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Q8.A four-stage single acting reciprocating air compressor is designed for minimum work with perfect intercooling. The inlet pressure and temperature is 1.0129 bar and 32°C respectively, the delivery pressure is 152 bar.

The clearance is negligible and the polytropic index of compression for each stage is 1.28.

(a) Calculate EACH of the following per kilowatt of indicated power:

(i) the free air delivery at 1 bar and O°C; (6)

(ii) the isothermal efficiency of the machine; (3)

(b) Sketch the cycle on a pressure-volume diagram showing EACH of the following:

(i) the stage pressures; (3)

(ii) the isothermal curve; (1)

(iii) the work saved by intercooling. (3)

Note: for air C_p = 1.005 kJ⁄(kg K)  and R = 0.287  kJ⁄(kg K)