Suppose the gasoline in a car engine burns at 650 o C,while the exhaust temperat

Question

Suppose the gasoline in a car engine burns at 650 oC,while the exhaust temperature (the temperature of the coldreservoir) is 129 oC and the outdoor temperature is 28.3oC. Assume that the engine can be treated as a Carnotengine (a gross oversimplification). In an attempt to increasemileage performance, an inventor builds a second engine thatfunctions between the exhaust and outdoor temperatures and uses theexhaust heat to produce additional work. Assume that the inventor'sengine can also be treated as a Carnot engine. Determine the ratioof the total work produced by both engines to that produced by thefirst engine alone.

Explanation / Answer

   from the given we can see that
   T1 = 924 K
   T2 = 403 K
   T3 = 302.3 K
   the efficiance of the engine or exhaust will be
   e1 = 1 - (T2 /T1)
       = ........
   the efficiency of the second engine will be
   e2 = 1 - (T3 /T2)
       = ........
   the work done by each segment is
   W1 = e1 QH1
   W2 = e2 QH2
        = e2 QC1
   now the ratio of the total work produced by bothengines to that produced by the first engine
   alone will be
   (W1 + W2) / W1 =(e1 QH1+ e1 QC1) /(e1 QH1)
   on solving we get
   (W1 + W2) / W1 = 1 +(e2 / e1) - e2

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