Air compressors and thermodynamics: The work done by an air compressor depends upon the manner (process path) in which the air is compressed (e.g., isothermal, adiabatic, or polytropic) and on clearance and intercooling details.

Introduction / Context:
Understanding what governs compressor work is fundamental in thermodynamics and gas power cycles. Designers minimize power input by choosing a suitable compression process path, staging, and cooling methods. This question probes whether compressor work is path dependent or not.

Given Data / Assumptions:

• Single or multi-stage air compression.
• Common idealized paths: isothermal, adiabatic (isentropic if reversible), and polytropic with index n.
• Same inlet state and the same final delivery pressure are assumed for comparison.

Concept / Approach:
For a perfect gas, compressor work is the area under the p–v curve. Different thermodynamic paths between the same end states trace different areas, hence different work. Isothermal compression yields the minimum theoretical work. Adiabatic compression requires the maximum work among the common idealized paths. Polytropic work lies between them and can be further reduced with intercooling in multi-stage arrangements.

Step-by-Step Solution:

Verification / Alternative check:
Plotting p–v diagrams for the three processes with the same p1, v1 and final pressure p2 shows clearly different areas (work inputs). Experimental data on multi-stage compressors with intercoolers confirm lower power draw than single-stage adiabatic compression to the same discharge pressure.

Why Other Options Are Wrong:

• Does not depend: Incorrect because work is path dependent.
• Depends only on inlet pressure: Discharge pressure and path also matter.
• Depends only on discharge pressure: Inlet state and process path matter as well.

Common Pitfalls:
Assuming fixed end pressures force identical work. Ignoring temperature rise and cooling strategies leads to wrong conclusions.

Final Answer:
depends