No further calculations need to be made for the wind farm, because there is no further land use change or consumption of material at a wind farm...

No further calculations need to be made for the wind farm, because there is no further land use change or consumption of material at a wind farm after construction is complete. So, we'll keep the power density estimate of 15 W/m2 for the wind farm through this exercise. Coal power plants do consume material and necessitate land use change on an annual basis. We'll explore this land use change over the typical 40 year lifespan of a coal power plant.

The average power capacity of a coal power plant in the United States is 500 MWe. That's 500 megawatts of electrical capacity. Most coal consumed in the United States for generating electricity is derived from Wyoming, and the biggest, most productive coal mine in Wyoming is the Black Thunder Mine, which produces 61,000,000 metric tons of coal each year. To produce this amount of coal on an annual basis, the mine is expanded each year by 5 km2. Use this information and the information listed below to calculate the area disturbed at the mine to produce enough coal for our single 500 MWe coal power plant over 40 years.

Power plant info:

Electrical capacity = 500 MWe

Efficiency = 33%

Lifespan = 40 years

Area occupied by the power plant = 2,600,000 m2 (national average for coal power plants)

Coal mine info:

Production: 61,000,000 metric tons per year

Expansion rate: 5 km2 per year or 5,000,000 m2 per year

Steps:

1) Calculate the rate at which chemical energy in the coal is converted into electricity using the electrical capacity and the efficiency of the power plant. Your answer reflects the thermal capacity of the power plant and should still be in megawatts (MW).

2) Assume that the power plant operates at full capacity each year. Take the number in step 1 above and multiply by the number of seconds in a year. This will give you the number of megajoules (MJ) consumed by burning coal each year.

3) Calculate the mass of coal consumed each year at the power plant by using the average coal energy density of 21 MJ/kg. You will need to convert your answer to metric tons.

4) Calculate the proportion of annual coal production at the Black Thunder Mine that goes to our power plant.

5) Use the proportion in step 4 to calculate how much land is disturbed each year to provide our power plant with coal.

6) Multiply your answer from step 5 by 40 years.

Please type the answer out in the following format:

Over the 40 year supply of coal to a 500 MWe coal power plant, the amount of land disturbed by coal mining = W.WW x 10W m2