Using a Jeep to Estimate the Energy in Gasoline

Problem:
Estimate the energy released in burning a gallon of gasoline in an automobile engine.

Solution:
I used my 1994 Jeep Wrangler to acquire data for this problem. The estimated weight of the Jeep is 3000 pounds, or 1400 kg. On the highway, the jeep travels about 20 miles per gallon of gasoline. The gasoline must be burned to keep the Jeep moving at a constant speed against internal friction and air resistance. To estimate the combined effect of these two forces, I drove until I came to a flat road surface, then shifted into neutral, and allowed the Jeep to decelerate. Counting by thousands to estimate time, it took about 11 sec for the speed to drop from 45 mph to 35 mph. These numbers provide an estimate for the acceleration due to combined friction and air resistance:

(10 mph)/(11 sec) = 0.91 mph/sec = 0.40 m/sec²

and the force slowing the Jeep:

(1400 kg) x (0.40 m/sec²) 560 nt

This force is the same force that must be overcome when driving the Jeep at constant speed. Since 20 miles/gal = 32,000 m/gal, the energy in j, expended by burning a gallon of gasoline to overcome 560 nt of force over the distance of one mile, is

(560 nt) x (32,000 m/gal) 2 x 10⁷ j/gal.

Since engine efficiency is 20%, the actual energy expended must be about 5 times the above stated amount, or

10⁸ j/gal,

the difference showing up as waste heat. Thus, burning a gallon of gasoline releases about 10⁸ j of energy.

Exploding a ton of TNT liberates about 4 x 10⁹ j, so that a gallon of gasoline is equivalent to about 50 pounds of TNT.