Answer:
The require number of acres is between 220714.991 acres and 4414287.982 acres
Explanation:
Given
Power = 4,000MW
Yield = 10,000lb - 20,000 lb/year
Electricity Efficiency = 35%
Required
Number of acres needed
To calculate the required number of acres, the following steps will be followed.
1. Calculate total energy
2. Calculate the intensity of energy
3. Calculate number of acres.
Calculating the total energy
Energy = Power * Time
From the question;
Power = 4,000MW
The crop yield is measured on a yearly basis. So, time = 1 year.
Convert time to seconds.
First, we convert to days
1 year = 365 days;
Then to hours
= 365 * 24
Then to minutes
= 365 * 24 * 60
Then to seconds
= 365 * 24 * 60 * 60
So,
1 year = 365 * 24 * 60 * 60
1 year = 31,536,000s.
Energy = 4,000 MW * 31,536,000
Emergy = 1.26144E11 MJ
Calculating the intensity of energy.
Energy Intensity = Required Energy * Efficiency
Efficiency = 35%
Calculating Required Energy
When Yield = 10,000 lb
First, we convert this to kilogram
1 lb = 0.453592 kg
10,000 lb = 10,000 * 0.453592
10,000 lb = 4535.92 kg
From energy characterisation factors and method table.
1 kg requires 18 MJ of energy.
4535.92 will require:
4535.92 * 18MJ
= 81646.56 MJ of energy.
Hence, Required Energy = 81646.56 MJ
So, Energy Intensity = 81646.56 MJ * 35%
Energy Intensity = 28576.296 MJ.
Hence, when yield = 10,000 lb; the energy intensity is 28576.296 MJ
When Yield = 20,000 lb
Energy Intensity = Required Energy * Efficiency
If the energy intensity is 28576.296 MJ when yield = 10,000 MJ
Energy Intensity = 2 * 28576.296 MJ
Yield = 2 * 10,000 lb
Hence, Energy Intensity = 2 *28576.296 MJ
Energy Intensity = 57152.592 MJ
Now, the number of acres can be calculated.
Number of acres = Total Energy ÷ Intensity.
Total Energy = 1.26144E11 MJ
When Yield = 10,000 lb, Intensity = 28576.296 MJ
Number of acres = 1.26144E11 ÷ 28576.296
Number of acres = 4414287.982 acres
When Yield = 20,000 lb, Intensity = 57152.592 MJ
Number of acres = 1.26144E11 ÷ 57152.592
Number of acres = 220714.991 acres
Hence, the require number of acres is between 220714.991 acres and 4414287.982 acres
