How Do You Solve These Blackbody Radiation Problems?

[Nebula]

A couple Blackbody Problems?

I'm a little confused about these two problems involving blackbodies, hopefully someone could give me a bit of insight. Thanks in advance.

1. For a blackbody we there is a frequency peak and a wavelennght peak. Let's call em v and w respectively. Now consider the derivations of the maximums dependent on temperature to prove v*w not equal to the speed of light.

Im not sure what to do here. No were in my text do they talk about the derivations for the maximums. So I am not really sure in what direction to head.



next question.

2. The peak value Mw(max) at the wavelength w(max) in the distribution of blackbody radiation increases with T (temperature). Show Mw(max) depends on T as:
Mw(max)=CT^p
where C is some constant and power p
so we have to find the constant and the power.

 

[Tide]

The Planck distribution depends on the temperature. To find the maximum you will need to differentiate with respect to the temperature and find the value of T that makes the derivative = 0.

 

[Nebula]

Right but what equations do I work with?

Any ideas about 2?

 

[Tide]

What was the source of your question? If it's a textbook or a course you're taking surely you have it available.

Here's a review of Plancks radiation law: http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html

 

[P3X-018]

Hey Tide
In that page they give placnk's law as

((8*pi*v^2)/c^3)*...

But look at the following page why do they give Planck's law with the term
http://scienceworld.wolfram.com/physics/PlanckLaw.html

(2v^2)/c^2

Why is the term ((8*pi*v^2)/c^3) different than the one giving in scienceworld??

 

[Tide]

Hey Tide
In that page they give placnk's law as

((8*pi*v^2)/c^3)*...

But look at the following page why do they give Planck's law with the term
http://scienceworld.wolfram.com/physics/PlanckLaw.html

(2v^2)/c^2

Why is the term ((8*pi*v^2)/c^3) different than the one giving in scienceworld??

One might be a flux and the other an intensity - I didn't have time to study them carefully. I recommend the orginal poster refer to his textbook for the correct version!

 

[Tide]

P3x,

I think for the problem at hand you should be focusing on the functional dependence which is
\frac {\nu ^3}{e^{\frac {h \nu}{kT}}-1}
to find the peak.

 

[P3X-018]

In the Physics Formulary, it says:
Planck's law for the energy distribution for the radiation of af black body is:

omega(v,T) = ((8pi*h*v^3)/c^3)*(exp(hv/kT)-1)^-1

"Energy distribution" is that the intensity or flux?
They define the flux as P/A
http://scienceworld.wolfram.com/physics/EnergyFlux.html

:S

 

[Tide]

Edited:

Yes, I agree with that. It's the same as what I wrote - I just left off the normalization!

 

[P3X-018]

So is this the flux:

omega(v,T) = ((8pi*h*v^3)/c^3)*(exp(hv/kT)-1)^-1 ?

 

[Tide]

That looks good!