$(20$ POINTS$)$ Applying the exergy analysis to the distillation of air

Apply an exergy analysis to the separation of air $($assumed here for simplicity to consist

of just nitrogen and oxygen at volume fractions $79$ and $21\%,$ respectively$)$ at $0\mathrm{.}1$MPa and

that the two products $($assumed pure Nitrogen and Oxygen$)$ are in the dry saturated vapor

state, conditions under which practically you can neglect any enthalpy changes between

the products and the feed of the distillation.

The following information can be used:

Minimum reflux ratio $=0\mathrm{.}402$

The heat loads of the reboiler and the condenser can be assumed to be the same $Q{B}_B=Q{D}_D$

$=16520k\frac{J}{kmol{O}_2}$ corresponding to the following temperatures, $T_B=90\mathrm{.}2K,T_D=77\mathrm{.}3K,$ with the temperature of the environment $T_0=293K.$ For this separation the

minimum exergy input to effect it$,$ has been calculated as Wmin$=6500k\frac{J}{kmol{O}_2}.$

Evaluate the thermodynamic efficiency of the process ${}_{\text{t}\text{h}\text{e}\text{r}\text{m}\text{o}}$ under ideal conditions

$($minimum reflux, no temperature difference in supplying the heat to the

reboiler$/$removing it from the condenser$)$ as well as when a$)$ the reflux ratio is $20\%$ higher

than the minimum and b$)$ the reflux ratio is $20\%$ higher than the minimum and there is a $3$

degrees difference in supplying the heat to the reboiler$/$removing it from the condenser

from the temperature at the bottom$/$top of the column. Comment on the results.