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Isentropic efficiencies of turbines and compressors

Real turbines and compressors generate entropy, so their outlet states differ from ideal reversible adiabatic reference states at the same inlet state and outlet pressure.

For a turbine, isentropic efficiency compares actual work output with the maximum isentropic output:

$$\eta_t=\frac{h_1-h_{2,a}}{h_1-h_{2,s}}.$$

For a compressor, it compares ideal required work with actual required work:

$$\eta_c=\frac{h_{2,s}-h_1}{h_{2,a}-h_1}.$$

Suppose a turbine has $h_1=1200$, $h_{2,s}=800\ \mathrm{kJ/kg}$ and $\eta_t=0.85$. Then

$$h_{2,a}=1200-0.85(1200-800)=860\ \mathrm{kJ/kg}.$$

The isentropic outlet is a reference state, not the real outlet. The same comparison principle is used for compressors, but the efficiency ratio is inverted because the desired performance is minimum work input rather than maximum work output.