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## Homework Statement

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 750 W/m^2 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.

## Homework Equations

dQ/dt=eσAT^4

T=(T_h^4-T_c^4)

e=5.67E-8 W/m^2*K[/B]

## The Attempt at a Solution

[/B]

Okay, so I know that Power is equivalent to dQ/dt. The emissivity(e) is equal to 1 because it is an ideal black collector plate. However, the question does not have the dimensions of the plate, so I am assuming it is 1. I know that I have to find the Hot temperature.

**P=eσA(T_h^4-T_c^4)**

P=eσA

(

P=eσA

**T_h^4-eσA****T_c^4**

P+P+

**eσA****T_c^4=eσAT_h^4**

**P+****eσA****T_c^4/(****eσA)=eσA****T_h^4**(

**P+****eσA****T_c^4/(****eσA))^1/4=T_h**

OR

T=((P/Aeσ)+T_c^4)OR

T=((P/Aeσ)+T_c^4)