(Solved): A three-stages air compressor with similar pressure ratio, swept and clearance volume, operatin ...

A three-stages air compressor with similar pressure ratio, swept and clearance volume, operating at $$1400\mathrm{rpm}$$. The compressor delivery pressure is set at $$12\mathrm{bar}$$ with free air delivery conditions of $$1.013\mathrm{bar}$$ and $$27^{?}\mathrm{C}$$. To minimize the work input, an intercooler is fitted in between stages and the air temperature flowing into the intermediate-pressure (IP) and high-pressure (HP) are $$40^{?}\mathrm{C}$$ and $$45^{?}\mathrm{C}$$ respectively. The swept volume and clearance volumes of each cylinder are $$1000{\mathrm{cm}}^3$$ and $$50{\mathrm{cm}}^3$$ respectively. The compression and expansion process of the air is done polytropically following, $$P{V}^{1.3}=$$ constant i) Sketch the indicator $$P_{?}V$$ diagram of the compressors. ii) Sketch the processes on a T-s diagram. iii) Calculate the pressure ratio of each cylinder. iv) Determine the indicated power for each compressor stage, $$\mathrm{kW}$$. v) Calculate the free air delivery, $${\mathrm{m}}^3/\min$$. vi) Calculate the volumetric efficiency of the low-pressure (LP) compressor, \%. vii) Determine the indicated power if the compression process is done in a single-stage compressor, $$kW$$. Take for air, $$\mathrm{R}=0.287\mathrm{kJ}/\mathrm{kg}?\mathrm{K}$$. (32 marks)