Air is composed of 21% O2 and 79% N2 (by mol). Both of these gases in their pure

Question

Air is composed of 21% O2 and 79% N2 (by mol). Both of these gases in their pure form are valuable products, so you decide to start a company separating air into pure oxygen and pure nitrogen that you can sell (it seems like a bright idea because air is free!). How much work would it require to separate this mixture? Suppose you start with air at 100°C and 1 bar, and you produce pure oxygen and pure nitrogen at the same temperature and pressure. Do the calculationassuming the following thermodynamic efficiencies for your process:(a) 100%(b) 30%

Explanation / Answer

from first law of thermodynamics change in internal energy= Q+W

since the tempeature is constant, change in internal energy= 0 and W= -Q

Entropy change due to separation= -R{x1lnx1+x2lnx2) x1=0.21 and x2=0.79

entropy change due to separation= -8.314*{(0.21ln(0.21+ 0.79*ln(0.79)}=4.273 J/mole.K

work required for separation = T* entropy change of mixing = (100+273.15)*4.273=1594.47 J/mol

This is assuming 100% efficiency. But majority of air separation plants will have efficiency around 30%.

Hence work required for separation =1594.47/0.3=5314.9 Joules/mole

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