You are designing a gas engine that operates on a Brayton cycle and uses air \((\gamma=1.4)\) as its working substance. By making the engine larger and larger, you can have the pressure ratio be \(16,17,18,19\), or 20 . At the higher pressure ratios, however, the efficiency is a smaller fraction of the ideal Brayton cycle efficiency. You determine that, over this range of ratios, the factor relating the efficiency of the real engine to that of the ideal cycle, \(\eta_{\text {real }}=f \eta_{\text {ideal }}\), can be described by the formula \(f=(1.45)\left(1-\eta_{\text {ideal }}\right)^{0.8}\).

(a) Which pressure ratio do you choose to maximize efficiency?

(b) This is a simplified problem. Other than increasing mass, what other reasons can you think of for why engine designers don't have the pressure ratio as great as possible?