Temperatures of a non-ideal blackbody (split from Hypothesis about temperature)

[KJW]

A long time ago on a different forum, I made the claim that only perfect black-body radiation, both in terms of its relative frequency distribution and its intensity, can have a single temperature attributed to it. Every other distribution of radiation has a pair of temperatures attributable to it. The lower temperature is defined as the temperature achieved by an absorption spectrum that minimises absorption and maximises emission, while the higher temperature is defined as the temperature achieved by an absorption spectrum that maximises absorption and minimises emission. Then one can construct an ideal heat engine based on these two temperatures to extract work from the radiation. One can't do that if the radiation is perfect black-body as this has only a single temperature.

 

[martillo]

5 minutes ago, KJW said:

A long time ago on a different forum, I made the claim that only perfect black-body radiation, both in terms of its relative frequency distribution and its intensity, can have a single temperature attributed to it. Every other distribution of radiation has a pair of temperatures attributable to it. The lower temperature is defined as the temperature achieved by an absorption spectrum that minimises absorption and maximises emission, while the higher temperature is defined as the temperature achieved by an absorption spectrum that maximises absorption and minimises emission. Then one can construct an ideal heat engine based on these two temperatures to extract work from the radiation. One can't do that if the radiation is perfect black-body as this has only a single temperature.

 

I don't understand how it would be possible. May be something to discuss in other thread.

[KJW]

Are you 

43 minutes ago, martillo said:

I don't understand how it would be possible. May be something to discuss in other thread.

Are you aware that the thermal emission spectrum of an external surface (the thermal radiation inside a cavity is black-body) is equal the product of the absorption spectrum and the black-body distribution? That is, good absorbers of a given wavelength are also good emitters of that wavelength. Therefore, by arranging the absorption spectrum of an object to absorb at all wavelengths other than that of the radiation, emission will be maximised, absorption will be minimised, and the temperature will equilibrate to a minimum which becomes the cold sink of a heat engine; and by arranging the absorption spectrum of another object to absorb at only the wavelengths of the radiation, emission will be minimised, absorption will be maximised, and the temperature will equilibrate to a maximum which becomes the hot source of the heat engine.

 

Edited March 17 by KJW

[martillo]

4 hours ago, KJW said:

Are you 

Are you aware that the thermal emission spectrum of an external surface (the thermal radiation inside a cavity is black-body) is equal the product of the absorption spectrum and the black-body distribution? That is, good absorbers of a given wavelength are also good emitters of that wavelength. Therefore, by arranging the absorption spectrum of an object to absorb at all wavelengths other than that of the radiation, emission will be maximised, absorption will be minimised, and the temperature will equilibrate to a minimum which becomes the cold sink of a heat engine; and by arranging the absorption spectrum of another object to absorb at only the wavelengths of the radiation, emission will be minimised, absorption will be maximised, and the temperature will equilibrate to a maximum which becomes the hot source of the heat engine.

 

That is a subject for another thread. You should open a new thread to discuss it.

[KJW]

9 hours ago, KJW said:

Every other distribution of radiation has a pair of temperatures attributable to it.

Although at the time I said a pair of temperatures, perhaps it is more appropriate to say a range of temperatures between these two extremes. Then an object with an arbitrary absorption spectrum will equilibrate to some temperature within this range. The minimum and maximum temperatures define the thermodynamic efficiency of extracting work from the radiation. This thermodynamic efficiency would apply not only to an ideal heat engine, but also to other means of extracting work such as a photovoltaic cell.

One thing I didn't mention is that the radiation being discussed is assumed to be isotropic.

 

[John Cuthber]

I think you just discovered Kirchhoff's radiation law.
https://en.wikipedia.org/wiki/Kirchhoff's_law_of_thermal_radiation

[MigL]

Also a good description of the global warming mechanism.
Earth absorbs radiation of a certain wavelength ( temperature ) and re-emits it at a much lower wavelength ( temperature ) that is intercepted ( absorbed and emitted ) by greenhouse gases, leading to a higher temperature equilibrium.

[KJW]

6 hours ago, John Cuthber said:

I think you just discovered Kirchhoff's radiation law.
https://en.wikipedia.org/wiki/Kirchhoff's_law_of_thermal_radiation

No, I simply applied it (although I had not read the Wikipedia article). What I consider to be my idea is that an arbitrary isotropic radiation wavelength distribution has a minimum and a maximum temperature (defined by the application of Kirchhoff's law) from which can be defined a maximum thermodynamic efficiency for the extraction of work from that radiation (a physical realisation of the two temperatures).