Suppose the gasoline in a car engine burns at 623 o C,while the exhaust temperat
ID: 1726675 • Letter: S
Question
Suppose the gasoline in a car engine burns at 623 oC,while the exhaust temperature (the temperature of the coldreservoir) is 94.2 oC and the outdoor temperature is29.1 oC. Assume that the engine can be treated as aCarnot engine (a gross oversimplification). In an attempt toincrease mileage performance, an inventor builds a second enginethat functions between the exhaust and outdoor temperatures anduses the exhaust heat to produce additional work. Assume that theinventor's engine can also be treated as a Carnot engine. Determinethe ratio of the total work produced by both engines to thatproduced by the first engine alone.
Explanation / Answer
Given : Total work produced by both engines / Heatabsorbed = 1 - ( T 3 / T 1 ) where T 1 = 623o C= 623 +273 K = 896 K T3 = 29.1 o C = 29.1+273 K = 302.1K Total work produced by both engines / Heatabsorbed = 1 - ( 302.1 / 896 ) = 0.663 work done by first engine alone / heat absorbed = 1 - ( T2 / T 1 ) where T2 = 94.2 o C = 94.2+273 K = 367.2 K work done by first engine alone / heat absorbed = 1 -( 367.2 / 896 ) = 0.591 So, required ration = 0.663 / 0.591 = 1.12 I hope it helps you where T 1 = 623o C= 623 +273 K = 896 K T3 = 29.1 o C = 29.1+273 K = 302.1K Total work produced by both engines / Heatabsorbed = 1 - ( 302.1 / 896 ) = 0.663 work done by first engine alone / heat absorbed = 1 - ( T2 / T 1 ) where T2 = 94.2 o C = 94.2+273 K = 367.2 K work done by first engine alone / heat absorbed = 1 -( 367.2 / 896 ) = 0.591 So, required ration = 0.663 / 0.591 = 1.12 I hope it helps youRelated Questions
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