When cruising at 75 MPH on a highway, a car's engine develops 45 hp. The car's engine has a thermodynamic efficiency of 25% and 1 gallon of gasoline has an energy content of 1.3 × 108 J.
HINT - Ratio reasoning is required in this problem; for example; MPH, Joules per gallon of gasoline, horsepower, and MPG are all ratios. The units in the ratios will help you determine how to use them in order to obtain a solution with the proper units.
(a) Given the power developed by the car and the efficiency of the engine, how much heat is extracted from the hot reservoir each second?
(b) How much heat is expelled to the surroundings each second?
(c) How many gallons of gasoline are consumed each second?
(d) What is the fuel efficiency (in MPG) of this car?
(e) Gasoline burns at about 257?C. Assuming the surrounding air is 30?C, what is the maximum efficiency of the car's engine?