An airplane flies at Mach 0.8 at an altitude of \(10 \mathrm{~km}\). Its engine draws in air from the free stream and raises its pressure by a factor of 80 by the time it exits the engine's compressor. Assume that the flow is steady, inviscid, and that air is a calorically perfect gas with \(c_{p}=1004.5 \mathrm{~J} / \mathrm{kg} \mathrm{K}\) and \(\gamma=1.4\). Also assume that the velocity of the flow exiting the engine's compressor is much smaller than the speed of sound (i.e., \(M_{2} \approx 0\) ). Please:

a. Find the total pressure and temperature of the air exiting the compressor and the work done on the air per unit mass (i.e., \(\mathrm{J} / \mathrm{kg}\) ) assuming that the entire compression process is isentropic. Note that the work input to the compression process equals the increase in enthalpy. You will learn why in the next problem (7.16).

b. Repeat part a assuming that \(0.1 \mathrm{~kJ} / \mathrm{kg}\) of entropy is generated during the compression process.

c. The efficiency of the compression process is the ratio of the work required by the ideal (i.e., isentropic) process divided by the work required by the real process. Calculate the efficiency of this compression process.

d. Sketch the ideal and real compression processes on a T-s diagram. Be sure that your diagram includes isobars corresponding to conditions in the free stream, compressor entrance, and compressor exit.

e. How does the T-s diagram change if the Mach number downstream of the compressor is not negligible? Where will the conditions at the exit of the engine's inlet-which sits between the free stream and the compressor's entrance appear in the T-s diagram? Sketch a new T-s diagram that shows these features and explain.