To determine the mass of fuel required for the expected energy consumption in the United States for the next 10 years, we will go through the following steps:
1. Calculate the total energy usage for one year:
The energy use per person per year in the United States is [tex]\(3.5 \times 10^{11}\)[/tex] Joules. Given that the current population is 310,000,000 people, the total energy usage for one year can be calculated by multiplying these two values:
[tex]\[ \text{Total energy use per year} = 3.5 \times 10^{11} \, \text{Joules/person/year} \times 310,000,000 \, \text{people} \][/tex]
2. Calculate the total energy usage for 10 years:
To find the total energy usage for the next 10 years, we will multiply the total energy usage for one year by the number of years (10 years):
[tex]\[ \text{Total energy use for 10 years} = \text{Total energy use per year} \times 10 \][/tex]
Using the given data, we find:
[tex]\[ \text{Total energy use per year} = 1.085 \times 10^{20} \, \text{Joules} \][/tex]
[tex]\[ \text{Total energy use for 10 years} = 1.085 \times 10^{20} \, \text{Joules/year} \times 10 \, \text{years} \][/tex]
[tex]\[ \text{Total energy use for 10 years} = 1.085 \times 10^{21} \, \text{Joules} \][/tex]
3. Determine the type of fuel and its energy content:
Suppose we use a common type of fuel such as gasoline. The energy content of gasoline is approximately [tex]\(44 \times 10^{6}\)[/tex] Joules per kilogram (J/kg).
4. Calculate the mass of fuel required:
To find the mass of fuel required, we will divide the total energy use for 10 years by the energy content of gasoline:
[tex]\[ \text{Mass of fuel required} = \frac{\text{Total energy use for 10 years}}{\text{Energy content of gasoline}} \][/tex]
Substituting the values we have:
[tex]\[ \text{Energy content of gasoline} = 44 \times 10^{6} \, \text{Joules/kg} \][/tex]
[tex]\[ \text{Mass of fuel required} = \frac{1.085 \times 10^{21} \, \text{Joules}}{44 \times 10^{6} \, \text{Joules/kg}} \][/tex]
Perform the division:
[tex]\[ \text{Mass of fuel required} = \frac{1.085 \times 10^{21}}{44 \times 10^{6}} \][/tex]
[tex]\[ \text{Mass of fuel required} \approx 2.466 \times 10^{13} \, \text{kg} \][/tex]
Therefore, the mass of gasoline required for the expected energy consumption in the United States for the next 10 years is approximately [tex]\(2.466 \times 10^{13} \, \text{kg}\)[/tex].
