In a two-stage reciprocating air compressor with an intercooler, how does the work saved with incomplete intercooling compare to that with complete (perfect) intercooling?

Introduction / Context:
Intercooling between compression stages reduces the temperature before the next stage, thereby lowering the work required. The question distinguishes between complete (perfect) and incomplete intercooling and asks which saves more work.

Given Data / Assumptions:

• Two stages, same mass flow.
• Intercooler effectiveness may be less than 100% for incomplete intercooling.
• Same final delivery pressure and overall pressure ratio.

Concept / Approach:
Compression work per kg is proportional to the enthalpy rise. Perfect intercooling restores the air to the initial suction temperature before the second stage, minimizing the second stage work. Any shortfall (incomplete intercooling) means higher inlet temperature into the second stage and therefore more work than the perfect case.

Step-by-Step Solution:

Verification / Alternative check:
Plotting compressor power vs. intercooler effectiveness shows monotonic decrease in power as effectiveness approaches 1. This corroborates that incomplete intercooling yields less work saving than perfect intercooling.

Why Other Options Are Wrong:

• More than complete: Impossible since perfect intercooling is the limiting best case.
• Exactly the same: Only if incomplete effectiveness were 100%, which contradicts the definition.
• Independent of performance/Zero: Intercooler effectiveness directly affects power; not independent or zero.

Common Pitfalls:
Assuming diminishing returns eliminate benefit; while returns diminish, maximum saving still occurs at perfect intercooling.

Final Answer:
Less than with complete intercooling