Question

g The state of Massachusetts at one time had considered generating electric power by harvesting energy crops and burning them. Assume that the state requires 4000 MW of electricity and that planted crops yield between 10,000 and 20,000 lb of dry biomass per acre per year that could be burned to produce electricity at 35% efficiency. How many acres would the state need to plant to supply all its electricity in this way? HTML EditorKeyboard Shortcuts

Answer 1

The require number of acres is between 220714.991 acres and 4414287.982 acres

Step-by-step 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