Talk:Josef Stefan

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I don't think "Austro-Hungary" is more common than "Austria-Hungary", see:

• http://search.britannica.com/eb/article?eu=11472&tocid=0&query=austria-hungary
• http://www.bartleby.com/61/0/A0530000.html
• Austria-Hungary

But perhaps we can write that he is an "Austro-Hungarian" from "Austria-Hungary" :-) User:Css

Okay. I agree since this term "Austro-Hungary", as it seems, is more common just in my native language and obviously not in English language. We can't write he was Austro-Hungarian because both his parents were Slovenes and there was no such nationality in those days. Best regards. --XJamRastafire 22:22 Oct 14, 2002 (UTC)

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In Joseph Stefan, 6 'graphs above the final section, "inductivity" is used where "inductance" might also work. They are not the same, but my physical intuition fails, and i have no idea whether this is

• a better choice,
• a poor choice bcz the more familiar one would serve as well, or
• a slip of the pen that makes the sentence false.

Brief attention, please, from the E&M professionals. --Jerzy 11:20, 2003 Dec 10 (UTC)

I guess that magnetic inductivity might work the best, if I understand what was your question :-) I'll check those meanings and I'll act according to my findings. --XJamRastafire 02:36, 29 Feb 2004 (UTC)

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Citizenship

Article says: citizenship, Austria; does this include Austrian Empire? --AndrejJ 13:27, 29 August 2007 (UTC)

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Not always equal

This text blurb: "As both incident radiation and blackbody emission are always equal" is wrong and violates 2LoT in the Clausius Statement sense.

The Prevost Theory of Exchanges claims that energy flows equally between objects regardless of energy density of the objects (and thus it claims that energy can flow without work being done). It's a theory from 1791 and considers radiation to be a rarefied material substance.

If one subscribes to the long-debunked Prevost Theory of Exchanges, one might be able to claim that incident radiation and blackbody emission are always equal at thermodynamic equilibrium. The Prevost Theory of Exchanges was replaced by the Kinetic Theory of Heat, which was replaced by Quantum Thermodynamics.

2LoT (in the Clausius Statement sense... "No process is possible whose sole result is the transfer of heat from a cooler to a hotter body") states that energy cannot flow from a lower to a higher-energy region without external work being done upon the system... not via conduction, not via radiative means, not macroscopically, not at the quantum scale [1], not ever. Do keep in mind the definition of heat: "an energy flux". Thus: "No process is possible whose sole result is an energy flux from a cooler to a hotter body" without external energy doing work upon the system.

Radiation energy density is proportional to T^4 and is derived via the thermodynamic relation between radiation pressure p and internal energy density u, using the electromagnetic stress–energy tensor: p = u/3, it represents the EM field contribution to the stress–energy tensor, describes the flow of energy in spacetime, and is a representation of the law of conservation of energy.

Free energy is defined as the capacity to do work. At thermodynamic equilibrium, the Helmholtz Free Energy is zero, thus photon chemical potential is zero, thus no work can be done by the photon, thus no energy can flow:

F = U - TS

Where:

F = Helmholtz Free Energy

U = internal energy

T = absolute temperature

S = final entropy

TS = energy the object can receive from the environment

If U > TS, F > 0... energy must flow from object to environment.

If U = TS, F = 0... no energy can flow to or from the object.

If U < TS, F < 0... energy must flow from environment to object.

If U = TS, p_photon = u/3 = p_object, energy cannot flow because no work can be done. Photon chemical potential is zero.

"Therefore, at thermodynamic equilibrium, the chemical potential of photons is always and everywhere zero. The reason is, if the chemical potential somewhere was higher than zero, photons would spontaneously disappear from that area until the chemical potential went back to zero; likewise, if the chemical potential somewhere was less than zero, photons would spontaneously appear until the chemical potential went back to zero." [2]

Thus photons from a lower energy density source are not even incident upon a higher energy density object. [3]

In a cavity (remember that blackbody radiation used to be called cavity radiation) at thermodynamic equilibrium, quantized standing-wave wavemodes are set up. The wavemode nodes are always at the cavity walls. The walls and the standing-wave wavemodes in the cavity space have the same energy density, thus photon chemical potential is zero, thus the photons cannot be absorbed and re-emitted by the cavity walls, they are reflected. The same thing occurs out here in the real world. Energy does not and cannot flow from lower energy density to higher energy density without external energy doing work upon the system.

"Another point which, this time, lies quite within the domain where our formulae are significant refers to the scattering of light by an elastically bound electron. Consider again our assembly of harmonic oscillators of frequencies k which we may imagine to take the discrete but very finely distributed values determined by [ kL - η(k) = π N (N = 1, 2, 3... ) ]. Let all of them be in the ground state (energy 3/2 ħ k) with the exception of one (frequency k') which has the energy 5/2 ħ k', the vibration parallel to - say - the x-axis being excited by one quantum ħ k'. In this situation light of frequency k' coming from all directions is continuously scattered by the electron.

...the light quanta in the external field... which are affected by the presence of the electron through the appearance of the phase shift η. We might also call them phase shifted light quanta..." [4]

IOW, the electric field of a non-resonant photon, ~100,000,000 times smaller than the Coulomb field seen by the bound electron(s), slightly changes the phase of the bound electron(s), as equally as it changes the phase of the incident photon... no energy is exchanged if the photon is not absorbed, only the phase is shifted, changing the photon's vector. This is how reflection from a step potential works. This is dependent upon the differential between energy density of the photon and atom / molecule. In the case of absorption, the photon constructively interferes with the available resonant quantum states of the atom or molecule. No phase shift

"This means that, at every point of the region of space that is in (pointwise) radiative equilibrium, the total, for all frequencies of radiation, interconversion of energy between thermal radiation and energy content in matter is nil (zero)." [5]

Again, photons from a lower energy density source will not even incide upon a higher energy density object. Thus they cannot be absorbed. They are reflected, which increases ambient field radiation pressure until the objects and the ambient field have the same energy density, whereupon the objects can no longer emit nor absorb, they can only reflect the photons in the quantized standing wavemodes in the ambient field.

In fact, not all photons of sufficient energy to be absorbed are absorbed due to the angular momentum selection rules... all quantum numbers (including angular momentum) must be conserved in order for a quantum transition to occur.

It's not that the object is absorbing radiation from the cooler ambient (or cooler object) thus slowing its cooling rate, it's that the radiation pressure of the cooler ambient (or cooler object) lowers radiative flux from the warmer object, thus lowering its cooling rate.

[1] https://www.pnas.org/content/112/11/3275

[2] https://en.wikipedia.org/wiki/Chemical_potential#Sub-nuclear_particles

[3] https://objectivistindividualist.blogspot.com/2017/11/solving-parallel-plane-black-body.html

[4] http://www.solvayinstitutes.be/pdf/Proceedings_Physics/1948.pdf#page253 — Preceding unsigned comment added by 71.135.33.222 (talk) 01:38, 6 February 2021 (UTC)