Suppose the gasoline in a car engine burns at 631C, while the exhaust temperatur

Question

Suppose the gasoline in a car engine burns at 631C, while the exhaust temperature (the temperature of the cold reservoir) is 139C and the outdoor temperature is 27C. 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 temperatures 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.

I used Kalvin conversion of 273.15

Explanation / Answer

T1 = 6310C = 904.15 K   ; T2 = 1390C = 412.15 K ; T3 = 300.15

efficiency of the first engine = e1 = 1 - ( T2/T1) = 0.544

efficiency of the second engine = e2 = 1 - ( T3/T2) = 0.272

work done by by the first engine W1 = e1.Q1

work done by the second engine W2 = e2.Q2.

Ratio = ( W1 +W2 )/( W1 ) = ( e1.Q1 +e2.Q2 )/(e1.Q1)

Ratio = 1 + [(e2.Q2)/(e1.Q1)..............(1)

in carnot engine we know efficiency also can write as e1 = 1 - (Q2/Q1)

                                                                                 Q2/Q1 = 1-e1 ..........(2)

subsitute eq(2) into eq(1) we find

Ratio = 1 + [(e2/e1).(1-e1)] = 1 + (e2/e1) - e2

Ratio = 1.228

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