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# Compare Compressors or Turbines with Different Efficiencies

This Demonstration compares two adiabatic compressors or turbines with different efficiencies. Air, which is assumed to be an ideal gas, is either compressed or expanded. Select "compressor" or "turbine" and whether to compare at the same outlet pressure or temperature, using buttons. Select the outlet pressure or temperature and efficiency of each turbine or compressor with sliders. The efficiency is relative to a reversible turbine or compressor.

### DETAILS

An ideal gas, air, enters a compressor at and or enters a turbine at and .
The energy balance in a steady-state, adiabatic system yields:
,
where is the heat capacity for a diatomic ideal gas, is the ideal gas constant, is shaft work and is the enthalpy change.
The efficiency for a compressor is:
,
and for a turbine:
,
where reversible work and irreversible work .
Shaft work for a reversible process is:
,
and from the energy balance , which when rearranged is . When both sides are integrated:
.
This equation and the efficiency are used to solve for the outlet temperature or pressure .
The screencast video at [1] explains how to use this Demonstration.
Reference
[1] Compare Compressors or Turbines with Different Efficiencies [Video]. (Sep 1, 2016) www.colorado.edu/learncheme/thermodynamics/CompareCompressorsOrTurbinesWithDifferentEfficiencies.html.

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