Isentropic Efficiency of Compressors

Compressors use work input to increase the pressure of a gas. In this case, the efficiency is given by:

$$\begin{array}{rl}{\eta }_C& =\frac{\text{Isentropic compressor work}}{\text{Actual compressor work}}=\frac{w_s}{w_a}\\ & \approx \frac{h_{2s}-h_1}{h_{2a}-h_1}\end{array}$$

Note that in this case, since work is the input, the above equation is the inverse of the isentropic efficiency of a turbine, since turbines produce work as an output.

Example