Contradiction with Kirchhoff's Radiation Law?

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Discussion Overview

The discussion revolves around the application of Kirchhoff's Radiation Law in real-world scenarios, particularly focusing on the relationship between absorptance and emissivity coefficients for different materials. Participants explore the apparent contradiction when these coefficients are not equal, questioning how this aligns with the law's implications for thermal equilibrium.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant notes that the spectrum of sunlight differs from that of thermal radiation, suggesting that emissivity and absorptance must be equal at specific wavelengths.
  • Another participant emphasizes that reported absorptance and emissivity values may be band-averages, raising concerns about the consistency of the wavebands used for measurement.
  • It is mentioned that rough surfaces may exhibit angle-dependent absorption and reflection, complicating the comparison between absorptance and emissivity values.
  • A participant clarifies that the emissivity coefficient pertains specifically to the thermal radiation spectrum, while absorptance values may encompass a broader range of wavelengths present in sunlight.
  • One participant points out that the temperature difference between the terrestrial object and the Sun could lead to comparing absorptivity for visible light with emissivity for infrared light, which are not directly comparable.

Areas of Agreement / Disagreement

Participants express differing views on the reasons for the discrepancies between absorptance and emissivity coefficients, indicating that multiple competing explanations exist without a clear consensus on which is most valid.

Contextual Notes

Participants highlight limitations in the definitions and measurements of absorptance and emissivity, including potential variations in wavebands and the effects of surface roughness, which remain unresolved in the discussion.

eat_2_much
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Hello everyone,

I am working on understanding how Kirchhoff's Radiation Law applies in the real world. Basically, the absorbed solar radiation must equal the thermal radiation if a surface is to be at equilibrium. Certain relationships follow from this assumption, namely, for an opaque material, absorptance is equal to emissivity coefficient.

Here is the problem I am having. If I look up radiation properties for different materials, I can find an absorptance coefficient and an emissivity coefficient and they are not equal. Why does this occur? This seems to contradict Kirchhoff's law! I have included a couple of links for an example of what I am talking about.

http://www.solarmirror.com/fom/fom-serve/cache/43.html
https://books.google.com/books?id=X...nepage&q=absorptance emissivity table&f=false

Can anyone resolve this contradiction for me?
 
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It's because the spectrum of sunlight is different from the spectrum of the thermal radiation. For any given wavelength, the emissivity and absorption must be equal.
 
eat_2_much said:
Here is the problem I am having. If I look up radiation properties for different materials, I can find an absorptance coefficient and an emissivity coefficient and they are not equal. Why does this occur? This seems to contradict Kirchhoff's law! I have included a couple of links for an example of what I am talking about.

http://www.solarmirror.com/fom/fom-serve/cache/43.html
https://books.google.com/books?id=Xn8KbsgeFrwC&pg=PA212&lpg=PA212&dq=absorptance+emissivity+table&source=bl&ots=Rm1mGpnfmB&sig=kLvSUxBKTntrP26lvc8j9CWaoiM&hl=en&sa=X&ved=0ahUKEwjP2-bp5vHRAhXBqFQKHeVHDFcQ6AEILjAD#v=onepage&q=absorptance emissivity table&f=false

Can anyone resolve this contradiction for me?

There are two important points- 1) the reported numbers are band-averages, and it's not clear if the waveband used for solar absorption is the same as used to report emissivity, and 2) rough surfaces often have angle-dependent absorption and reflection, and it is not clear if the absorption and emissivity values are angle-averaged.

Some of point #1 is addressed both in the CRC text and in the mirrored URL http://www.redrok.com/concept.htm#emissivity

The second point is a little more tricky than the first: for example, the solar absorption can mean normal incidence, but the emissivity means 'emitted into the full hemisphere'.

Does this help?
 
Andy - I understand what you are saying! Your post was helpful - Thanks!

To make sure I understand Khashishi correctly - The emissivity coefficient only applies for the thermal radiation spectrum; however, sunlight consists of other wavelengths of radiation - not just thermal radiation. Absorpstance values can be a average over the entire sunlight spectrum while the emissivity coefficient is just governing the thermal radiation spectrum. This can create absorpstance and emissivity coefficients that are not equal.

Does this seem reasonable? At least it represents one reason among the several given here why the values could be different.
 
Basically, Andy's first point covers the same thing as I was saying. Presumably, the terrestrial object is at a much lower temperature than the Sun, so you are comparing the absorptivity for visible light to the emissivity for infrared light. Not the same thing.
 

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