The efficiency of a heat engine is calculated as ##\eta = |W|/|Q_h| = 1- |Q_c|/|Q_h|##. If this engine operates between the temperatures ##T_c## and ##T_h##, then Carnot's theorem states that ##\eta<\eta_C = 1-T_c/T_h##. This means ##T_c/T_h < |Q_c|/|Q_h|##.
Now assume that the heat engine is...
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