Radiative exchange in an ultrafine dust

[KarenRei]

If we had a solid object of 1 square meter surface area, its maximum rate of radiation would be that of a blackbody of the same surface area, correct?

Now, if we had a cloud of ultrafine (<100nm) dust wherein the surface area of the *cloud* was 1 square meter, would it be similarly limited? Or would it be capable of significantly exceeding this, depending on the circumstances, due to the vastly increased surface area of the individual dust particles?

Now, obviously the dust particles aren't just going to be radiating their heat to the exterior - there's also going to be radiative exchange with each other, as particles both give off heat but also receive them from each other. If they were equally effective at radiatively emitting heat as they were at receiving it, one would expect the cloud to have the same limits as a solid 1-square-meter blackbody, since the only true radiative heat loss would be done at the surface.

However, is it possible that the particles could be effective emitters at a given frequency without being effective absorbers of that frequency? If that would be the case, then it would seem that the dust could emit at a greater rate than that of a solid 1-square-meter blackbody. But is that even possible?

If the above is not directly possible, the other thing that seems like it could distort the situation is if the emission of a photon cooled the dust particle enough to change its optical properties. After all, if a dust is fine enough and contains a small enough number of atoms, a single photon emission could have a relevant impact on its temperature. However, if this was the case we'd expect to see this effect most pronouncedly with the smallest possible "particles" - that is, simple gases. Do we? Are there gases that emit at a given frequency than they absorb it? But that would seem to imply a gas which emits faster than its blackbody temperature, which I've never heard of. Yet conceptually, if a material is changing in temperature, it only seems logical that it should be able to change in optical properties...

Just trying to get a better handle, conceptually, on these aspects of radiative heat transfer. :)

 

[mfb]

If your cloud is within a volume that has a surface area of 1m^2, then the blackbody power of a solid object is an upper limit on the emission of this cloud. To reach this upper limit, the cloud has to be completely intransparent, which requires a minimal density of this cloud (not as dense as a solid object of course). There is no way to get more power - the total surface area of the dust particles is huge, but the equilibrium energy density is independent of this. That is true for every wavelength independently and therefore for the whole spectrum, too.

Particles smaller than the wavelength of the relevant light are special on their own. Their emission spectrum often depends on their size.

Are there gases that emit at a given frequency than they absorb it?

Not in equilibrium, that would violate thermodynamics. If the gas is hotter than the environment, it emits more than it absorbs, if it is colder it absorbs more than it emits; but that does not allow to exceed cooling power of a black body.

 

[KarenRei]

Do you care to elaborate? I asked questions more specific than that. In particular:

1) "However, is it possible that the particles could be effective emitters at a given frequency without being effective absorbers of that frequency?"

2) The situation where, by emitting a photon, a substance cools and thus its optical properties are altered

3) Why #2 either doesn't occur or is inapplicable to gases.

I'm just trying to understand the rules better, their limitations, and why they are what they are. :)

Ed: When talking about "optical properties", I'm referring to the fact that substances, whether gases, dusts, whatever are not all equally good at absorbing in different frequencies - hence the reason that things like a greenhouse effect can occur. Dust particles are different sizes at different temperatures and size matters a lot on the optical particles sub-micron particles. For any type of matter state changes can occur, even reversible chemical reactions between different temperatures.

 

[KarenRei]

Not in equilibrium, that would violate thermodynamics. If the gas is hotter than the environment, it emits more than it absorbs, if it is colder it absorbs more than it emits; but that does not allow to exceed cooling power of a black body.
.

Is that to say, if there is a substance that is not an effective emitter for a certain frequency of light, then it's inherently an equivalently poor absorber of said frequency, and vice versa?

(note that this doesn't deal with #2 and #3 above)

 

[mfb]

1) "However, is it possible that the particles could be effective emitters at a given frequency without being effective absorbers of that frequency?"

This is not possible, it would violate the laws of thermodynamics.

Is that to say, if there is a substance that is not an effective emitter for a certain frequency of light, then it's inherently an equivalently poor absorber of said frequency, and vice versa?

Correct.

2) The situation where, by emitting a photon, a substance cools and thus its optical properties are altered

At least for atoms and molecules this is certainly possible, but due to the statistical nature of the process it does not help. The energy levels will follow the same distribution independent of the properties of individual transitions.

The greenhouse effect is possible only because the sun is a very hot and very collimated source of light. The Earth converts the directed visible light to undirected infrared emissions.
If the sun would be everywhere around us, our surface temperature would be equal to the surface temperature of the sun, without any greenhouse effect possible.

 

[KarenRei]

At least for atoms and molecules this is certainly possible, but due to the statistical nature of the process it does not help.

I'm not clear on how it wouldn't help. If a substance emits/receives better when hot than when cold, and of course naturally hot particles emit more than cool ones proportional to T^4, then why wouldn't it emit more? Hmm... I think I need to think about it more, maybe sketch it out on paper... Anyway, thanks :)

 

[mfb]

The blackbody intensity is the upper limit. If the intensity is lower than that it is possible to have more emission than absorption, if the intensity is higher than that it is not possible. There is no process that would allow more emission beyond the blackbody intensity. And there is no process that would transfer heat from a colder object to a hotter one.

Population inversion can get emission beyond the blackbody intensity for the "regular" temperature, but you cannot get population inversion with thermal processes.

 

[KarenRei]

I sketched it out in the 1 dimensional case and what you wrote makes sense. But something else occurred to me: I presume that the blackbody limit only the limit for a body in thermal equilibrium? That is to say, the energy of a set of particles does not follow a perfect Maxwellian distribution then the emission may deviate from the blackbody limit for an object of the same geometry, material, and average particle energy?

 

[mfb]

The limit depends on the temperature, of course. Hotter particles will lead to more emission. You cannot make the outermost particles hotter than the inside, however, because that would need some active cooling mechanism for the inside.

 

[KarenRei]

I wasn't thinking about an anisotropic temperature differential between different regions, rather a substance that as a whole is not in thermal equilibrium. For example, the case of two optically opaque plasmas whose only differences are that one is maxwellian and the other non-maxwellian, but whose average particle energy is the same. I presume that they would not have the same radiation rate - is that correct?

 

[KarenRei]

Interesting - this paper describes how it's actually common for electron and ion velocities in dusty plasmas in common real-world situations of interest to deviate significantly from a Maxwellian distribution:

http://www.researchgate.net/profile/Shikha_Misra/publication/258169488_Charging_kinetics_of_dust_particles_in_a_non-Maxwellian_Lorentzian_plasma/links/00b495375b884f176d000000.pdf

No information (at least that I'm getting from it) about how this would change the total radiation versus a blackbody of the same average energy, however. My expectation would be that it would have a significant effect, given that matter radiates proportional to T^4 but mean energy is just a linearly weighted average. But it'd be nice to have something more concrete than just an "expectation".