Calculate the work per pound of gas required to compress air from $70^{\circ} \mathrm{F}$ and 1 atm to $2000 \mathrm{psi}$ with an $80 %$ efficient compressor under the following conditions:

(a) Single-stage isothermal compression.

(b) Single-stage adiabatic compression.

(c) Five-stage adiabatic compression with intercooling to $70^{\circ} \mathrm{F}$ and optimum interstage pressures.

(d) Three-stage adiabatic compression with interstage cooling to $120^{\circ} \mathrm{F}$ and optimum interstage pressures.

(e) Calculate the outlet temperature of the air for cases (b), (c), and (d) above. For air: $c_{p}=$ $0.24 \mathrm{Btu} /\left(\mathrm{lb}_{\mathrm{m}}{ }^{\circ} \mathrm{F}\right), k=1.4$.