A real heat engine working between heat reservoirs at 987 K and 659 K produces 5

Question

A real heat engine working between heat reservoirs at 987 K and 659 K produces 540 J of work per cycle for a heat input of 2400 J. (a) Compare the efficiency of this real engine to that of an ideal (Carnot) engine. % of ideal (b) Calculate the total entropy change of the universe per cycle of the real engine. J/K (c) Calculate the total entropy change of the universe per cycle of a Carnot engine operating between the same two temperatures. J/K

Explanation / Answer

(a) Actual efficiency is ? = W/Q_h = 540J / 2400J = 0.225 The efficiency of a Carnot engine operating between these temperatures would be: ?_c = 1 - T_c/T_h = 1 - 659K/987K = 0.33232 hence, ? / ?_c = 0.225/0.33232 =0.677 = 67.7% (b) Heat rejected to cold reservoir is: Q_c = Q_h - W = 2400J - 540J = 1860 J => ?S = Q_c/T_c - Q_h/T_h = 1860J/659K - 2400J/987K = 0.39J/K (c) Ideal Carnot engine operates reversibly, hence, ?S = 0 J/K

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