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Why must all reversible engines (operating between the same reservoirs) have the same efficiency? Try an argument by contradiction: imagine that two reversible engines exist with e1 > e2. Reverse one of them (into a heat pump) and use the work output from the engine to run the heat pump. What happens? (If it seems fine at first, switch the two.)

Consider the closed-loop system in Figure AP6.5. Suppose that all gains are positive, that is, K1 > 0, K2 > 0, K3 > 0, K4 > 0, and K5 > 0.

(a) Determine the closed-loop transfer function T(s) = Y(s)/R(s).

(b) Obtain the conditions on selecting the gains K1, K2, K3, X4, and K5, so that the closed-loop system is guaranteed to be stable.

(c) Using the results of part (b), select values of the five gains so that the closed-loop system is stable, and plot the unit step response.