A jet engine for a supersonic transport (SST) propels the airplane at Mach 3 at an altitude of 50,000 ft where the temperature is 217°K and the ambient pressure is 0.115 atm. The maximum temperature that the advanced turbine blades can handle is 1900°K. The engine operates at a compressor pressure ratio that allows the engine to achieve maximum work. The temperature at the entrance to the compressor is 595.7K. Assume that γ = 1.4 and Cp = 1004 J/kg-°K throughout the engine. If the engine inlet isentropically slows down the incoming freestream air such that the Mach number of the flow just upstream of the compressor is 0.3,

a) How many stages should the aircraft engine compressor have if the compression pressure ratio of each stage is 1.2? b) Please plot the cycle on a T-s diagram labeling only the temperature at each point? c) What is the thermal efficiency of the engine? d) What is the absolute highest possible thermal efficiency one can expect from a machine operating within the range of temperatures involved in this problem? e) What is the amount of heat per unit mass of working fluid that is needed to be generated by the combustion of fuel in the engine burner?