An automobile uses 1.5 104 W (20 hp) of mechanical power against air resistance

Question

An automobile uses 1.5 104 W (20 hp) of mechanical power against air resistance and rolling friction while traveling at a constant speed of 24 m/s.
(a) The heat of combustion of gasoline is 11 kcal/g and its density is 0.74 g/cm3. Find the energy content of gasoline in units of J/L.
(b) If the efficiency of the engine is 22%, find the energy used by the car per distance traveled in units of J/km.
(c) Find the distance traveled by the car per volume of gasoline used in units of km/L and mi/gal (1 mi = 1.61 km, and 1 gal = 3.79 L).

Explanation / Answer

1 cal = 4.186 J 11 kcal/gm = 11*4186*0.74 J/cm3 =34074.04 J/cm3 = 34074.04 J/(1/1000L) = 34074040 J/L = heat of combustion TIme = 1000m/23(m/s) = 43.4782 m/s Energy per km = (14104/0.22)*43.4782 = 2787347.8763 J/km 1 L gasoline = 34074040 J 34074040 = (14104/0.22)*(x/23) x = 12224.52 = 12.2254 km/l (12.2254/1.61)/(1/3.79) = 28.7790 mi/gal

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