Which one is correct method to find work done by a isentropic compressor?
Compressor power = mCpdT
Where m = mass flow rate
Cp = specific heat at constant pressure
dT = Temperature difference at inlet and outlet
Compressor work = (P2V2 - P1V1)/(1 - γ)
Where γ = specific heat ratio
As this formula represent work done by gas so inversely we can say work done by compressor.
compressor power = mCvdT
Where Cv = specific heat at constant volume
We know dq = du + dw. Here dq = 0 since it is isentropic process. So dw= -du and du = mCvdT. It seems that if precise calculation is done method-2 and method-3 give same result.
I applied three method with a sample math. Three method gives three result but I am not sure which one is to be accepted. Please see the photos below for clear understanding.