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Oct
10
comment Why do Oreo crumbs float to a single glob at the very center in a glass of milk?
If this were happening at the bottom of the cup, it would be explained in the same way as the so-called "tea leaf paradox" (en.wikipedia.org/wiki/Tea_leaf_paradox). But the fact that it's happening at the surface means something else is going on.
Sep
30
awarded  Explainer
Aug
19
comment How can the black body radiation formula be so general?
@EmilioPisanty yes, the answer could be clarified to give the explicit statement that both free electrons and free positive charges are required for bremsstrahlung, although this is a minor amendment (and could be implicitly understood because of charge conservation).
Aug
16
comment How can the black body radiation formula be so general?
@EmilioPisanty if positive ions are present, free electrons allow for bremsstrahlung, which is often responsible for generating thermal radiation.
Aug
9
awarded  Benefactor
Aug
8
comment Maintaining local thermodynamic equilibrium (LTE) in radiating gas with a broad atomic transition line
Yeah, I'm not sure about the thermal broadening yet, either. But you've definitely clarified some things for me.
Aug
8
comment Maintaining local thermodynamic equilibrium (LTE) in radiating gas with a broad atomic transition line
Ah, this is a promising perspective. I'll think about it some more to see if I agree. Most likely I'll end up giving you the bounty. Thanks for your help.
Aug
5
comment Maintaining local thermodynamic equilibrium (LTE) in radiating gas with a broad atomic transition line
Yes, the relations between the Einstein coefficients are often derived with the assumption of negligible line broadening. If these relations need to be refined for broad lines, that would be good to know. So now, which do you think is the most promising explanation here: the relations between the Einstein coefficients need to be refined, the application of the Boltzmann factor for the level population densities needs to be reconsidered, or both? I'd like to pinpoint in detail how this all works out.
Aug
4
comment Maintaining local thermodynamic equilibrium (LTE) in radiating gas with a broad atomic transition line
Hmm. Perhaps. I appreciate the contribution, although I am also not entirely sure this is the correct explanation. If this could be backed up with a more detailed derivation, or a reference, that would be most helpful.
Aug
3
comment Maintaining local thermodynamic equilibrium (LTE) in radiating gas with a broad atomic transition line
@RobJeffries Thanks, that is another good perspective from which to view my question, specifically "How could you expect LTE in a situation where the radiation field changes appreciable over the width of a line?" Any further help would be greatly appreciated.
Aug
1
awarded  Promoter
Aug
1
comment Why is bandwidth, range of frequencies, important when sending wave signals, such as in radio?
Beautifully explained
Aug
1
comment Shallow water wave question from Acheson's book
I think that the condition $\eta \ll h$ might just be the regime in which the shallow water results are valid. If your initial conditions lead to a situation where this is no longer true, then you can no longer use the shallow water equations. I don't think the condition can be 'derived.'
Aug
1
comment Maintaining local thermodynamic equilibrium (LTE) in radiating gas with a broad atomic transition line
@JánLalinský Thanks. In that case, my question is "what is the other line of reasoning needed to arrive at the Planck function for a single level transition?" And where exactly does the simplistic derivation in my question break down?
Jul
31
comment Maintaining local thermodynamic equilibrium (LTE) in radiating gas with a broad atomic transition line
@JánLalinský Even if there are only 2 levels in the atom, the line profile is not a delta function - there are a still a range of frequencies over which the atom can radiate for the single transition. (I think in Einstein's derivation he implicitly assumed that the line profile is a delta function, but I don't want to make that approximation). I'd expect based on thermodynamic arguments that you'd still get the Planck source function over all of those frequencies in the width of the line, not just the center of the line. Is that the case?
Jul
31
revised Maintaining local thermodynamic equilibrium (LTE) in radiating gas with a broad atomic transition line
added 29 characters in body
Jul
31
awarded  Curious
Jul
30
revised Maintaining local thermodynamic equilibrium (LTE) in radiating gas with a broad atomic transition line
added 84 characters in body
Jul
30
asked Maintaining local thermodynamic equilibrium (LTE) in radiating gas with a broad atomic transition line
Jul
4
revised Compressibility and the form of Newton's second law in fluid mechanics
added 409 characters in body