Energy flux versus temperature change

[kmarinas86]

If I have two spheres of the same radius, they can still have different temperatures. However:

What if the colder sphere is closer to the ideal of being a blackbody than the hotter sphere?

http://en.wikipedia.org/wiki/Emissivity

In an open system without internal energy generation, both spheres would get colder. However, the colder sphere would lose energy faster than the hotter sphere. In other words, the temperature difference between the two spheres would increase.

However, if enough of the energy of one sphere were to be lost to the other sphere, and vice versa, then it would mean that the hotter sphere would receive more energy than it lost, while the colder sphere would lose more energy than it gained.

What is obvious is a net transfer of energy. What is not obvious is what exactly that would do to the hotter sphere. Would it get hotter? Or would contribute to a phase change in the hotter sphere?

 

[Dale]

Are you envisioning that these two spheres are only in thermal contact with each other and that the only means of heat transfer is via radiation?

 

[kmarinas86]

Are you envisioning that these two spheres are only in thermal contact with each other and that the only means of heat transfer is via radiation?

Yes.

 

[Dale]

Then I think that the only effect of one body being a graybody is to slow the approach to thermal equilibrium. Any radiation emitted by the blackbody at one of the reflective frequencies of the graybody will simply be re-absorbed by the black body, slowing the heating of the blackbody. Any radiation emitted by the graybody will be absorbed better by the blackbody.

 

[Dale]

Then I would imagine it would go even slower. In the limit of a graybody where there was no absorption/emission at other than a single frequency and that frequency did not match then they would simply remain the original temperatures and not transfer any energy at all.

 

[kmarinas86]

Then I think that the only effect of one body being a graybody is to slow the approach to thermal equilibrium. Any radiation emitted by the blackbody at one of the reflective frequencies of the graybody will simply be re-absorbed by the black body, slowing the heating of the blackbody. Any radiation emitted by the graybody will be absorbed better by the blackbody.

What if both are graybodies?

Then I would imagine it would go even slower. In the limit of a graybody where there was no absorption/emission at other than a single frequency and that frequency did not match then they would simply remain the original temperatures and not transfer any energy at all.

What if the colder sphere has a high emissivity at low-frequencies, the same frequency range where it peaks (thus helping it to emit heat), and a low emissivity at high-frequencies of which is scant inside the colder sphere (so negligible effect on limiting emission), the same high-frequencies which are at the same time being emitted by the hotter sphere (thus the heat of the hotter sphere is reflected away by the colder sphere), while the hotter sphere has a low emissivity in high-frequency range in which it would otherwise peak (thus reducing the emission of its own heat, providing yet another limitation on the transfer of heat from the hotter sphere to the colder sphere), while it has high emissivity at low-frequencies of which are scant inside the hotter sphere (so negligible effect on increasing emissions by the hotter sphere), permitting heat flux of low-frequencies from the colder sphere. Let's say that there exist super-low-frequencies which the colder sphere has a high emissivity for, while the hotter sphere has a low emissivity for them. So energy received by the hotter sphere from the colder sphere as low-frequencies get downgraded as super-low frequencies that get trapped by the hotter sphere. The result of all that is a net energy flux from the colder sphere to the hotter sphere. What does the energy affect when it is transferred like that?

 

[Dale]

Let's say that there exist super-low-frequencies which the colder sphere has a high emissivity for, while the hotter sphere has a low emissivity for them.

If the hot sphere has a low emissivity for them then it also has a low absorptivity. It will not absorb the radiation emitted by the colder sphere. This is approximately the situation that I was describing earlier where they simply do not interact thermally.

The result of all that is a net energy flux from the colder sphere to the hotter sphere.

The result is never a net energy flux from the colder to the hotter sphere.

 

[kmarinas86]

If the hot sphere has a low emissivity for them then it also has a low absorptivity. It will not absorb the radiation emitted by the colder sphere. This is approximately the situation that I was describing earlier where they simply do not interact thermally.

The result is never a net energy flux from the colder to the hotter sphere.

Imagine that we are talking about spherical shells filled with inert gases. A mirror-like low emissitivity shell limits the transfer of radiation in both directions, not just into the sphere. But this value depends on the frequency of the light. Light into a greenhouse experiences higher emissitivity going in, but due to scattering, a frequency reduction, and thus lower emissitivity going out. Thus it is easier to absorb it at first, but once it is in, it is not so easy for it to escape.

