1. Apr 20, 2013

### Physics Monkey

Obtaining the correct black body spectrum is one of the great triumphs of quantum physics. It is also touted as a total failure of classical physics, since with very basic assumptions, namely thermal equilibrium and the validity of Maxwell's equations, one gets the well known divergent spectrum.

I was wondering if anyone had any information about how physicists of the time tried to get around this problem. In particular, something which always seemed natural to me was the relaxing of the thermal equilibrium assumption. For example, its not obvious to me (given 19th century knowledge) why extremely high frequency light should be in thermal equilibrium with ordinary matter. Did the physicists of the time think about such high energy physics?

2. Apr 20, 2013

### SteamKing

Staff Emeritus
3. Apr 20, 2013

### atyy

Wikipedia gives a derivation of the Stefan-Boltzmann law from classical thermodynamics. I think the Stefan-Boltzman law was also already known from experiments. So maybe this was why they considered equilibrium.
http://en.wikipedia.org/wiki/Stefan–Boltzmann_law#Thermodynamic_derivation

Apparently Wien's law also has a thermodynamic derivation. I think they could also have done experiments which would verify the relation. http://en.wikipedia.org/wiki/Wien's_displacement_law

If so, both would be laws which although derivable from Planck's law, also have independent derivations from classical thermodynamics.

Last edited: Apr 20, 2013
4. Apr 20, 2013

### Jano L.

The divergence comes out because the processes of radiation are replaced by an idea of an infinite system of harmonic oscillators of unlimited frequency, and the energy of these oscillators is assumed to be $kT$.

The assumption of equilibrium and validity of Maxwell's equations should not be blamed for the wrong result, since these are adopted in the quantum theory, from which the Planck formula is derived today.

To my knowledge, the divergence of the spectrum lead Jeans to propose that the establishment of the equilibrium may take very long time, so that the measured emission curve does not correspond to equilibrium between radiation and matter. Rayleigh had reservations to derivations of the equipartition theorem, and wrote

"
it seems to me that we must admit the failure of the law of equipartition in these extreme cases
"
in the paper "The dynamical theory of gases and of radiation".

I think these and other older physicists concerned with the thermal radiation thought that some modifications of the theory will be necessary, but they did not think that the Rayleigh-Jeans formula presents a failure of the whole then known physics. That would be an interpretation that is more properly assigned to younger physicists who developed quantum theory and its exponents, like Einstein, Debye, Heisenberg (and others).

5. Apr 21, 2013

### atyy

Gasiorowicz says they did have data confirming Wien's displacement law (which is different from the approximate Wien formula mentioned below). He credits Lummer and Pringsheim, and Rubens and Kurlbaum.
http://www.otto-lummer.de/waermestrahlung.html

Planck in 1918 mentions "general, well-established displacement law by Wien", which did not need correction. The formula which is corrected by quantum calculations he calls "Wien's energy distribution law". He mentions many experimentalists. http://www.nobelprize.org/nobel_prizes/physics/laureates/1918/planck-lecture.html

Wikipedia references Wannier's text for the thermodynamic derivation. Looking on Google books, Wannier memtions a number of other properties which classical thermodyanmics gets correct from several other theorists. He says it was only the energy distribution that they could not get (I guess that's stat mech).

Last edited by a moderator: May 6, 2017
6. May 27, 2013

### ashi123

i need to find the view factor of a point source at a distance of 120 m from one end of a square body, considered to be at origin. can you help me find the limits of integral?
for the square to be of dimension 500*500

7. May 27, 2013

### George Jones

Staff Emeritus
Last edited by a moderator: May 6, 2017