It is desired to compress ethylene gas $left[mathrm{MW}=28, k=1.3, c_{p}=0.357 mathrm{Btu} /left(mathrm{lb}_{mathrm{m}}{ }^{circ} mathrm{F} ight) ight]$ from

It is desired to compress ethylene gas $\left[\mathrm{MW}=28, k=1.3, c_{p}=0.357 \mathrm{Btu} /\left(\mathrm{lb}_{\mathrm{m}}{ }^{\circ} \mathrm{F}\right)\right]$ from $1 \mathrm{~atm}$ and $80^{\circ} \mathrm{F}$ to $10,000 \mathrm{psia}$. Assuming ideal gas behavior, calculate the compression work required per pound of ethylene under the following conditions:

(a) A single-stage isothermal compressor

(b) A four-stage adiabatic compressor with interstage cooling to $80^{\circ} \mathrm{F}$ and optimum interstage pressures

(c) A four-stage adiabatic compressor with no intercooling, assuming the same interstage pressures as in (b) and $100 %$ efficiency