Question about Planck's Law of Radiation

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Discussion Overview

The discussion revolves around the high and low temperature limits of Planck's Law of Radiation, exploring their mathematical implications and the distinctions between classical and quantum physics. Participants seek clarification on how these limits relate to the behavior of the radiation formula and the underlying physics principles.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants inquire about the mathematical conditions for the high and low temperature limits of Planck's Law and their implications.
  • One participant suggests that the high temperature limit leads to an undefined value, referencing the ultraviolet catastrophe, while the low temperature limit approaches zero.
  • Another participant emphasizes the need to discuss frequency dependency rather than solely focusing on temperature as a variable.
  • There is a contention regarding whether the high temperature limit is part of classical theory, with some arguing it should be framed in terms of frequency rather than temperature.
  • Participants express confusion over the relationship between temperature and frequency, with some asserting that classical physics fails to predict behavior at high frequencies, while quantum theory accounts for all frequencies.
  • One participant asserts that classical theory predicts an infinite amount of energy radiated at all frequencies, contrasting it with Planck's Law, which provides a finite prediction.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of high and low temperature limits, with multiple competing views on the relationship between temperature and frequency, as well as the implications for classical versus quantum physics.

Contextual Notes

Some participants express uncertainty about the definitions and implications of the high and low temperature limits, indicating a need for clarity on the mathematical steps involved and the assumptions underlying classical and quantum interpretations.

mathlete
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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.
 
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Please take the following limits
[tex]h\nu>>kT[/tex] (1)
and
[tex]h\nu<<kT[/tex] (2)

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

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

Daniel.
 
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")?
 
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.
 
dextercioby said:
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.
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 :confused:
 
I'm sorry,but your problem is meant to confuse...Trust me,u should discuss frequency dependence...


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


Daniel.
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?
 
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.
 
dextercioby said:
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.
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
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
dextercioby said:
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.
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
you messed up the whole concept already, mathlete...there are only ONE Planck law, we use that law for ALL temperature...
[tex]h\nu>>kT[/tex] 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 want to see how the graph looks like, here you go
http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html
 
  • #13
vincentchan said:
you messed up the whole concept already, mathlete...there are only ONE Planck law, we use that law for ALL temperature...
[tex]h\nu>>kT[/tex] 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 want to see how the graph looks like, here you go
http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html
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! :cool:
 
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  • #14
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 want to 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... :wink:
 
Last edited:
  • #15
vincentchan said:
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 want to 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... :wink:
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 :confused:

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
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
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.
 

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