Overall (plant) isothermal efficiency of a compressor system: Choose the correct definition used in practice for overall isothermal efficiency.

Introduction / Context:
Different efficiency definitions exist for compressors: isentropic, polytropic, isothermal, and volumetric. “Overall isothermal efficiency” is a plant-level metric that compares the ideal isothermal requirement with the actual shaft input to the compressor drive (motor or engine).

Given Data / Assumptions:

• Continuous operation at steady conditions.
• Isothermal power computed for the same inlet and discharge states.
• Shaft power is the brake power delivered to the compressor input shaft.

Concept / Approach:

Overall isothermal efficiency, η_iso,overall = P_isothermal / P_shaft. It judges how close the whole system (including mechanical and internal losses) operates to the theoretical minimum work case (isothermal). It is distinct from cylinder/process isothermal efficiency (option a) and from isentropic efficiency (option d). Volumetric efficiency (option c) is capacity-related, not energy-related.

Step-by-Step Solution:

Verification / Alternative check:

Manufacturer test codes report both isentropic and isothermal efficiencies; the latter referenced to shaft input for overall comparisons.

Why Other Options Are Wrong:

Option (a) is a process efficiency inside the machine; (c) is volumetric efficiency; (d) defines isentropic efficiency, not isothermal.

Common Pitfalls:

Confusing “overall” with “internal”; mixing thermodynamic and volumetric metrics.

Final Answer:

Isothermal power divided by the shaft power (brake power) supplied to the compressor drive