Join the conversation on IDNLearn.com and get the answers you seek from experts. Get timely and accurate answers to your questions from our dedicated community of experts who are here to help you.
Sagot :
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].
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].
Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. Accurate answers are just a click away at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.
