Randall D. Knight — Work, Heat, and the First Law of Thermodynamics: Problem 68

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 \(800\text{ W/m}^2\) 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 \(20^\circ\text{C}\), 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.