# Fuel Economy and Second Law of Thermodynamics for Otto-cycle of a certain car

The Otto-cycle of a certain car has a compression ratio r=8.5. The fuel economy rating of this car is 25 miles per gallon at 105km/h. Gasoline has a heat of combustion of 4.60x10^7J/kg, and its density is 740kg/m^3.

a. At 105km/h, what is the rate of gasoline consumption in L/h?

b. What is the theoretical efficiency of the engine? Use γ=1.40

c. How much power is the engine producing at 105km/h? Assume that the engine is operating at its theoretical efficiency, and give your answer in watts and in horsepower. By comparison, the engine of the car has a maximum power of 236hp.

I think I have part b. using the termal efficiency formula for the otto cycle(e=1-1/(rγ-1)). The other two parts I'm completely stuck on.

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#### Solution Preview

a.)

speed = 105 km/hr

milage = 25 mile/gallon = 25*1.609/3.785 km/liter

because, 1 gallon = 3.785 litres and 1 mile= 1.609 km

=>milage = 10.627 km/l

hence consumption rate of gasoline = speed/milage = 105/10.627

= 9.88 ...

#### Solution Summary

The fuel economy is analyzed using the second law of thermodynamics. The Otto-cycle of a certain car is analyzed. The compression ratio is given. With good explanation and full calculations, the problems are solved.