Compressor Temperature Elevation

Item Data
Formula For 1 compressor stage, the isentropic compression is the following

Calculation of power required for a compressor
A compression is said isentropic when it is carried out by an ideal compressor, without friction, without internal leakage and while being perfectly insulated. To account for non idealities, the calculation will have to be corrected by an efficiency coefficient (η) dependent on the technology used.
Nomenclature Pis=Power (kW)
Tsuct=Temperature inlet compressor (K)
Tdischarge=Temperature outlet compressor (K)
M=Molar weight of gas (g/mol)
Qm=Compressor throughput (t/h) k=Gas isentropic coefficient
Usual values For air k=1.4
Reciprocating compressor high compression rate η=0.75
Reciprocating compressor low compression rate η=0.75
Rotary compressors η=0.7
Centrifugal compressors η is calculated from the polytropic efficiency given by the manufacturer. A chart is then used to calculate the polytropic coefficient of the gas, then the discharge temperature calculated and then the actual power needed thanks to the formula above.
Source IFP