 

[Dale]

Absorptivity and emissitivity are not proportional. One can be high while the other is low. Or vice versa. Just as both can be high or both can be low. The is no universal proportionality constant between. They both depend on the qualities of the medium.

Not only are they proportional, they are equal:
http://en.wikipedia.org/wiki/Kirchhoff's_law_of_thermal_radiation

"a corollary of Kirchhoff's law is that for an arbitrary body emitting and absorbing thermal radiation in thermodynamic equilibrium, the emissivity is equal to the absorptivity"

 

[kmarinas86]

Not only are they proportional, they are equal:
http://en.wikipedia.org/wiki/Kirchhoff's_law_of_thermal_radiation

"a corollary of Kirchhoff's law is that for an arbitrary body emitting and absorbing thermal radiation in thermodynamic equilibrium, the emissivity is equal to the absorptivity"

I have corrected this in my previous post. They are not constant with wavelength, even if they are proportional. As energy scatters inside the sphere, n*h increases and f declines, so wavelength increases. This can have negative effects on *subsequent* emission (via lower emissitivity of the sphere at longer wavelengths), while absorption is still as normal for the incoming light (prior to scattering inside).

 

[Dale]

They are not constant with wavelength, even if they are proportional.

I understand that we are talking about emissivity functions which are not constant wrt wavelength. That is what I have been describing for the last several posts. It doesn't matter.

Pick any given wavelength.

If the hot body and the cold body both have high emissivity or both have low emissivity then obviously energy at that wavelength goes from hot to cold.

If the hot body has high emissivity and the cold body has low emissivity then the hot body produces a lot of radiation at that wavelength and the cold body absorbs some small fraction and reflects the rest, with net energy from hot to cold.

If the cold body has high emissivity and the hot body has low emissivity then the cold body emits some modest amount of radiation which is almost entirely reflected by the hot body and the hot body emits a small amount of radiation which is almost entirely absorbed by the cold body, with net energy transfer from hot to cold.

Repeat at every other wavelength.

 

[kmarinas86]

I understand that we are talking about emissivity functions which are not constant wrt wavelength. That is what I have been describing for the last several posts. It doesn't matter.

Pick any given wavelength.

If the hot body and the cold body both have high emissivity or both have low emissivity then obviously energy at that wavelength goes from hot to cold.

If the hot body has high emissivity and the cold body has low emissivity then the hot body produces a lot of radiation at that wavelength and the cold body absorbs some small fraction and reflects the rest, with net energy from hot to cold.

If the cold body has high emissivity and the hot body has low emissivity then the cold body emits some modest amount of radiation which is almost entirely reflected by the hot body and the hot body emits a small amount of radiation which is almost entirely absorbed by the cold body, with net energy transfer from hot to cold.

Repeat at every other wavelength.

You're not poining out the fact that we have a changing wavelength when the light scatters. You are comparing different scenarios, each with a different wavelength. That's different than one scenario with separate before and after wavelengths.

 

[Dale]

You're not poining out the fact that we have a changing wavelength when the light scatters. You are comparing different scenarios, each with a different wavelength. That's different than one scenario with separate before and after wavelengths.

Scattering doesn't change the wavelength, except via Doppler shift. I was assuming that the bodies were at rest wrt each other.

 

[kmarinas86]

Scattering doesn't change the wavelength, except via Doppler shift. I was assuming that the bodies were at rest wrt each other.

You don't even need the Doppler effect. Phosphorescent glow under UV light is a case in point.

 

[Dale]

That isn't scattering. That is absorption and emission. It always goes from hot to cold as I described above.

 

[kmarinas86]

That isn't scattering. That is absorption and emission. It always goes from hot to cold as I described above.

The point is that "absorption and emission", to not use the word "scattering", mind you, can change the wavelength.

You just assumed "that the bodies were at rest wrt each other" to argue that the wavelength does not change. The wavelength does change. So your assumption is wrong.

