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Chapter 29: Problem 66

Your roommate's father is CEO of a coal company, so your roommate is understandably skeptical of alternative energy proposals. He claims that there's no future for solar energy, because the power in sunlight is insufficient to meet humankind's energy demand. Is he right? To find out, compare the solar power incident on Earth with our human energy consumption rate of about 15 TW.

Short Answer

Expert verified
The total solar power incident on Earth is approximately 174 PW, which is several times the human energy consumption rate (15 TW). So, the claim that solar energy is not enough to meet humans' demand is incorrect. Therefore, solar energy has potential to be a sustainable energy source with further development and investment in technology.

Step by step solution

01

Understanding the Information

Firstly, find the total power in sunlight that the Earth receives. To achieve this, it's necessary to know about the solar constant, which is the power per unit area received from the Sun in the form of electromagnetic radiation. The solar constant is approximately \(1361W/m^2\) on a surface perpendicular to the Sun's rays at the Earth's average distance from the Sun. Note that this value varie throughout the year due to Earth's ellipsoid orbit.
02

Calculate Total Solar Power Received by the Earth

The total solar power received by the Earth is the solar constant times the cross-sectional area of the Earth (i.e., the area of the disc the Earth would form if viewed from the sun). Remember Earth's radius is approximately 6371 kilometers. So, the formula to use is \(P_{solar} = solar\_constant × πr^2\), where \(r\) is the Earth's radius in meters. This gives a total power of approximately \(174 PW\).
03

Comparing Solar Power with Humankind’s Energy Consumption

Compare the total solar power received by the Earth to our human energy consumption rate which is approximately 15 TW. A comparison of these two values indicates that the solar power incident on Earth is several orders of magnitude greater than our present energy consumption.

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