Sure! Let's determine the mass of fuel required for the expected energy consumption in the United States for the next 10 years, given the information provided.
1. Energy use per person per year:
Each person in the United States consumes [tex]\(3.5 \times 10^{11}\)[/tex] Joules of energy per year.
2. Current population:
The current population of the United States is [tex]\(310,000,000\)[/tex] people.
3. Time period:
We are interested in the energy consumption over the next 10 years.
4. Total energy consumption over 10 years:
To find the total energy consumption, we need to multiply the energy use per person by the population and then by the number of years.
Therefore, the total energy consumption is:
[tex]\[
\text{Total energy consumed} = (\text{Energy use per person per year}) \times (\text{Population}) \times (\text{Number of years})
\][/tex]
Now plug in the values:
[tex]\[
\text{Total energy consumed} = (3.5 \times 10^{11} \text{ Joules/person/year}) \times (310,000,000 \text{ people}) \times (10 \text{ years})
\][/tex]
Simplifying this further:
[tex]\[
\text{Total energy consumed} = 1.085 \times 10^{21} \text{ Joules}
\][/tex]
5. Determine the mass of the fuel required:
Now we need to find out the mass of the fuel required to generate this amount of energy. Let's assume that we are using a common fuel source such as coal, which releases approximately [tex]\(2.5 \times 10^7\)[/tex] Joules of energy per kilogram of coal.
To find the mass of coal required, we use the ratio:
[tex]\[
\text{Mass of coal} = \frac{\text{Total energy consumed}}{\text{Energy per kilogram of coal}}
\][/tex]
Plugging in the values:
[tex]\[
\text{Mass of coal} = \frac{1.085 \times 10^{21} \text{ Joules}}{2.5 \times 10^7 \text{ Joules/kilogram}}
\][/tex]
[tex]\[
\text{Mass of coal} = 4.34 \times 10^{13} \text{ kilograms}
\][/tex]
So, the mass of coal required to meet the expected energy consumption in the United States for the next 10 years is [tex]\(4.34 \times 10^{13}\)[/tex] kilograms.
