Air is to be compressed from $1 \mathrm{~atm}$ and $70^{\circ} \mathrm{F}$ to 2000 psia. Calculate the work required to do this per pound of air using the following methods:

(a) A single-stage $80 %$ efficient isothermal compressor.

(b) A single-stage $80 %$ efficient adiabatic compressor.

(c) A five-stage $80 %$ efficient adiabatic compressor with interstage cooling to $70^{\circ} \mathrm{F}$.

(d) A three-stage $80 %$ efficient adiabatic compressor with interstage cooling to $120^{\circ} \mathrm{F}$. Determine the expression relating the pressure ratio and inlet temperature for each stage for this case by induction from the corresponding expression for optimum operation of the corresponding two-stage case.

(e) Calculate the final temperature of the gas for cases (b), (c), and (d).