A sunspot has a temperature 80% as large as the rest of the Sun's surface.How much LESS light does it produce per unit area than the rest of the Sun?

Question

Quizplus · Accepted Answer

The total amount of light produced by the sunspot per unit area depends on both its temperature and surface area. However, since the temperature is the only variable given, we can assume that the surface area is constant. According to the Stefan-Boltzmann law, the total energy emitted by a blackbody (or, in this case, a non-blackbody) is proportional to the fourth power of its temperature. Therefore, the ratio of the energy emitted by the sunspot to that emitted by the rest of the Sun per unit area is:

(0.8)^4 = 0.41

This means that the sunspot emits only 41% as much light per unit area as the rest of the Sun, which is equivalent to saying that it emits 59% less light per unit area. Therefore, the correct answer is C) 40% as much.

A Sunspot Has a Temperature 80% as Large as the Rest