Question

question 9
gasoline yields 4.8×10^7 joules per kg when burned. the density of gasoline is approximately the same as that of water, and 1 gal = 3.8 l. how much energy does your car use on a trip of 100 mi if you get 25 mi per gallon? show your work for credit.

Explanation:

Step1: Calculate gallons of gasoline used

The car gets 25 miles per gallon and travels 100 miles. The number of gallons of gasoline used $V$ is calculated by the formula $V=\frac{\text{distance}}{\text{miles per gallon}}$. So $V = \frac{100}{25}=4$ gallons.

Step2: Convert gallons to liters

Given that 1 gallon = 3.8 L, then the volume of gasoline in liters is $V_{L}=4\times3.8 = 15.2$ L.

Step3: Calculate mass of gasoline

Since the density of gasoline is approximately the same as that of water ($
ho = 1000$ kg/m³ or 1 kg/L), the mass $m$ of the gasoline is $m=
ho V_{L}$. So $m = 1\times15.2=15.2$ kg.

Step4: Calculate energy used

Gasoline yields $4.8\times 10^{7}$ joules per kg when burned. The energy $E$ used is $E=m\times(4.8\times 10^{7})$. Substituting $m = 15.2$ kg, we get $E=15.2\times4.8\times 10^{7}=7.296\times 10^{8}$ joules.

Answer:

$7.296\times 10^{8}$ joules