Minimum compression work (single-stage, no clearance): For a single-stage, single-acting reciprocating air compressor without clearance, which ideal process yields the minimum work input for a given pressure ratio?

Introduction / Context:
For a fixed inlet/outlet pressure, different compression paths require different works. Comparing isothermal, polytropic, and isentropic processes clarifies why intercooling is beneficial in multistage compressors.

Given Data / Assumptions:

• Ideal gas behavior with constant properties.
• No clearance; steady operation.
• Same pressure ratio across all compared processes.

Concept / Approach:

Work input is the integral of p dV. For a given pressure ratio, the area under the curve is smallest for the isothermal path (n = 1), larger for general polytropic (1 < n < k), and largest for adiabatic/isentropic (n = k). Hence, if one could remove heat continuously to maintain constant temperature, isothermal compression would consume the least work.

Step-by-Step Solution:

Verification / Alternative check:

Analytic expressions confirm: w_isothermal = RT1ln(p2/p1), while w_isentropic = (k/(k−1))RT1*[(p2/p1)^((k−1)/k) − 1], with the latter numerically larger for the same ratio.

Why Other Options Are Wrong:

Isentropic has the highest work for a given ratio; generic polytropic lies in between; “none” is incorrect because isothermal is the known minimum.

Common Pitfalls:

Assuming “adiabatic is efficient” in compressors; forgetting that heat removal during compression reduces required input work.

Final Answer:

Isothermal compression