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Thermodynamics

Isentropic compressor efficiency

How close a real adiabatic compressor comes to the ideal isentropic work.

Ref: THE-06
Rev: v1
Field: Thermodynamics
Result: η_c

η_{c} = \frac{h_{2s} - h_{1}}{h_{2a} - h_{1}}

Adiabatic compressor with negligible kinetic and potential energy changes. Compare the actual outlet 2a with the isentropic outlet 2s at the same discharge pressure. For a compressor the ideal work is the smaller number.

A real compressor needs more work than the ideal one; the efficiency is ideal work divided by actual work.

Calculator

Solve for

η_cCompressor efficiencyComputed

h₁Inlet enthalpy

kJ/kg

100800

h_2sIsentropic outlet enthalpy

kJ/kg

1501,500

h_2aActual outlet enthalpy

kJ/kg

1501,500

Actual work input340 kJ/kg
Isentropic (ideal) work280 kJ/kg

What drives the result

Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.

Compressor efficiency () current value 0.8235

h_2aActual outlet enthalpyKey driver

−18.79.33

h₁Inlet enthalpy

−174

h_2sIsentropic outlet enthalpy

−0.4413.53

Efficiencies of 75–88% are typical for axial and centrifugal compressors.
The actual outlet is hotter than the ideal one, which reduces the efficiency.

Chart data as tables

Ranked variables

Variable	Typical range	Lowest result	Highest result	Swing ()	Local step	Change in result
h_2a Actual outlet enthalpy	150 to 1,500 kJ/kg	−18.67	9.333	28	+10%	−0.13
h₁ Inlet enthalpy	100 to 800 kJ/kg	−17	4	21	+10%	−0.0171
h_2s Isentropic outlet enthalpy	150 to 1,500 kJ/kg	−0.4412	3.529	3.971	+10%	+0.171

Sweep of Actual outlet enthalpy

Actual outlet enthalpy (kJ/kg)	Compressor efficiency
150	−1.867
318.8	14.93
487.5	1.493
656.3	0.786
825	0.5333
993.8	0.4036
1,163	0.3246
1,331	0.2715
1,500	0.2333

Sweep one variable

Vary

Compressor efficiency ()Hover, touch, or use the arrow keys on the chart

Variables and how each one contributes

η_c

Compressor efficiency

Result ·

What the equation gives you. Everything else feeds it.

h₁

Inlet enthalpy

kJ/kg · typical 100 to 800

Inlet specific enthalpy. Shifts both work terms.

h_2s

Isentropic outlet enthalpy

kJ/kg · typical 150 to 1,500

Outlet enthalpy for ideal compression. Raises the ideal work.

h_2a

Actual outlet enthalpy

kJ/kg · typical 150 to 1,500

Actual outlet enthalpy. Raises the real work and lowers the efficiency.

Worked example with the values above

Ideal work: h_2s − h₁ = 580 − 300 = 280 kJ/kg.
Actual work: h_2a − h₁ = 340 kJ/kg.
η_c = 280 / 340 = 0.8235.

Assumptions and limits

Adiabatic compressor.
Same discharge pressure for 2a and 2s.

Common mistakes

Using the turbine form of the ratio.
Comparing states at different pressures.

Statistics and uncertainty

As for turbines, efficiency from a ratio of enthalpy differences is sensitive to temperature-measurement errors.

Where it is used

Compressor testing and map reading.
Gas-turbine cycle calculations.

Maths you need

Enthalpy: h
Isentropic process: constant entropy

Related formulas

Practise this formula