You have a requirement to compress natural gas $(k=1.3, \mathrm{MW}=18)$ from $1 \mathrm{~atm}$ and $70^{\circ} \mathrm{F}$ to 5000 psig. Calculate the work required to do this per pound of gas in a $100 %$ efficient compressor under the following conditions:

(a) Isothermal single-stage compressor

(b) Adiabatic three-stage compressor with interstage cooling to $70^{\circ} \mathrm{F}$

(c) Adiabatic two-stage compressor with interstage cooling to $100^{\circ} \mathrm{F}$