Determine the amount of gasoline consumed per second by the automobile in Example 4.9 if it was travelling at 41. m/s. (Assume power required increases as the cube of speed)

Example 4.9

If gasoline contains 1.3 × 10⁵ kJ/gallon, how many gallons of gasoline must be used per second to provide the energy needed to sustain travel at 65. miles per hour on a level road? From this, estimate the fuel economy in mpg (miles per gallon).

Need: Amount of gasoline consumed per second in gallons.

Know: An automobile traveling at 65. miles per hour transfers about 80. kW or 80. kJ/s (or 110 hp) into various forms of energy.

How: Apply the principle of the conservation of energy. The energy lost by the car through the boundary of the control surface must come from somewhere. The only place it can come from within the car is by the decrease in the chemical energy of some of the gasoline. By the principle of conservation of energy, the decrease in chemical energy must equal the transfer out of the dotted lines of all the other types of energy.