If a sunspot appears one-quarter as bright as the surrounding photosphere,and the average temperature of the photosphere is 5,800 K,what is the temperature of the gas in this sunspot?

Question

Quizplus · Accepted Answer

The brightness of an object is directly proportional to the fourth power of its temperature. Using this, we can set up the following equation:

(1/4)^4 = (Tspot/Tphotosphere)^4

Where Tspot is the temperature of the sunspot and Tphotosphere is the temperature of the surrounding photosphere. Solving for Tspot, we get:

Tspot = Tphotosphere * (1/4)^(1/4)

Tspot = 5,800K * 0.667

Tspot = 4,100K

Therefore, the temperature of the gas in this sunspot is 4,100K (Choice A).

If a Sunspot Appears One-Quarter as Bright as the Surrounding