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Compressor isentropic efficiency compares ideal isentropic enthalpy rise with actual enthalpy rise at the same outlet pressure.
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Formula
η dimensionless; h in J/kg; 1 inlet, 2 actual outlet, 2s isentropic outlet
| Symbol | Meaning | Unit |
|---|---|---|
| Compressor isentropic efficiency | dimensionless | |
| Specific inlet enthalpy | J/kg | |
| Ideal isentropic outlet enthalpy at outlet pressure | J/kg | |
| Actual specific outlet enthalpy | J/kg |
\eta_{is,c}=\frac{h_{2s}-h_1}{h_2-h_1}For an adiabatic real compressor, actual work is typically greater than the isentropic minimum, so efficiency is normally below one. State 2s has the same inlet entropy as state 1 and the same outlet pressure as state 2. With appreciable heat transfer or a different convention, another efficiency measure may be required.
For an adiabatic real compressor, actual work is typically greater than the isentropic minimum, so efficiency is normally below one. State 2s has the same inlet entropy as state 1 and the same outlet pressure as state 2. With appreciable heat transfer or a different convention, another efficiency measure may be required.
Compressor isentropic efficiency compares ideal isentropic enthalpy rise with actual enthalpy rise at the same outlet pressure.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Isentropic efficiency of a compressor” and check its unit and magnitude.
For h1=300 kJ/kg, h2s=340 kJ/kg and h2=350 kJ/kg, ηis,c=40/50=0.80.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: η dimensionless; h in J/kg; 1 inlet, 2 actual outlet, 2s isentropic outlet.
Formula cluster
Compressor isentropic efficiency compares ideal isentropic enthalpy rise with actual enthalpy rise at the same outlet pressure.
For h1=300 kJ/kg, h2s=340 kJ/kg and h2=350 kJ/kg, ηis,c=40/50=0.80.
Compare real compressor work with an ideal isentropic reference.
Here is how to work through a typical Isentropic efficiency of a compressor (ηis,c = (h₂s−h₁)/(h₂−h₁)) task step by step:
Task
Work through the numerical example for “Isentropic efficiency of a compressor” and check its unit and magnitude.
Solution path
For h1=300 kJ/kg, h2s=340 kJ/kg and h2=350 kJ/kg, ηis,c=40/50=0.80.
h2s represents the ideal minimum outlet enthalpy for isentropic compression to the same final pressure. h2 is the actual outlet state. Their ratio to the actual enthalpy rise expresses the ideal minimum relative to real compressor input. Subscript s marks a reference state, not an extra stage. The isentropic outlet is a reference at actual outlet pressure and inlet entropy. Enthalpy differences need consistent property basis and units. The definition assumes compressor work input and an appropriate adiabatic comparison; it does not cover every polytropic or heat-leaking compressor convention.
Set inlet entropy s1 and actual outlet pressure p2 as conditions for the ideal reference state. Find h2s from an appropriate property model or chart. For an ideal gas with constant cp, isentropic temperature follows from pressure ratio and γ; real gases need property data. The isentropic outlet is a reference at actual outlet pressure and inlet entropy. Enthalpy differences need consistent property basis and units. The definition assumes compressor work input and an appropriate adiabatic comparison; it does not cover every polytropic or heat-leaking compressor convention.
For an ordinary adiabatic compressor, actual work is at least the reversible ideal minimum, so ηis is typically between zero and one. A larger result often signals mismatched states, incompatible enthalpy basis, measurement error or another definition. First check pressure, entropy and reference states. The isentropic outlet is a reference at actual outlet pressure and inlet entropy. Enthalpy differences need consistent property basis and units. The definition assumes compressor work input and an appropriate adiabatic comparison; it does not cover every polytropic or heat-leaking compressor convention.
Write the quantity and unit from the variable list next to every value: η dimensionless; h in J/kg; 1 inlet, 2 actual outlet, 2s isentropic outlet. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example For h1=300 kJ/kg, h2s=340 kJ/kg and h2=350 kJ/kg, ηis,c=40/50=0.80. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. The isentropic outlet is a reference at actual outlet pressure and inlet entropy. Enthalpy differences need consistent property basis and units. The definition assumes compressor work input and an appropriate adiabatic comparison; it does not cover every polytropic or heat-leaking compressor convention.
The background states this starting condition: For an adiabatic real compressor, actual work is typically greater than the isentropic minimum, so efficiency is normally. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. The isentropic outlet is a reference at actual outlet pressure and inlet entropy. Enthalpy differences need consistent property basis and units. The definition assumes compressor work input and an appropriate adiabatic comparison; it does not cover every polytropic or heat-leaking compressor convention.
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