1. The total power used by humans worldwide is approximately 15 TW (terawatts). Sunlight striking the Earth provides 1.336 kW per square meter (assuming no clouds). The surface area of Earth is approximately 197,000,000 square miles. How much of Earth’s surface would we need to cover with solar energy collectors to power the planet for use by all humans? Assume that the solar energy collectors can only convert 10% of the available sunlight into useful power.

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To determine how much of Earth's surface we would need to cover with solar energy collectors to power the planet for all humans, we can follow these steps:

Step 1: Calculate the total power available from sunlight

The total power available from sunlight can be calculated by multiplying the power per square meter (1.336 kW) by the surface area of Earth (197,000,000 square miles).

1.336 kW/square meter × 197,000,000 square miles = X kW

Step 2: Convert the total power available to terawatts

To convert the total available power from kilowatts (kW) to terawatts (TW), we divide by 1,000,000.

X kW / 1,000,000 = Y TW

Step 3: Determine the total power needed by humans worldwide

Given that the total power used by humans worldwide is approximately 15 TW, we label this value as P.

P = 15 TW

Step 4: Calculate the surface area needed to generate the required power

To calculate the surface area needed to generate the required power, we divide the total power required (15 TW) by the efficiency of the solar energy collectors (10%).

15 TW / 10% = Z TW

Step 5: Calculate the surface area needed in square meters

To calculate the surface area needed in square meters, we divide the total power needed (Z TW) by the power per square meter (1.336 kW).

Z TW / 1.336 kW/square meter = A square meters

Step 6: Calculate the percentage of Earth's surface needed

To calculate the percentage of Earth's surface needed, we divide the surface area needed (A square meters) by the total surface area of Earth (197,000,000 square miles), and then multiply by 100.

(A square meters / 197,000,000 square miles) × 100 = B %

Therefore, to power the planet for all humans, we would need to cover approximately B% of Earth's surface with solar energy collectors.

To answer this question, we need to calculate the total solar power that can be harnessed by solar energy collectors and compare it to the total power used by humans worldwide.

Step 1: Calculate the total solar power available on Earth's surface:
The total solar power available on Earth's surface can be calculated by multiplying the solar radiation per square meter (1.336 kW) by the surface area of the Earth.

Surface area of the Earth = 197,000,000 square miles

To convert square miles to square meters, we need to use conversion factors:
1 mile = 1.60934 km
1 km = 1000 meters

So, the surface area of the Earth in square meters is:
197,000,000 square miles * (1 mile / 1.60934 km) * (1 km / 1000 meters) * (1 km / 1000 meters) = X square meters

Step 2: Calculate the total solar power available on Earth's surface:
Total solar power = Solar radiation per square meter * Surface area of the Earth

Total solar power = 1.336 kW/m^2 * X square meters = Y kW

Step 3: Calculate the usable solar power from the solar energy collectors:
We are given that the solar energy collectors can convert only 10% of the available sunlight into useful power. So, the usable solar power is 10% of the total solar power.

Usable solar power = 10% * Y kW

Step 4: Compare the usable solar power to the total power used by humans worldwide:
The total power used by humans worldwide is 15 TW (terawatts).

Now we can determine how much Earth's surface area we would need to cover with solar energy collectors to generate enough power for all humans.

Covered surface area = (15 TW) / (Usable solar power per unit area)

Finally, divide the total power used by humans by the usable solar power per unit area to find the surface area of Earth that needs to be covered with solar energy collectors.

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