The total rate at which power is used by humans worldwide is...

The total rate at which power is used by humans worldwide is approximately 15 TW (terawatts). The solar flux averaged over the sunlit half of Earth is $680 \mathrm{~W} / \mathrm{m}^{2}$ (assuming no clouds). The area of Earth's disc as seen from the Sun is $1.28 \times 10^{14} \mathrm{~m}^{2}$. 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 convert only $10 \%$ of the available sunlight into useful power.

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Key Concepts

Global Power Consumption

Global power consumption, often expressed in terawatts, represents the total rate at which energy is used worldwide. Understanding this figure is essential when sizing energy generation systems, as it provides the target power output needed to sustain humanity's energy demands.

Power Density and Area Calculation

Power density is the measure of power per unit area, and it is crucial when calculating the area needed to generate a given amount of power. By dividing the total required power by the product of solar irradiance and conversion efficiency, one can estimate the necessary collector area.

Solar Irradiance

Solar irradiance refers to the amount of solar power received per unit area, typically measured in watts per square meter. It is a key input in determining how much energy can be harvested from sunlight for any given surface area under ideal conditions.

Energy Conversion Efficiency

Energy conversion efficiency is the percentage of incident energy that a system can convert into useful work or power. In the context of solar energy collectors, it determines how effectively the incoming solar energy is converted into electrical energy, which directly impacts the required size of the collector array.

Transcript

00:01 We are asked to do some calculations for some power generation here on earth.

00:08 We're given the following information.

00:11 The total rate at which power is used by humans worldwide is approximately 15 terawatts.

00:19 The solar flux averaged over the sunlit half of the earth is 680 watts per square meter.

00:31 This assumes no clouds.

00:33 The area of the earth's disk, as seen from the sun, is 1 .28 times 10 to the 14th square meters.

00:56 The surface area that earth is approximately, earth area, total area, is 997 million miles squared.

01:22 We're asked how much of the earth's surface would we need to cover with solar energy collectors to power the planet for use by all human beings.

02:21 Power all.

02:23 And we're going to assume 10 % efficiency for the collectors.

02:37 So this is all information we're given.

02:42 For conversions, i like to make a plan.

02:45 So my plan here is to take my terawatts and 10 % efficiency.

03:02 We'll account for that.

03:04 And then we'll change that to meters squared.

03:08 Next thing we'll do is we'll take the miles squared and convert that to meters squared.

03:20 Then we'll calculate the percent of the earth's surface.

03:27 Let's begin...