Total Emissivity as a Function of Temperature (Ceramics)

[jdawg]

TL;DR Summary

How is total emissivity for a real material effected by temperature

Hello,

I’m trying to better my understanding of how the total emissivity changes with temperature for ceramic materials. Currently it is my understanding that non-metals typically have a high emissivity. A sanded surface will result in a higher emissivity, and that spectral emissivity varies greatly with wavelength for non-metals.

For black bodies, you should expect the emissivity to increase as temperature increases (molecules vibrating faster, therefore emit more energy)

Of course real materials don’t behave as black bodies... how would you expect the total emissivity to change as you increase the temperature for the following scenarios?:

total emissivity integrated over X-ray spectrum?
total emissivity integrated over IR?
Total emissivity integrated over microwave?
Total emissivity integrated over RF?

I was reading a paper on the subject that I can’t seem to find again. In the paper they had total emissivity plotted as a function of temperature, but emissivity values dropped as the temperature increased... how is this possible? Does this have to do with the wavelengths they integrated over? I can’t remember what part of the spectrum the paper was looking at. Since black bodies see more energy emitted for higher frequencies as temperature increases, would you expect less energy emitted for lower wavelengths? Perhaps even a drop in emissivity values as temperature increases?

Please correct any inconsistencies in my line of thinking. Any information or papers that someone can share with me is greatly appreciated!

 

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Summary:: How is total emissivity for a real material effected by temperature

how the total emissivity changes with temperature

Do you mean, I think you mean emittance - radiant power emitted per unit area per time.

For black bodies, you should expect the emissivity to increase as temperature increases (molecules vibrating faster, therefore emit more energy)

For black bodies emissivity =1, by definition.
For grey bodies, emissivity <1.

The emittance will increase with temperature for a black, or grey body.

Since black bodies see more energy emitted for higher frequencies as temperature increases, would you expect less energy emitted for lower wavelengths? Perhaps even a drop in emissivity values as temperature increases?

For a black body, all wavelengths will emit more power. the peak power output shifts to shorter wavelengths.
Again, in this context emissivity for a black body = 1 at all frequencies.

 

[jdawg]

This was helpful, thank you. It straightened out some inconsistencies in how I was thinking.

Do you mean, I think you mean emittance - radiant power emitted per unit area per time.

No, I mean the emissivity. I'm trying to figure out how the emissive properties of a material change with temperature.

For black bodies emissivity =1, by definition.
For grey bodies, emissivity <1.

The emittance will increase with temperature for a black, or grey body.

Oh gosh, how embarrassing. I promise I knew blackbody emissivity is 1. Yes you're right, that should say emissive power here.

For a black body, all wavelengths will emit more power. the peak power output shifts to shorter wavelengths.
Again, in this context emissivity for a black body = 1 at all frequencies.

Ok, that sounds familiar. I think this is the plot describing what you're talking about for blackbodies, would you expect to see a similar trend for a real material?

I did a little mental exercise to see what would happen if I used approximate values from the diagram above to plot ε vs temperature... Using this relationship: ε = E/(σT⁴)

Anddd for a blackbody it looks like emissivity decreases as temperature increases (at least for one wavelength, probably reasonable to assume that the total emissivity would follow a similar trend)! So I think you helped me answer my own question! I got caught up in the emissivity component of the Stefan-Boltzmann equation and wasn't taking into consideration that the T⁴ value in the denominator is really going to dominate how the emissivity behaves.

Do you think my reasoning makes sense?

If so, how would you explain the emissivity of a real ceramic material increasing with temperature? Perhaps after experiencing elevated temperatures the material undergoes some sort of change in its microstructure? Or the surface becomes rougher, therefore increasing the emissivity? How would you explain an increase in emissivity if one occurred?

And now I'm curious about how the spectral absorptivity would change with temperature for a real material?