The polytropic or small stage efficiency of a compressor η,C is defined as the ratio of the

The polytropic or small stage efficiency of a compressor ηˆž,C is defined as the ratio of the actual differential work done on the fluid to the isentropic differential work done on the flowing through the compressor ηˆž,C = dhs/dh. Consider an ideal gas with constant specific heats as the working fluid undergoing a process in a compressor in which the polytropic efficiency is constant. Show that the temperature ratio across the compressor is related to the pressure ratio across the compressor by

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Pi