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Q8. A single acting two stage reciprocating air compressor has an initial pressure and temperature of 1 bar and 15℃ respectively.

The pressure and temperature at entry to the second stage are 5 bar and 25℃ respectively. The delivery pressure is 30 bar.

The polytropic index for expansion and compression in both stages is 1.25.

The first stage cylinder has a swept volume of 0.0196 m³ and the volumetric efficiency is 85% at a speed of 300 Rev/min.

(a) Sketch the cycle on a Pressure-volume diagram indicating the pressures and volumes. (2)

(b) Calculate EACH of the following:

(i) The compressor power; (6)

(ii) The first stage clearance volume; (2)

(iii) The heat rejected during the first stage compression process. (6)

Note: for air R = 287 J/kg K, C_V = 718 J/kg K.