Question

If a sunspot has a temperature of 4,760 K and the solar surface has a temperature of 5,800 K, how many times brighter is the surface compared to the sunspot? (Hint: Use the Stefan-Boltzmann law.)

Answer 1

Brightness of sun surface = 2.2045 times of brightness of sunspot

Step-by-step explanation:

We have given temperature of sunspot
`T_1=4760K`

Temperature of solar surface
`T_2=5800K`

Now according to Stefan's law

`(L)/(A)=\sigma T^4`, here L is radiated power, A is area,
`\sigma` is stefan constant

As the brightness depends on the radiated power

So
`(brightness\ of\ sunspot)/(brightness\ of\ sun\ surface)=(T_1^4)/(T_2^4)`

`(brightness\ of\ sunspot)/(brightness\ of\ sun\ surface)=(4760^4)/(5800^4)=0.4536`

Brightness of sun surface = 2.2045 times of brightness of sunspot