You would like to put a solar hot water system on your roof, but you\'re not sur

Question

You would like to put a solar hot water system on your roof, but you're not sure it's feasible. A reference book on solar energy shows that the ground-level solar intensity in your city is 700W/m2 for at least 5 hours a day throughout most of the year.

Assuming that a completely black collector plate loses energy only by radiation, and that the air temperature is 20 ?C, what is the equilibrium temperature of a collector plate directly facing the sun? Note that while a plate has two sides, only the side facing the sun will radiate because the opposite side will be well insulated.

Explanation / Answer

It doesn't matter how big the plate is, but for the sake of making computations easy, let's assume it is 1 m^2 in area. Then the power of the sun hitting it is 700 watts.

As the plate is neither heating nor cooling, the power that the plate is radiating must be equal to 700 watts

P = s * T^4, where P is power, s is the S-B constant, and T is absolute temperature. Set the left side to 700, and you can solve for temperature

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