Calculating Sun's Surface Temperature using Wien's Law

[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

$$\omega_{max}=\frac{2.82144 \cdot k_B}{\hbar}T$$ (Wien's Law)

The Attempt at a Solution

$$f=\frac{c}{\lambda_{max}}$$
$$\omega=2\pi f$$

I'm getting a wrong result, knowing that the correct answer is about 5.500K. Thanx in advance!

 

[Kurdt]

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 $\lambda_{max} T = 2.898x10^{-3}$ 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.

 

[Astronuc]

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.

 

[PhysiSmo]

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!

 

[Astronuc]

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

$$f=\frac{c}{\lambda_{max}}$$ and

$$\omega=2\pi f$$


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 $\hbar\,=\,h/2\pi$ and E = h$\nu$, 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