In Arizona, where there are 305 sunny days per year, it requires 320 acres of land to generate 300 MW of average annual power. If there are only 157 sunny days per year in Pennsylvania, how many acres of land would it require to generate the same average annual power? Please round to the nearest acre. Note: assume that a cloudy day delivers 0 watts/acre of solar power. This is not true, but it simplifies the problem for us.
Question
In Arizona, where there are 305 sunny days per year, it requires 320 acres of land to generate 300 MW of average annual power. If there are only 157 sunny days per year in Pennsylvania, how many acres of land would it require to generate the same average annual power? Please round to the nearest acre. Note: assume that a cloudy day delivers 0 watts/acre of solar power. This is not true, but it simplifies the problem for us.
Solution
To solve this problem, we first need to understand that the amount of solar power generated is directly proportional to the number of sunny days.
In Arizona, 320 acres of land generate 300 MW of power in 305 sunny days. So, the power generated per acre per sunny day is 300 MW / 320 acres / 305 days = 0.00308 MW/acre/day.
In Pennsylvania, there are only 157 sunny days per year. To find out how many acres are needed to generate the same 300 MW of power, we can use the formula:
Acres = Power / (Power per acre per day * number of sunny days)
Plugging in the values:
Acres = 300 MW / (0.00308 MW/acre/day * 157 days)
This gives us approximately 645,299 acres. Rounding to the nearest acre, it would require 645,299 acres of land in Pennsylvania to generate the same average annual power as in Arizona.
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