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 600 W/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. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

We know that from the Stefan-Boltzmann Law

(Q/dt)=e*sA(Th4-Tc4) and

P=(Q/dt) so

P=e*sA(Th4-Tc4)

Q=Heat

dt=time period

e=emissivity

s=5.67*108(Stefan–Boltzmann constant)

A=area ,consider it as 1

Th=hot side temp

Tc=cold side temp (20 C = 293.15 K)

P=power (solar intensity = 600)

600=1*(5.67*10-8)*1*(Th4-293.154)

Th=((600/(1*(5.67*10-8)*1))+293.154) = 342.02667 K = 69 C

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