Physics Help Forum Rayleigh-Jeans law

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 Jul 20th 2019, 05:27 AM #1 Junior Member   Join Date: Jul 2019 Posts: 26 Rayleigh-Jeans law Good Afternoon, As I told you in my presentation, at 70 years old, I start to learn physics. My brain is a little bit slow and confused…so sorry for my (most of prabable) trivial question. I read on a website that the law of Rayleigh-Jeans is given for the radiance function of wavelenght (λ) Radiance (function of wavelength)=2ckT/λ square Radiance (function of frequency)=(2kT/c square). v square with λ=c/v and the partial derivative dλ/dv=c/v square v is the frequency...don't found to type the greek letter My questions: 1.How to reach the second equation starting from the first one (please detailed step by step explanation ? 2.In the second equation why a partial derivative has to be added ? 3. How to reach for the partial derivative dλ/dv the value c/v square...trivial, sorry Thanks in advance and best regards
 Jul 20th 2019, 06:11 AM #2 Senior Member   Join Date: Aug 2010 Posts: 434 $\lambda$ is the wavelength in, say, meters, $\nu$ is the frequency in, say, "waves per second", and c is the wave speed in meters per second. Imagine standing by a fixed point, watching the waves go by. In "T" seconds, you will have seen waves to a total length of cT meters go by. Since each wave has length $\lambda$ you will have seen $\frac{cT}{\lambda}$ waves. So $\nu T= \frac{cT}{\lambda}$ or $\nu= \frac{c}{\lambda}$. That can also be written as $\lambda\nu= c$ or $\lambda= \frac{c}{\nu}$. If the wave has constant wave speed (as, for example, light in vacuum) then we could easily switch between wave length and frequency using $\lambda= c\nu$: to go from Radiance (function of wavelength)=$\frac{2ckT}{\lambda^2}$ Radiance (function of frequency)=$\frac{2kT\nu^2}{c}$ replace $\lambda^2$ with $\left(\frac{c}{\nu}\right)^2= \frac{c^2}{\nu^2}$: $\frac{2ckT}{\lambda^2}= \frac{2ckT}{1}\frac{\nu^2}{c^2}= \frac{2ckT\nu^2}{c^2}= \frac{2kT\nu^2}{c}$. If the wave speed, c, is NOT constant but varies with time then the relationship between wave length and frequency varies so we need that partial derivative topsquark likes this.
 Jul 20th 2019, 02:44 PM #3 Junior Member   Join Date: Jul 2019 Posts: 26 Rayleigh-Jeans law Dear friend, Thanks for the reply, however is something I don't understand. For the Radiance L (function of wave length) as denominator you write lambda square. From what I read on the net, the denominator written is lambda exponent 4 Please, can you clarify this point Thanks in advance and best regards
Jul 21st 2019, 11:30 AM   #4
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Join Date: Aug 2010
Posts: 434
I was just going by what you wrote:
 I read on a website that the law of Rayleigh-Jeans is given for the radiance function of wavelenght (λ) Radiance (function of wavelength)=2ckT/λ square Radiance (function of frequency)=(2kT/c square).
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 Jul 21st 2019, 07:01 PM #5 Junior Member   Join Date: Jul 2019 Posts: 26 Sorry to bother you with that... As you see I'm a zero I must have misread the article. So I reformulate after having reading few more articles L fact wave length(T) = 2ckT/ lambda power 4 Knowing lambda= c/v and d lambda=(c/v square) d v Give d lambda= (c/v square) DV Then Lv(T) = (2kT/c square) v square C= light speed in vacuum K= Boltzmann contacts T= temperature I don't understand how to go from first equation to second. Please and thanks in advance to write a line by line. Im sure that my problem is coming from this partial derivative. As well I don't understand how from lambda=c/v reaching d lambda= (c/v square) DV No. My case is not desperate... It just I start from scratch at 70. Thanks in advance and regards Philippe
 Jul 21st 2019, 11:13 PM #6 Junior Member   Join Date: Jul 2019 Posts: 26 Dear All, After spending few time... I find and I understand. The only question remaining is to know how Rayleigh and Jeans discover L(lambda) = (2ckT) / lambda power 4 Empirical or from theory? Thanks and regards
 Jul 22nd 2019, 12:52 AM #7 Junior Member   Join Date: Jul 2019 Posts: 26 Hello, Continuing reading what I find on the subject The rayleigh-Jeans law will come from the equipartition theorems? WHAT IS THAT??? If someone can give me some clues I remember you that Wikipedia is blocked here. I would like to understand equipartition and the way to followed to reach the rayleigh-Jeans law Thanks and best regards Philippe
Jul 22nd 2019, 02:24 AM   #8
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Join Date: Oct 2017
Location: Glasgow
Posts: 426
 Originally Posted by philippe Hello, Continuing reading what I find on the subject The rayleigh-Jeans law will come from the equipartition theorems? WHAT IS THAT??? If someone can give me some clues I remember you that Wikipedia is blocked here. I would like to understand equipartition and the way to followed to reach the rayleigh-Jeans law Thanks and best regards Philippe
The equipartition theorem states that for every degree of freedom of a gas molecule, there exists a quantity of energy $\displaystyle \frac{1}{2}kT$ that can be absorbed as heat (i.e. to heat capacity).

There is a derivation here:
Rayleigh-Jeans Law Development

Let me know if you can access it or not.

 Jul 23rd 2019, 03:58 AM #9 Junior Member   Join Date: Jul 2019 Posts: 26 Dear All, You are lucky to have access to Wikipedia. Now I'm in definition I'm searching what is the emitted flux density (Wm*2) and the emitted energy (J m*-3) it's related to my learning on black body. As well what is the irradiance? Of course again trivial basic questions. Sorry for that. Thanks in advance and regards Philippe
 Jul 23rd 2019, 04:43 AM #10 Senior Member   Join Date: Oct 2017 Location: Glasgow Posts: 426 Sorry, I replied to this in the other thread: Introducing myself...Philippe from China

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