Thermodynamics

Isentropic Efficiencies of Compressors and PumpsThe isentropic efficiency of a compressor is defined as the ratio of thework input required to raise the pressure of a gas to a specified value in anisentropic manner to the actual work input:Isentropic compressor workh C w s(7–62)Actual compressor work w ahChapter 7 | 3732ah 2ah 2s2s ActualprocessNotice that the isentropic compressor efficiency is defined with the isentropicwork input in the numerator instead of in the denominator. This isbecause w s is a smaller quantity than w a , and this definition prevents h Cfrom becoming greater than 100 percent, which would falsely imply that theactual compressors performed better than the isentropic ones. Also noticethat the inlet conditions and the exit pressure of the gas are the same forboth the actual and the isentropic compressor.When the changes in kinetic and potential energies of the gas being compressedare negligible, the work input to an adiabatic compressor becomesequal to the change in enthalpy, and Eq. 7–62 for this case becomesh C h 2s h 1(7–63)h 2a h 1where h 2a and h 2s are the enthalpy values at the exit state for actual andisentropic compression processes, respectively, as illustrated in Fig. 7–51.Again, the value of h C greatly depends on the design of the compressor.Well-designed compressors have isentropic efficiencies that range from 80to 90 percent.When the changes in potential and kinetic energies of a liquid are negligible,the isentropic efficiency of a pump is defined similarly ash P w s v 1P 2 P 1 2(7–64)w a h 2a h 1When no attempt is made to cool the gas as it is compressed, the actualcompression process is nearly adiabatic and the reversible adiabatic (i.e.,isentropic) process serves well as the ideal process. However, sometimescompressors are cooled intentionally by utilizing fins or a water jacketplaced around the casing to reduce the work input requirements (Fig. 7–52).In this case, the isentropic process is not suitable as the model process sincethe device is no longer adiabatic and the isentropic compressor efficiencydefined above is meaningless. A realistic model process for compressorsthat are intentionally cooled during the compression process is thereversible isothermal process. Then we can conveniently define an isothermalefficiency for such cases by comparing the actual process to areversible isothermal one:h 1w aw s1s 2s = s 1InletstateExitpressureIsentropicprocessFIGURE 7–51The h-s diagram of the actual andisentropic processes of an adiabaticcompressor.COMPRESSORP 2P 1sh C w t(7–65)w awhere w t and w a are the required work inputs to the compressor for thereversible isothermal and actual cases, respectively.AirCoolingwaterFIGURE 7–52Compressors are sometimesintentionally cooled to minimize thework input.