The hoover dam produces 2x10 to the 9 W

of electricity. It is composed of 7x10 to the 9 kg of concrete. To produce 1 kg of concrete requires 1 MJ of energy. How much energy did it take to produce the dam? How long was the "energy payback time" for the dam?

The area of Lake Mead, formed by Hoover Dam, is 247 mi squared. Assuming that 250 W/m squared of sunlight falls on Lake Mead, how much energy could you produce if instead of the lake you installed solar cells that were 12% efficient?

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To calculate how much energy it took to produce the Hoover Dam, we need to find the total energy required to produce the 7x10^9 kg of concrete.

It is given that 1 kg of concrete requires 1 MJ of energy. So, to produce 7x10^9 kg of concrete, we can calculate the total energy as follows:

Total energy required = (Energy per kg) x (Total kg of concrete)
= (1 MJ/kg) x (7x10^9 kg)

Converting MJ (megajoules) to J (joules), we have:
Total energy required = (1 x 10^6 J/kg) x (7x10^9 kg)
= 7x10^15 J

Therefore, it took approximately 7x10^15 joules of energy to produce the Hoover Dam.

Next, let's calculate the "energy payback time" for the dam. The energy payback time represents the time required for the dam to "pay back" the energy it took to produce it through electricity generation.

Given that the Hoover Dam produces 2x10^9 W (watts) of electricity, we can calculate the energy payback time by dividing the total energy required to produce the dam by the power generated:

Energy payback time = (Total energy required) / (Power generated)

In this case:
Energy payback time = (7x10^15 J) / (2x10^9 W)
= 3.5x10^6 seconds

Converting seconds to years, we get:
Energy payback time = (3.5x10^6 seconds) / (60 seconds/minute x 60 minutes/hour x 24 hours/day x 365 days/year)
≈ 111 years

Therefore, the energy payback time for the dam is approximately 111 years.

Moving on to the second part of the question, we need to calculate how much energy could be produced if solar cells were installed instead of the lake, assuming a sunlight intensity of 250 W/m^2 and an efficiency of 12%.

The area of Lake Mead is given as 247 mi^2. To convert this to square meters, we use the conversion:
1 mi^2 ≈ 2.59 x 10^6 m^2

So, the area of Lake Mead in square meters is:
Area = (247 mi^2) x (2.59 x 10^6 m^2/mi^2)
≈ 6.40 x 10^8 m^2

Next, we calculate the total energy that can be produced by the solar cells using the formula:

Total energy produced = (Sunlight intensity) x (Efficiency) x (Area)

Plugging in the values:
Total energy produced = (250 W/m^2) x (0.12) x (6.40 x 10^8 m^2)
= 1.92 x 10^10 W

Therefore, if solar cells with 12% efficiency were installed on the area of Lake Mead, they could produce approximately 1.92 x 10^10 watts of energy.