Calculating Equilibrium Temperature for a Solar Hot Water System

[rinchan4]

Homework Statement

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 celsius, what is the equilibrium temp of a collector plate directly facing the sun?

Homework Equations

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

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?

 

[ehild]

No, you do not need the area. Do you know the meaning of the formula you cited?

ehildS

 

[rinchan4]

isn't it the equation for radiation?

 

[rinchan4]

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

 

[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 20C^o ambient?

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

ehild

 

[rinchan4]

awesome thank you!