So that assumption must be unnecessary for your earlier argument to be valid. This assumption however, IS required for your reasoning to work:

I understand that we are talking about emissivity functions which are not constant wrt wavelength. That is what I have been describing for the last several posts. It doesn't matter.

Pick any given wavelength.

...obvious lack of a plural.

If the hot body and the cold body both have high emissivity or both have low emissivity then obviously energy at that wavelength goes from hot to cold.

For an energy in-of-itself to go from "hot to cold" implies a wavelength increase. A wavelength increase affects its relationship with the material that it may interact with. Thus, a material may be better or worse at emitting it. This relationship is by no means monotonic:

http://en.wikipedia.org/wiki/Optical_window

Thus, as energy can be downgraded in frequency it may lead to increases or decreases in the energy's ability to be absorbed and re-emitted by the atmosphere. The "optical window" as the picture depicts, represents a region of the EM spectrum in which the Earth's atmosphere has a low emissivity. Those regions largely ignore the atmosphere and pass right through.

If the hot body has high emissivity and the cold body has low emissivity

This is where you get it completely wrong. A greybody (whether hot or cold) cannot be reduced to simplistic notions as having "high" or "low" emissivity. A simple grasp of the nature of the optical window proves that such a simplistic viewpoint is wrong. These variations in emissivity are VERY significant, and they cannot be described using simplistic formulas because the actual values depend on the atmospheric composition, consisting of a various mixture of chemicals.

then the hot body produces a lot of radiation at that wavelength and the cold body absorbs some small fraction and reflects the rest, with net energy from hot to cold.

A notable amount of radiation is generated due to re-emission of energy at different wavelengths. The amount of visible rays absorbed by the Earth is greater than the amount of visible rays emitted by the Earth because the visible rays get re-emitted at lower frequencies, while UV part of the spectrum is past the Sun's peak color, so it doesn't quite make up for that drop in visible light.

Your analysis (along together with your prior statement that "not only are they proportional, they are equal"), in contrast, projects that the amount of light at a given wavelength absorbed by a body will equal the amount of light at that wavelength emitted by a body. That is simply not right in the case of anything capable of emitting or absorbing a broken visible and/or infrared spectrum. Such are deviations from Maxwell-Boltzmann statistics, and thus they are automatically non-equilibrium in nature.

If the cold body has high emissivity and the hot body has low emissivity then the cold body emits some modest amount of radiation which is almost entirely reflected by the hot body and the hot body emits a small amount of radiation which is almost entirely absorbed by the cold body, with net energy transfer from hot to cold.

Repeat at every other wavelength.

See above.

What if the colder sphere has a high emissivity at low-frequencies, the same frequency range where it peaks (thus helping it to emit heat), and a low emissivity at high-frequencies of which is scant inside the colder sphere (so negligible effect on limiting emission), the same high-frequencies which are at the same time being emitted by the hotter sphere (thus the heat of the hotter sphere is reflected away by the colder sphere), while the hotter sphere has a low emissivity in high-frequency range in which it would otherwise peak (thus reducing the emission of its own heat, providing yet another limitation on the transfer of heat from the hotter sphere to the colder sphere), while it has high emissivity at low-frequencies of which are scant inside the hotter sphere (so negligible effect on increasing emissions by the hotter sphere), permitting heat flux of low-frequencies from the colder sphere? Let's say that there exist super-low-frequencies which the colder sphere has a high emissivity for, while the hotter sphere has a low emissivity for them. So energy received by the hotter sphere from the colder sphere as low-frequencies get downgraded as super-low frequencies that get trapped by the hotter sphere. The result of all that is a net energy flux from the colder sphere to the hotter sphere. What does the energy affect when it is transferred like that?

 

[Dale]

The point is that "absorption and emission", to not use the word "scattering", mind you, can change the wavelength.

You are interested in the process of energy transfer from one body to the other. Absorption and emission do not change the wavelength during energy transfer. A given wavelength that is emitted by one body is either absorbed or reflected by the other. It is simply not possible for the wavelength emitted by one to be different from the wavelength absorbed by the other in this scenario.

Once the wavelength is absorbed the energy and temperature of the absorbing body increases. It then emits the energy according to its own characteristic emission spectrum, but that is a new emission-absorption transfer of energy. In each emission-absorption transfer the wavelength does not change.

