1. Jan 26, 2005

mathlete

Basically I have to discuss what the high temperature limit/low temperature limits of Planck's Law are, what they mean mathematically, and why the first is "classical" and the second can't be obtained from "classic" physics. If anyone could clarify what these points mean i'd be grateful. I think it has something to do with the exponential in the denominator of the equation, but i'm not sure.

2. Jan 26, 2005

dextercioby

$$h\nu>>kT$$ (1)
and
$$h\nu<<kT$$ (2)

in the Planck's law which gives the spectral volume energy density:
$$\rho_{\nu,T} =\frac{8\pi h}{c^{3}}\frac{\nu^{3}}{e^{\frac{h\nu}{kT}}-1}$$ (3)

and obtain the "classical" limits gotten by Rayleigh & Jeans and Wien,respectively...

Daniel.

3. Jan 26, 2005

mathlete

Hi, thanks for the response. I had that figured out to the most part, I think. As T goes to infinity, the whole value approaches an undefined value (the "high" temp limit I assume). Is this what they meant by ultraviolet catastrophe?

For the second part, as T goes to 0 the whole thing goes to 0. This part confused me however, why can't that be obtained from classical physics? Or is it that classical physics predicted it would go to infinity (hence this is where the ultraviolet catastrophe is predicted - but that what makes the first one "classical")?

4. Jan 26, 2005

dextercioby

That T is a "tunable" parameter...In fact u must discuss various behavior wrt to the frequency...

So leave temperature alone...Take it as constant (fixed) and discuss frequency dependency...

Daniel.

5. Jan 26, 2005

mathlete

OK... so how come the problem states something about "high/low temperature limit"? I thought that T is the parameter being changed to see what happens

6. Jan 26, 2005

dextercioby

I'm sorry,but your problem is meant to confuse...Trust me,u should discuss frequency dependence...

Daniel.

7. Jan 26, 2005

mathlete

Not that I don't believe you, but why frequency dependence? I read the problem almost word for word off the page, and it says temperature limits. I guess i'm just confused, but isn't temperature the independent variable?

8. Jan 26, 2005

dextercioby

The Planck's radiation formula is a function of 2 INDEPENDENT VARIABLES:temperature & frequency...If u want to take limits wrt to temperature,please by my guest...

Daniel.

9. Jan 26, 2005

mathlete

I see. Is it wrong to do it that way though? Basically at this point I just can't understand why the "high" temperature limit is part of classic theory, and why "low" temperature limit is quantum theory.

10. Jan 26, 2005

dextercioby

No,no,let's not mix things...Low-energy approximation is one thing and high temperature approximation is another...This distribution is entirely quantum.Its classical limits are obtained by taking the limits wrt to ENERGY/FREQUENCY,not temperature.

Daniel.

11. Jan 26, 2005

mathlete

Hrm. OK, let me ask this then - what did classical physics predict the graph of Energy v. Temperature would look like, and what did it actually look like (which quantum predicted)?

Let me give you exactly what I have word for word so you see what i'm dealing with:

"What is the high temperature limit of the Planck law? What is the condition mathematically, and how do you go about getting the high T limit? Why is this "classical"?"

And: "What is the low temperature limit of the Planck law? What is the condition mathematically? This is not 'classical' and can't be obtained from any classical physics - why?"

12. Jan 26, 2005

vincentchan

you messed up the whole concept already, mathlete.....there are only ONE planck law, we use that law for ALL temperature.....
$$h\nu>>kT$$ read as "when the frequency is much much greater than kT", not the other way.... you ain't set the temperature low, oppositely, you set the frequency high....
the "high temperature limit" you mentioned is a misleading.... you should say the "low frequency limit" instead....
classical theory won't work at "high frequency limit".... if you wanna see how the graph looks like, here you go
http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html

13. Jan 26, 2005

mathlete

Ah, I see. I just gave you what was on the hand out - thanks for that link. Will it be right to tell the class it isn't actually set by temp, but by frequency? I don't want to seem to be correcting the professor or anything. I think I get everything now though, thanks. Just one side note out of curiosity - how is frequency set?

edit: By the way, thanks for the help VERY much everyone!

Last edited: Jan 26, 2005
14. Jan 26, 2005

vincentchan

you do not set the frequency, at a fixed temperature, let's say 6000 degree. a blackbody emits photons of all frequency... classical theory failed to predict the number of photons with high frequency... and quantum theory works at ALL frequency

if you wanna know what is HIGH FREQUENCY... read the 2nd post again... wish you don't misunderstand what dextercioby said this time

PS. if you have time, read all the posts in this thrend again... if you understand what dextercioby trying to tell you, and know what was your mistake.... that's mean you started to understand the concept.....

Last edited: Jan 26, 2005
15. Jan 26, 2005

mathlete

See, I get confused since you seem to keep changing what you're saying (to me, anyway).

These are two quotes directly from you:
"you set the frequency high"
"you do not set the frequency"

????

I'll try reading the thread over again, maybe i'll catch my mistake

edit: I do realize that a particular temperature has a set max frequency (a la Wein's Displacement Law), but why does that mean you don't set the temperature? If anything, i'd assume you DO set the temperature, not the frequency

16. Jan 26, 2005

vincentchan

sorry for my confusion.... let me rephase what i said

"you set the frequency high"--->>> at high frequency

you always FIXED the temperature and see what happened at different frequency....

17. Jan 28, 2005

VincentS

classic vs QM

Classic states that a object should radiate at every frequency, so technically anything that radiates would give off an infinite amount of energy. Which is like saying your thermo blanket gives off the same amount of energy as the sun. Using classic you can find the low frequency but to find the max freq you have to use Plancks.

Planck states that a object will only radiate at a frequency if it has enough energy to do so, basically. So at higher frequencies which require higher energies there is a limit. So putting a limit on the max energy out and getting rid of those pesky infinities.