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Multi-stage compression with intercooling - Pressure ratio

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We know from the previous section that the minimum air compressor work is achieved with isothermal compression. In practical way, we try to achieve that by involving some cooling during compression process that leads to Polytropic compression process. Normally, this can be achieved by dividing air compression into 2 stages. The first stage builds up the pressure from P1 to Px then the compressed air is cooled by the intercooler and the second stage compressor builds up the pressure again from Px to the final pressure P2. See the following figures to understand how the energy can be saved by using intercooling between each stage. Fig.1 P-v diagram of polytropic compression process with intercooling Fig.2 T-s diagram of polytropic compression process with intercooling We can see from Fig. 1 that the amount of compressor work saved is related to the pressure Px. What is the optimal value of Px that yields maximum compressor work saved? The total compressor work, for this case, is the s...