All of my comments above apply.

This is where you get it completely wrong. A greybody (whether hot or cold) cannot be reduced to simplistic notions as having "high" or "low" emissivity.

I never said that it did. I made the big deal of picking a wavelength in the beginning so that I wouldn't have to keep on writing "at that wavelength" throughout the description. And at a given wavelength a greybody can be reduced to having a "high" or "low" emissivity in this scenario, which can change at a different wavelength. Which is what I said.

Your analysis (along together with your prior statement that "not only are they proportional, they are equal"), in contrast, projects that the amount of light at a given wavelength absorbed by a body will equal the amount of light at that wavelength emitted by a body.

I certainly never said that, nor does it follow from my analysis. I never discussed energy absorbed and emitted by the same body at all. I only discussed energy emitted by one body and absorbed by the other, which is the only mechanism of energy transfer in this scenario. Wavelength does not change in that process, which is the energy transfer process.

 

[kmarinas86]

You are interested in the process of energy transfer from one body to the other. Absorption and emission do not change the wavelength during energy transfer.

http://en.wikipedia.org/wiki/File:Fluorescent_minerals_hg.jpg - Collection of various fluorescent minerals under ultraviolet UV-A, UV-B and UV-C light. Chemicals in the rocks absorb the ultraviolet light and emit visible light of various colors, a process called fluorescence.

The wavelength changes in the above picture "scenario".

It seems like energy transfer goes both ways. We have a chain of energy transfers, one after the other. The wavelength cannot be conserved, and it is not realistic to think that it is. Don't you think?

What if the colder sphere has a high emissivity at low-frequencies, the same frequency range where it peaks (thus helping it to emit heat), and a low emissivity at high-frequencies of which is scant inside the colder sphere (so negligible effect on limiting emission), the same high-frequencies which are at the same time being emitted by the hotter sphere (thus the heat of the hotter sphere is reflected away by the colder sphere), while the hotter sphere has a low emissivity in high-frequency range in which it would otherwise peak (thus reducing the emission of its own heat, providing yet another limitation on the transfer of heat from the hotter sphere to the colder sphere), while it has high emissivity at low-frequencies of which are scant inside the hotter sphere (so negligible effect on increasing emissions by the hotter sphere), permitting heat flux of low-frequencies from the colder sphere? Let's say that there exist super-low-frequencies which the colder sphere has a high emissivity for, while the hotter sphere has a low emissivity for them. So energy received by the hotter sphere from the colder sphere as low-frequencies get downgraded as super-low frequencies that get trapped by the hotter sphere. The result of all that is a net energy flux from the colder sphere to the hotter sphere. What does the energy affect when it is transferred like that?

 

[Dale]

The wavelength changes in the above picture "scenario".

Sure, but the "above picture 'scenario'" is not relevant to your scenario. The "above picture 'scenario'" is fluorecense. That is energy which is absorbed by some object, A, at one wavelength and emitted by that same object, A, at a different wavelength.

In your scenario you are interested in energy which is emitted by A and then absorbed by some other object, B. The wavelength of energy emitted by A is always the same as the wavelength of energy absorbed by B, absent any Doppler or relativistic effects. Do you disagree with that?

 

[kmarinas86]

Sure, but the "above picture 'scenario'" is not relevant to your scenario. The "above picture 'scenario'" is fluorecense. That is energy which is absorbed by some object, A, at one wavelength and emitted by that same object, A, at a different wavelength.

In your scenario you are interested in energy which is emitted by A and then absorbed by some other object, B. The wavelength of energy emitted by A is always the same as the wavelength of energy absorbed by B, absent any Doppler or relativistic effects. Do you disagree with that?

Do you even know what the scenario is?

It is not "my" scenario. The topic is the system to be described, including all absorption, re-emission etc. not mentioned in the opening post. The OP is what, apparently, you think establishes the full context of the scenario. It does not.

The broader context:
A and B emit.
A and B absorb.
A and B re-emit.
A and B absorb.
etc.

 

[Dale]

The broader context:
A and B emit.
A and B absorb.
A and B re-emit.
A and B absorb.
etc.

I see you avoided answering the question. In the broader context, do you agree or disagree that the wavelength of any radiation emitted by A and absorbed by B is the same when it is emitted by A as when it is absorbed by B?

