When one gallon of gasoline is burned in a car engine, 1.20 108 J of internal energy is released. Suppose that 0.99 108 J of this energy flows directly into the surroundings (engine block and exhaust system) in the form of heat. If 5.0 105 J of work is required to make the car go one mile, how many miles can the car travel on one gallon of gas?

To determine the number of miles the car can travel on one gallon of gas, we need to calculate the total energy available from one gallon of gas and then divide it by the energy required to travel one mile.

First, let's calculate the total energy available from one gallon of gas. Given that 1.20 x 10^8 J of internal energy is released and 0.99 x 10^8 J of this energy flows into the surroundings as heat, the remaining energy available for work is:

Total energy available = Internal energy - Heat energy
= 1.20 x 10^8 J - 0.99 x 10^8 J
= 0.21 x 10^8 J
= 2.1 x 10^7 J

Now, we divide this energy by the energy required to travel one mile. From the question, we know that it takes 5.0 x 10^5 J of work to make the car go one mile.

Number of miles = Total energy available / Energy required per mile
= (2.1 x 10^7 J) / (5.0 x 10^5 J per mile)
= 42 miles

Therefore, the car can travel approximately 42 miles on one gallon of gas.