What is the minimum amount of work required to separate, Chemistry

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What is the minimum amount of work required to separate

1. What is the minimum amount of work required to separate 1mol of air at 27°C and 1atm pressure (assumed to be composed of 1/5 O₂ and 4/5 N₂₎ into O₂ and N₂, each at 27°C and 1atm pressure?

2. Prove that:

(a) Td(A/T) = -(U/T)dT - PdV + Σu_j d_nj.

(b) d(PV) = SdT + V dP + Σn_j d_uj.

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