This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

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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 (as implied by "compression law pvc" for typical reciprocating compressors). • For two-stage compression, ideal intercooling to the initial temperature () is assumed, and the intermediate pressure () 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
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• Air behaves as an ideal gas. • Polytropic compression with an index n = 1.3 (as implied by "compression law pvc" for typical reciprocating compressors).
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.