Calculate the work required for single-stage and two-stage compression of air from 1 bar to 10 bar, assuming polytropic compression with n=1.3 and ideal intercooling for the two-stage case.

Here are the calculations to determine the cheaper option and the delivery temperatures.

Assumptions:

• Air behaves as an ideal gas.
• Polytropic compression with an index $n = 1.3$ (as implied by "compression law pvc" for typical reciprocating compressors).
• For two-stage compression, ideal intercooling to the initial temperature ($T_1$) is assumed, and the intermediate pressure ($P_i$) is optimized for minimum work.

Given Data:

• Initial volume flow rate, $V_1 = 16 , m^3/min = \frac{16}{60} , m^3/s = 0.2667 , \text