Take temperatures and efficiencies to be exact . The autoignition temperature of

Question

Take temperatures and efficiencies to be exact.
The autoignition temperature of a fuel is defined as the temperature at which a fuel-air mixture would self-explode and ignite. Thus, it sets an upper limit on the temperature of the hot reservoir in an automobile engine. The autoignition temperatures for commonly available gasoline and diesel fuel are about 495 F and 600 F, respectively.

What are the maximum Carnot efficiencies of a gasoline engine and a diesel engine if the cold reservoir temperature is 38 C?

Explanation / Answer

hot reservor tempature of the gasoline engine is 495 F

then converting into celsius

then using C/5 = (F-32)/9 = (495-32)/9 = 257.22 C

Th = 257.22 + 273.15 = 530.37 K

Tc = 38 C + 273.15 = 311.15 K

maximum carnotefficiency is Eta = 1-(Tc/Th) = 1-(311.15/530.37) = 0.4133= 41.33 %

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for diesel engine

hot reservoir temparaturre is 600 F

in celsius C/5 = (600-32)/5 = 568 C

in Kelvins Th = 568+273.15 = 841.15 K

for cold resrvoir 38 + 273.15 = 311.15 K

then maximum efficiency of diesel engine is eta = 1-(Tc/Th) = 1-(311.15/841.15) =0.63 = 63 %

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