Problem 19PE

Construct Your Own Problem

Consider a car trip into the mountains. Construct a problem in which you calculate the overall efficiency of the car for the trip as a ratio of kinetic and potential energy gained to fuel consumed. Compare this efficiency to the thermodynamic efficiency quoted for gasoline engines and discuss why the thermodynamic efficiency is so much greater. Among the factors to be considered are the gain in altitude and speed, the mass of the car, the distance traveled, and typical fuel economy

Solution 19PE

Let m be the mass of the car. Let v be the speed gained by the car and h be the altitude the car reaches. Let M be the mass of fuel burned and E be the energy in Joules release by burning 1 kg of fuel. Therefore,

Input energy = (M) (E)

Also,

Output work = 1 mv2 +mgh

2

The overall efficiency of the car is lower than thermodynamic efficiency because the fuel conversion efficiency is very low.