Suppose the gasoline in a car burns at 631 degrees Celsius, while the exhaust te

Question

Suppose the gasoline in a car burns at 631 degrees Celsius, while the exhaust temperature (the temperature of the cold reservoir) is 139 degrees Celsius and the outdoor temperature is 27 degrees Celsius. Assume that the engine can be treated as a Carnot engine (a gross oversimplification). In an attempt to increase mileage performance, an inventor builds a second engine that functions between the exhaust and outdoor temperature and uses the exhaust heat to produce additional work. Assume the inventor's engine can also be treated as a Carnot engine. Determine the ratio of the total work produced by both engines to that produced by the first engine alone.

Explanation / Answer

     QH2 = QC1

Now examine (W1 + W2)/W1 to find the ratio of the total work produced by both engines to that produced by the first engine alone.

(W1 + W2)/W1 = (e1QH1 + e2QC1)/(e1QH1) = 1 + (e2/e1)(QC1/QH1)

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