# Solar hot water system

1. Nov 10, 2009

### rinchan4

1. The problem statement, all variables and given/known data
You would like to put a solar hot wate system on your roof, but you'r not sure it's feasible. A reference book on solar energy shows that the ground-level solar intensity in your city is 850 W/m2 for at least 5 hours a day throughout most of the year. Assuming that a completely black collector plate loses enerty only by radiation, and that the air temp is 20 degrees celcius, what is the equilibrium temp of a collector plate directly facing the sun?

2. Relevant equations

Q/delta t= e sigma AT4
sigma= 5.67*10^-8

3. The attempt at a solution
So I tried to change the W/m2 into just W by multiplying by the area but i couldn't figure out the area. I think this is my biggest problem. I think once i find out how to find out the area i can plug it into the equation above and solve for T. Would this be the correct path?

2. Nov 11, 2009

### ehild

No, you do not need the area.

Do you know the meaning of the formula you cited?

ehild

S

3. Nov 11, 2009

### rinchan4

isn't it the equation for radiation?

4. Nov 11, 2009

### rinchan4

ok so i figured it out thank you for your help. :) That pointed me in the right direction.

5. Nov 12, 2009

### ehild

Yes, it is, if you write T^4 instead of T4, but what do the letters Q, e, A, T mean?

The collector plate is totally black. What does it mean for "e"?

Now, how much energy does 1 m2 area of the collector plate gain in one second from the sun, and how much energy comes from the 20Co ambient?

This absorbed energy has to be equal to the energy emitted by 1 m2 collector plate in one second.

ehild

6. Nov 12, 2009

### rinchan4

awesome thank you!!!