Suppose one gallon of gasoline produces 1.01×108 J of energy, and this energy is sufficient to operate a car for 18.2 miles. An aspirin tablet has a mass of 332 mg. If the aspirin could be converted completely into thermal energy, how many miles could the car go on a single tablet?
2. Relevant equations
3. The attempt at a solution
1 gallon of gas= (1.01E8) J
Distance of car(on gas)= 18.2 miles
Mass(aspirin)= 332 mg
Distance of car(on asprin)=???
I converted the mass from grams to kilograms.
332mg = (332E-3)g = (332E-6)kg
*After this I’m not sure if I’m doing the right thing.*
The problem says "converted completely into thermal energy" so I’m assuming that this means I need to find the rest energy.
Erest=mc^2 [m=mass in kg; c=speed of light=(3E8)m/s]
I then set up the energy of gas, distance on gas and the energy I found abvoe of the asprin, to solve for distance on asprin?
(distance of gas)/(energy of gas)=(distance of aspirin)/(energy of aspirin)
=(18.2 miles)/((1.01E8)J)=(?distace of asprin?)/((2.988E13)J)
=5384316.832 miles = (5.38E6) miles
However that answer is incorrect and I’m not sure if I am even using the right formulas for this problem.
Any help would be greatly appreciated!