In large gas-compression stations (for example, on a natural gas pipeline), the compression is done in several stages as in Fig. P7–252. At the end of each stage, the compressed gas is cooled at constant pressure back to the temperature at the inlet of the compressor. Consider a compression station that is to compress a gas (say methane) from P1 to P2 in N stages, where each stage has an isentropic compressor coupled to a reversible, isobaric cooling unit. Determine the N–1 intermediate pressures at the outlet of each stage of compression that minimize the total work required. How does this work compare
to the work needed to do the entire compression with one isentropic compressor?

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P1,T P2, T P3, T P2, T2 P3, T3 P4, T4