 

[kmarinas86]

In the broader context, do you agree or disagree that the wavelength of any radiation emitted by A and absorbed by B is the same when it is emitted by A as when it is absorbed by B?

No.

A emits radiation to B.
The wavelength is the same - AT FIRST - (obviously ignoring Doppler effects here).
BUT THEN, the energy sent to B is then absorbed and emitted WITHIN B.
Now the wavelength is NOT the same (even if you ignore Doppler effects).
Then B can ABSORB that energy AGAIN (more photons, but at lower frequency)!
So the wavelength is -NOT- the same!
Then that energy may be trapped for an extended period of time, because absorption and emission both take time to happen.
It means that energy will accumulate.
Yes, it does max out, but that accumulation does not fall back if you continue to have sufficient emissions from the other object.
Furthermore, the photons with the lower frequency may take more time being emitted or absorbed (hand-in-hand with the lower-frequency (longer time interval) of undulations which emit them), so the emissivity they experience can be less, which depends on the presence of appropriate carriers of energy at such levels. Thus the hot object may then emit less of such radiation than its temperature alone would imply, depending on the composition of the object.
The ability to be absorbed and reabsorbed at one level (the atomic level) can have a detrimental effect as to its ability to be emitted at a higher level (such as the level of the object itself). So you could even say that emissivity depends on the scale of matter, so it's NOT LIMITED to just wavelength, frequency, temperature, and incidence angle.

 

[kmarinas86]

The ability to be absorbed and reabsorbed at one level (the atomic level) can have a detrimental effect as to its ability to be emitted at a higher level (such as the level of the object itself). So you could even say that emissivity depends on the scale of matter, so it's NOT LIMITED to just wavelength, frequency, temperature, and incidence angle.

Here's a simple example of this.

Let's have colors red, green, and blue.

Blue travels through the Earth's atmosphere without as much problem as red and green do.The light that does gets absorbed and re-emitted gets downgraded to lower frequencies. Red and green soon convert to thermal. The upper and lower atmosphere have no problem absorbing and reabsorbing thermal energy, when you compare it to the blue light.

A greater amount of blue light "gets in and gets out" of the Earth's atmosphere without much problem. So, to a distant observer, the Earth appears to have a high ability to absorb and emit blue light (i.e. the emissivity of the Earth at blue wavelengths appears rather high). This was due in fact to the reality that the atmosphere was less able to absorb the blue light, and less able to downgrade the blue light to lower frequencies. In other words, the fact that:
* The blue light was subjected to lower emissivity as far as the atmosphere was concerned.
Results in the following:
* The blue light experiences a high level of emissivity (easy to get in and easy to get out) as far as the Earth is concerned.

As far as the red and green are concerned, they get in and out of the atoms in the atmosphere more readily, and even more so when they convert to thermal, but this occurs at the expense of being as able to get out of the planet itself.

 

[Dale]

A emits radiation to B.
The wavelength is the same - AT FIRST - (obviously ignoring Doppler effects here).

OK, so this transfer is governed by the principles I outlined above. It always goes from hot to cold.

BUT THEN, the energy sent to B is then absorbed and emitted WITHIN B.
Now the wavelength is NOT the same (even if you ignore Doppler effects).
Then B can ABSORB that energy AGAIN (more photons, but at lower frequency)!
So the wavelength is -NOT- the same!

That is fine, this is all within B so there is no energy transfered.

Thus the hot object may then emit less of such radiation than its temperature alone would imply, depending on the composition of the object.

True. And if it does emit less of such radiation than its temperature would indicate, then it will also absorb less of such radiation, as I outlined above. Leading to transfer only from hot to cold.

So you could even say that emissivity depends on the scale of matter, so it's NOT LIMITED to just wavelength, frequency, temperature, and incidence angle.

You seem to be proposing new physics here. Do you have any mainstream scientific references that can corroborate? If not, then it is speculative and doesn't belong on PF.

 

[kmarinas86]

The example that I just posted referred to the Earth's atmosphere. No new laws of physics were invoked.

 

[Dale]

The example you posted also didn't show that the Earth could heat the sun nor any other object warmer than the earth, nor did it show that emissivity depends on "the scale of matter". All it showed is that the Earth is not a blackbody, to which I completely agree.

