An ideal gas, air, enters a compressor at T1 = 300 K and P1 = 2 bar or enters a turbine at T1 = 550 K and P1 = 10 bar.
The energy balance in a steady-state, adiabatic system yields:
W = ΔH = Cp ΔT,
where Cp = 7/2 R is the heat capacity for a diatomic ideal gas, R is the ideal gas constant, W is shaft work and ΔH is the enthalpy change.
The efficiency η for a compressor is:
η = Wrev / Wirr,
and for a turbine:
η = Wirr / Wrev,
where reversible work Wrev = Cp(T2,rev − T1) and irreversible work Wirr = Cp(T2,irr − T1).
Shaft work for a reversible process is:
dWrev = V dP = RT (dP / P),
and from the energy balance RT (dP / P) = Cp dT, which when rearranged is (dP / P) = (Cp / R)(dT / T). When both sides are integrated:
Cp ln(T2,rev / T1) − R ln(P2 / P1) = 0.
This equation and the efficiency are used to solve for the outlet temperature T2,irr or pressure P2.
This simulation 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 select whether to compare at the same outlet "pressure" or "temperature" using the buttons. Select the outlet pressure or temperature, and select the efficiency of each turbine or compressor with sliders. The efficiency is relative to a reversible turbine or compressor.
This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by Sneha Nagaraju under the direction of Professor John L. Falconer and Michelle Medlin. It is a JavaScript/HTML5 implementation of a Mathematica simulation by Rachael L. Baumann. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988) in collaboration with Washington State University. Address any questions or comments to LearnChemE@gmail.com.