In a three-stage compression system, air enters the first stage at a pressure of 100 kPa and a temperature of 20 C. The exit pressure from the third stage is 6400 kPa. Between stages the air is passed through an intercooler that brings the temperature back to 20 C. The expression for the work of compression per unit mass in an ideal process is TRT [1-(1)-1)/ where subscript 1 refers to the entering conditions and subscript 2 to the leaving conditions. a) With the intermediate pressures chosen so that the total work of compression is a minimum, what is the minimum work required to compress 1 kg of air, assuming that the compressions are reversible and adiabatic? b) What are the intermediate pressures that result in this minimum work of compression? c) Discuss the relative energy consumption by each compressor and the progression of the pressure through the three compressors.