 

[kmarinas86]

True. And if it does emit less of such radiation than its temperature would indicate, then it will also absorb less of such radiation, as I outlined above. Leading to transfer only from hot to cold.

To test:
We should analyze the following scenario:

Quote unparsed:

What if the colder sphere has a high emissivity at low-frequencies, the same frequency range where it peaks (thus helping it to emit heat), and a low emissivity at high-frequencies of which is scant inside the colder sphere (so negligible effect on limiting emission), the same high-frequencies which are at the same time being emitted by the hotter sphere (thus the heat of the hotter sphere is reflected away by the colder sphere), while the hotter sphere has a low emissivity in high-frequency range in which it would otherwise peak (thus reducing the emission of its own heat, providing yet another limitation on the transfer of heat from the hotter sphere to the colder sphere), while it has high emissivity at low-frequencies of which are scant inside the hotter sphere (so negligible effect on increasing emissions by the hotter sphere), permitting heat flux of low-frequencies from the colder sphere? Let's say that there exist super-low-frequencies which the colder sphere has a high emissivity for, while the hotter sphere has a low emissivity for them. So energy received by the hotter sphere from the colder sphere as low-frequencies get downgraded as super-low frequencies that get trapped by the hotter sphere. The result of all that is a net energy flux from the colder sphere to the hotter sphere. What does the energy affect when it is transferred like that?

Parsing this
The colder sphere:
- (A) Would peak at low frequencies (if it were an ideal black body)
- (B) High emissivity at low and super-low frequencies
- (C) Low emissivity at high frequencies
The hotter sphere:
- (X) Would peak at high frequencies (if it were an ideal black body)
- (Y) High emissivity at low frequencies
- (Z) Low emissivity at high and super-low frequencies
High frequencies:
- (P) May be downgraded to low frequency after absorbed
- The colder sphere emits little of it. Reasons are (A) and (C).
- The colder sphere absorbs little of it, and thus may re-emit little of it. Reason is (C).
- The hotter sphere emits little of it. Reason is (Z).
- The hotter sphere absorbs little of it, and thus may re-emit little of it. Reason is (Z).
Low frequencies:
- (Q) May be downgraded to super-low frequency after absorbed
- The colder sphere emits largely this amount, closer to the ideal black-body. Reasons are (A) and (B).
- The colder sphere may not have much to absorb at this frequency. Reason is (X). Or:
- The colder sphere may have much to absorb at this frequency. Reason is (Y).
- (R) The colder sphere does not keep much of it, whether or not the light was downgraded. Reason is (B).
- The hotter sphere emits some, but it's not a big fraction of its total output. Reason is (X).
- The hotter sphere may have much to absorb. Reasons are (A), (B), (Y), and (R).
- The hotter sphere may retain the energy of them. Reasons are (Q) and (Z).
Super-low frequencies:
- (T) The colder sphere emits some fraction of its output as super low frequencies, but less than it does in low frequencies. Reason is (A).
- The colder sphere cannot retain them. Reason is (B).
- The hotter sphere can generate much of it. Reasons are (A), (Y), and (Q).
- The hotter sphere can retain them after generating them. Reason is (Z).
- (L) The hotter sphere can retain most of the system's super-low frequency energy. Reasons are (T), (A), (Y), (Q), and (Z).
- (N) The hotter sphere cannot absorb much from the outside. Reason is (Z). This is insignificant. Reason is (L).
- Both emit little, though the colder sphere emits a relatively larger fraction of its output at these frequencies than does the hotter sphere. Reasons are (A) and (X).

Extension:
- Corollary of the above - If the colder sphere has high emissivity for "super-super low" frequencies, etc., while the hotter sphere has various emissivities, varying from high to low, for different frequencies of such, then the "super-super low" frequencies, etc. may persist longer in the hotter sphere than colder sphere and thus still maintain a higher concentration of them.
- At some point, the frequencies could be downgraded so many times, that they would cause only very slight movements similar to quakes.

 

[Dale]

I didn't see anything in there to indicate net energy transfer from cold to hot at any frequency. As such, I didn't see anything major to disagree with.