Calculating Sun's Surface Temperature using Wien's Law

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In summary, using Wien's displacement law and the given maximum wavelength of solar radiation, the temperature of the surface of the sun can be calculated to be approximately 5500-6000 Kelvin. However, the exact value may vary depending on the text used. It is important to note that the equation should be written in terms of wavelength and not angular frequency in order to obtain the correct result.
  • #1
PhysiSmo

Homework Statement


Given that the spectrum of solar radiation is that of a black body, and that the maximum wavelength is about 4800x10^(-10)m, calculate the temperature of the surface of the sun

Homework Equations


[tex]\omega_{max}=\frac{2.82144 \cdot k_B}{\hbar}T[/tex] (Wien's Law)

The Attempt at a Solution


[tex]f=\frac{c}{\lambda_{max}}[/tex]
[tex]\omega=2\pi f[/tex]

I'm getting a wrong result, knowing that the correct answer is about 5.500K. Thanx in advance!
 
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  • #2
I can't recall seeing Wien's law written in those terms before. Granted it was a while since I did anything on black body radiation. If you try [itex]\lambda_{max} T = 2.898x10^{-3}[/itex] one should obtain an answer of about 6000 Kelvin. One should know that the surface sun temperature has a range of values depending on what text you're using generally 5500-6000 degrees C. So anything in this range is normally ok.
 
  • #3
I agree with Kurdt. See - http://hyperphysics.phy-astr.gsu.edu/hbase/wien.html

Certainly the value of 2.812144 differs from 2.898 x 10-3 m-K.

I recommend re-writing the Wien displacement law in terms of wavelength.

For T=5500 K, one should obtain a peak wavelength of ~526.9 nm with the formula given by Kurdt.
 
  • #4
But my equation also contains the hbar and KΒ, and also expresses the ω(max), not the λmax with respect to T. So, the constants can't be equal, can they?

Anyway, the form with λmax is quite easier to work with. Thanx a lot!
 
  • #5
PhysiSmo said:
But my equation also contains the hbar and KΒ, and also expresses the ω(max), not the λmax with respect to T. So, the constants can't be equal, can they?

But one wrote

[tex]f=\frac{c}{\lambda_{max}}[/tex] and

[tex]\omega=2\pi f[/tex]


So one has a relationship for angular frequency and frequency and wavelength. Wien's displacement law is normaly written in wavelength, but it could also be written in frequency.

Also don't forget [itex]\hbar\,=\,h/2\pi[/itex] and E = h[itex]\nu[/itex], and Boltzmann's constant figures in the relationship between kinetic energy of gas molecules and temperature -
http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html

and it's found in the Planck radiation formula
http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html#c3
 

1. How does Wien's Law help in calculating the Sun's surface temperature?

Wien's Law states that the peak wavelength of radiation emitted by a blackbody is inversely proportional to its temperature. By measuring the peak wavelength of the Sun's radiation, we can use Wien's Law to calculate its surface temperature.

2. What is the peak wavelength of the Sun's radiation?

The peak wavelength of the Sun's radiation falls in the visible spectrum, specifically in the yellow-green range at approximately 500 nanometers.

3. What is the formula for calculating the Sun's surface temperature using Wien's Law?

The formula is T = 2.898 x 10^(-3) / λ, where T is the temperature in Kelvin and λ is the peak wavelength in meters.

4. Are there any limitations to using Wien's Law to calculate the Sun's surface temperature?

Yes, there are a few limitations. First, Wien's Law assumes that the Sun is a perfect blackbody, which is not entirely accurate. Second, it only gives an approximation of the surface temperature as it does not take into account other factors such as the Sun's atmosphere.

5. Can Wien's Law be used to calculate the surface temperature of other stars?

Yes, Wien's Law can be applied to any object that emits thermal radiation, including stars. However, the accuracy of the calculation may vary depending on the object's properties and conditions.

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