A real heat engine working between heat reservoirs at 977 K and 661 K produces 5

Question

A real heat engine working between heat reservoirs at 977 K and 661 K produces 521 J of work per cycle for a heat input of 2110 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 = 521J / 2110J = 0.2469 The efficiency of a Carnot engine operating between these temperatures would be: ?_c = 1 - T_c/T_h = 1 - 661K/977K = 0.3234 hence, ? / ?_c = 0.2469/03234 = 0.7633 = 76.33% (b) Heat rejected to cold reservoir is: Q_c = Q_h - W = 2110J - 521J = 1589J => ?S = Q_c/T_c - Q_h/T_h = 1589J/661K - 2110J/977 = 0.2442J/K (c) Ideal Carnot engine operates reversibly, hence, ?S = 0 J/K 3 years ago

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