Overall isothermal efficiency of a compressor In compressor terminology, the “overall isothermal efficiency” is defined as the ratio of the isothermal power (minimum theoretical power to compress the given mass flow between the same pressures) to the shaft power or brake power supplied to drive the compressor. State whether this definition is correct.

Introduction / Context:
Compressors are assessed using several efficiencies that compare real performance with idealized limits. One widely used metric is overall isothermal efficiency. Understanding its definition helps learners connect actual shaft power consumption with the theoretical minimum power required if compression could proceed at constant temperature (isothermal), which represents the lowest possible work input for a given pressure ratio.

Given Data / Assumptions:

• Steady operation of a compressor handling a given mass flow rate between fixed inlet and delivery pressures.
• Isothermal power means the theoretical power if the gas were compressed isothermally between the same pressure limits.
• Shaft power (brake power) is the mechanical power measured at the compressor shaft from the driving motor or engine.

Concept / Approach:
Overall isothermal efficiency compares a theoretical best-case work input with the real shaft power. By definition: overall isothermal efficiency = (isothermal power) / (brake power). Because real compression involves irreversibilities, heat transfer limitations, valve losses, and mechanical losses, the measured brake power is always higher than the isothermal power, making the efficiency less than 1.

Step-by-Step Solution:

Verification / Alternative check:
Other efficiencies exist, such as isentropic (adiabatic) and polytropic efficiencies. Their definitions use isentropic or differential reference processes in the numerator. The isothermal version specifically uses isothermal power in the numerator and brake power in the denominator, matching the present definition.

Why Other Options Are Wrong:

False: contradicts the standard definition used in compressor testing and textbooks.“True only at design point” and “depends on staging or intercooling” confuse definition with magnitude; the definition does not change with operating point or hardware configuration.“True only if intercooling is perfect” is irrelevant; intercooling alters power magnitudes, not the definition.

Common Pitfalls:
Mixing overall isothermal efficiency with isentropic or polytropic efficiencies, or mistakenly using indicated power instead of brake power in the denominator. Always pair the chosen ideal reference (isothermal) with the actual shaft input when computing the overall isothermal efficiency.

Final Answer:

True