Whaaa Calculating the temperature of the suns surface

[Lisa...]

Hi you all!

I'm having difficulties with estimating the temperature of the surface of the sun from a given solar spectrum. I've already determined the photon energy of the most common photons (1.15 eV). I also know that the curve of the solar spectrum (photon energy on the x-axis and intensity on the y-axis) is described with (hf^3)/((e^(hf/Kb T))-1) where the frequency f corresponding to 1 eV energy is 2.417970 x 10^14 Hz.

Now the way to retrieve the correct answer is the following:
1) Differentiate the formula.
2) Calculate the frequency of the most common photons and fill that in the formula.
3) Solve the equation where the differentiated formula (with f filled in) is set zero. (This may be done with a graphic calculator)

The only problem is that I don't seem to differentiate the formula correctly, because my calculator just can't find the points where it's zero. Could someone pleaaaaaaaaaaaaaaaaase help me to differentiate it the right way?

 

[Andrew Mason]

Look up Wien's Displacement Law: http://scienceworld.wolfram.com/physics/WiensDisplacementLaw.html

AM

 

[quicknote]

Hi there,

Calculating the temperature of the sun's surface is a complex task that requires careful consideration of various factors. The approach you have outlined is a good starting point, but there are a few things to keep in mind.

Firstly, the formula you mentioned, (hf^3)/((e^(hf/Kb T))-1), is known as the Planck function and is used to describe the spectral energy distribution of a blackbody. However, the sun is not a perfect blackbody, so this formula may not give an accurate estimate of its surface temperature.

Secondly, the most common photons in the solar spectrum do not necessarily correspond to the peak of the Planck function. The peak will depend on the temperature of the sun's surface, so it cannot be assumed that the frequency of the most common photons will be the same as the frequency at which the Planck function is zero.

In order to accurately estimate the temperature of the sun's surface, it is important to consider other factors such as the composition of the sun's atmosphere, the effects of absorption and scattering, and the emission from different layers of the sun's atmosphere.

I would recommend consulting with a solar physicist or using more advanced techniques, such as fitting the observed solar spectrum to a model, to obtain a more accurate estimate of the sun's surface temperature. I hope this helps and good luck with your research!