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 surfaceis 5800 k?
a. 4400 k
b. 470,000 k
c. 1900 k
d. 7600 k
e. 1400 k

If the temperature of the solar surface is 5800 K then the approximate temperature of the sunspot is a) 4400 K.

Explanation:

The most straightforward way to solve this is using Stefan-Boltzmann law that states that I the energy radiated per unit surface area per unit time (watt per unit area ) of a black body is proportional to the fourth power of the temperature T of the body:

with being the Stefan constant.

A black body is an idealized physical body that is a perfect absorber because it absorbs all incident electromagnetic radiation and is also an ideal emitter. The Sun is considered to be a black body at different layers and different temperatures.

We are told that the intensity of a sunspot is found to be 3 times smaller than the intensity emitted by the solar surface , that means that:

then using the expression of Stefan-Boltzmann law we get that

we cross out and use the fourth root in each side of the equation

then we use that

So finally we get that

0.93xc=0.93x3x10^8m/s

2.54cm is 1 inch

360seconds i 1 hr