# Behold The Power Of The Sun

Solar collector power generation plants, such as this one in Spain, work by concentrating solar energy into a small region to drive a steam turbine.

Direct sunlight delivers about $$1000~\mbox{Watts/m}^2$$ of energy in the infrared, visible, and ultraviolet parts of the spectrum. I want to use mirrors with a total effective area $$A$$ to direct this solar energy into a cube $$1~\mbox{m}$$ on a side, heating the cube to a steady $$100^\circ$$ Celsius so I can start generating steam and running a turbine. What is the necessary effective mirror surface area $$A$$ in $$\mbox{m}^2$$ to do this?

Note that your $$A$$ will be smaller than you might expect. This is because we have used components that are 100% efficient - all the solar energy gets directed onto the cube. In a real life situation the amount of solar energy redirected by the mirrors is much, much less.

Assumptions

• The temperature of the air is 20 $$^\circ$$C

Image credit: Abengoa

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