Work saving with intercooling in multi-stage compression For a two-stage reciprocating air compressor, is the saving in compression work maximised with incomplete intercooling or with perfect (complete) intercooling between stages?

Introduction / Context:
Intercooling in multi-stage compression reduces the temperature of the air between stages, lowering the work input required in the subsequent stage. The question distinguishes between incomplete and perfect intercooling with respect to work minimisation.

Given Data / Assumptions:

• Two compression stages with an intercooler.
• Same mass flow through both stages.
• Comparison is between incomplete cooling and perfect cooling back to the initial intake temperature.

Concept / Approach:
Compression work for a given pressure ratio increases with inlet temperature to the stage. Perfect intercooling restores the air temperature before the second stage to the original intake temperature, thereby minimising the total work. Incomplete intercooling leaves the air hotter than ideal, increasing the second-stage work and the total work.

Step-by-Step Solution:
Assume equal pressure ratio per stage for minimum work.Write stage work trend: W_stage ∝ T_in when pressure ratio is fixed.Perfect intercooling → T_in,HP = T_initial; incomplete intercooling → T_in,HP > T_initial.Therefore, W_total is minimised with perfect intercooling.

Verification / Alternative check:
Textbook derivations show the minimum work condition when p2 = sqrt(p1 p3) and the intercooler returns temperature to the initial intake value; any temperature above this increases work.

Why Other Options Are Wrong:

• Saying incomplete intercooling saves more work contradicts the temperature–work relationship.
• “Same saving” or “independent” ignore the direct dependence on intercooler effectiveness.
• Aftercooling affects delivery temperature, not the interstage work minimum.

Common Pitfalls:
Confusing aftercooling (post-compression cooling) with intercooling (between stages), and ignoring the strong effect of inlet temperature on compression work.

Final Answer:
Disagree — maximum work is saved with perfect intercooling