The intensity of a sunspot is found to be 3 times smaller than the intensity emitted by the solar surface. What is the approximate temperature of this sunspot if the temperature of the solar surface is 5800 K
A)4400 K
B)470,000 K
C)1900 K
D)7600 K
E)1400 K

Question

Quizplus · Accepted Answer

The intensity of radiation (I) emitted by a black body (like a sunspot or the solar surface) is related to its temperature (T) through the Stefan-Boltzmann law, which states I ∝ T^4. If the intensity of a sunspot is 3 times smaller than the solar surface, it means the intensity is 1/3 of the solar surface intensity. Let Ts be the temperature of the sunspot and T the temperature of the solar surface (5800 K). According to the relation (Ts/T)^4 = 1/3, solving for Ts gives a temperature lower than the solar surface, which matches closest to 4400 K when calculated.

The Intensity of a Sunspot Is Found to Be 3