Worked example - solar power - yes or no?

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A-level Maths By: Please log in to see tutor details
Subject: Maths » A-level Maths
Last updated: 15/08/2012
Tags: energy, geometry, maths, physics, solar cells

In 2008, total worldwide energy consumption was at a rate of 1.504×1013 W. So would it be possible to generate all this energy from solar power? A simple consideration of geometry can give us a first rough estimate.

First we must know the total power output of the Sun which is readily available as 3.846×1026 W. This is defined as the total energy radiating from the Sun every second. When this energy reaches the Earth it will have travelled evenly in every direction out from the Sun. We can then say the energy is spread over an area the size of a sphere with a radius the distance between the Earth and the Sun. So the power per unit area at the Earth orbit distance of 1.496×1011 m is

 3.846 x 1026/(4 x π x (1.496×10^11)2 = 1.367 x 103 Wm-2

Now the area of this sphere which the Earth will insect is a circle with radius the size of the Earth's radius. So the area of sunlight captured will be

π x (6.4 x 106)2 = 1.287 x 1014 m2

So to find the power incident on the Earth from the Sun we multiply the two answers together

1.287 x 1014 x 1.367 x 103 = 1.760 x 1017 W

Which is far greater than the required amount of 1.504×1013 W.

So it would appear that solar power is a possible power source. However, there are several factors which are not considered. First would be the efficiency of cells reducing the number by a factor of 10. There are also things such as absorption of light in the atmosphere and cloud cover which unfortunately would mean a very large portion of the Earth would need to be covered with solar cells. The cost of this would be huge and hence solar power is not feasible as a long term power solution unless efficiency of solar cells is increased. For this reason solar cell research is a very active area hoping to increase our ability to capture energy from the Sun.

Sam S A-level Physics Tutor (North London)

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