Answer:
4400 K approximately
Explanation:
Stefan-Boltzmann law establish that the power radiated from a black body in terms of its temperature which is proportional to [tex]T^4[/tex]
[tex]i = aT^4[/tex] with a Stefan-Boltzmann constant
Also we know that [tex]i_{sunspot}[/tex] is three times [tex]i_{sun}[/tex]
[tex]i_{sun}=3i_{sunspot}[/tex] or [tex]\frac{i_{sun}}{i_{sunspot}} = 3[/tex]
Using the Stefan-Boltzmann we can write
[tex]\frac{i_{sun}}{i_{sunspot}} = 3 = \frac{aT_{sun}^4}{aT_{sunspot}^4}[/tex]
solving for [tex]T_{sunspot}[/tex]
[tex]T_{sunspot} = \left(\frac{T_{sun}^4}{3}\right)^{1/4}[/tex]
Replacing the value of [tex]T_{sun}[/tex] (5800 K) it is obtained that [tex]T_{sunspot}[/tex] is 4407.05
