Two-stage compression with intercooling: typical simplifying assumptions Which of the following assumptions are commonly made for analytical treatment of two-stage air compression with an intercooler?

Introduction / Context:
When analyzing multistage compression with intercooling, textbooks adopt idealized assumptions so that closed-form expressions for work, temperatures, and optimal intermediate pressure can be derived. Knowing these assumptions helps students judge the applicability of results to real machines.

Given Data / Assumptions:

• Two stages: low-pressure (LP) and high-pressure (HP) cylinders with an intercooler in between.
• Objective: obtain tractable formulae for work and temperature.

Concept / Approach:
Common idealizations are: negligible pressure loss in the intercooler and associated piping; polytropic compression in each stage to represent real heat transfer (with exponent n between 1 and k); and essentially constant suction and delivery pressures at each cylinder end, ignoring small valve losses. These assumptions allow determination of the minimum-work condition and the equal pressure-ratio rule.

Step-by-Step Solution:

Verification / Alternative check:
Relaxing these assumptions (e.g., including pressure loss) shifts the optimum slightly and increases total work; however, the equal-ratio rule remains a good first estimate.

Why Other Options Are Wrong:

Selecting only some assumptions omits standard simplifications used together to build the classical solution.

Common Pitfalls:
Assuming perfect isothermal stages; real compressors are better represented by polytropic behavior. Also, forgetting that even “constant pressure” suction/delivery hides valve-flow irreversibilities present in practice.

Final Answer:

All of the above