Chapter 8, Problem 42P

A compressor is operating at compression ratio $R_c$ of 3.0 (the pressure of gas at the outlet is three times greater than the pressure of the gas at the inlet). The power requirements of the compressor $H_p$ can be determined from the equation below. Assuming that the power requirements of the compressor are exactly equal to $zR{T}_1/\text{MW}$, find the polytropic efficiency n of the compressor. The parameter z is compressibility of the gas under operating conditions of the compressor, R is the gas constant, $T_1$ is the temperature of the gas at the compressor inlet, and MW is the molecular weight of the gas.

$\text{HP}=\frac{zR{T}_1}{\text{MW}}\frac{n}{n-1}\left(R_c^{\left(n-1\right)/n}-1\right)$