1.98 kg/m^3 @ 1 bar, 2.5l of CO2 is about 5 grams. 7.5J/K for our minute dose. 4KW for 1 minute is 240 kJ. 240,000/7.5... 32,000 Kelvins. So, we're about 31,000 Kelvins ahead of the target. An extra cooling system is a must.
