A geothermal power souce is used to operate a plant to produce oxygen. A deep well of water with volume 1000 m3 at initial temperature 100 Celsius is used as the power source for the plant. There is an infinite lake nearby at a temperature 5 Celcius. The plant will separate O2 from the air at 1 atm pressure and 20o Celcius. The air is a mix of ideal gases (O2 and N2) with mole fractions 1/5 for 02 and 4/5 for N2.
Assuming Carnot efficiency, how many moles of 02 can be separated out before the power source is depleted (remember: the temperature of the well decreases as energy is extracted from it).