You would like to find out the work of a compressor, but you are not sure if you can use your typical work equation for expansion/compression work for the open flow compressor (W = -pdV). Starting from this definition for reversible expansion/compression work, prove that for an ideal gas, you can simplify the work equation for this polytropic process to get either W = CvT or CpT (I'm not telling you which one).

Hint - remember that for a polytropic compressor for an ideal gas, the n value comes from n = Cp/Cv. Based on this answer, how do you recommend finding the work for the compressor?