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 Watts/m21000~\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 AA to direct this solar energy into a cube 1 m1~\mbox{m} on a side, heating the cube to a steady 100100^\circ Celsius so I can start generating steam and running a turbine. What is the necessary effective mirror surface area AA in m2\mbox{m}^2 to do this?

Note that your AA 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 ^\circC

Image credit: Abengoa

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