Question

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?

Answer 1

4400 K approximately

Step-by-step explanation:

Stefan-Boltzmann law establish that the power radiated from a black body in terms of its temperature which is proportional to
`T^4`

`i = aT^4` with a Stefan-Boltzmann constant

Also we know that
`i_(sunspot)` is three times
`i_(sun)`

`i_(sun)=3i_(sunspot)` or
`(i_(sun))/(i_(sunspot)) = 3`

Using the Stefan-Boltzmann we can write

`(i_(sun))/(i_(sunspot)) = 3 = (aT_(sun)^4)/(aT_(sunspot)^4)`

solving for
`T_(sunspot)`

`T_(sunspot) = \left((T_(sun)^4)/(3)\right)^(1/4)`

Replacing the value of
`T_(sun)` (5800 K) it is obtained that
`T_(sunspot)` is 4407.05