I understand that the usable energy of a high-temperature region depends on the low-temperature region you dump waste heat into - the lower temperature your sink, the less of your energy you have to dissipate into it as heat and the more of it you can capture as useful work. This quantity of "useful work" is the exergy of the {source + sink} system, and it's calculated using the Carnot cycle.
As far as I know, some kinds of energy are entirely capturable as work (such as electric current and macroscopic kinetic energy), but there's another example of one that isn't - EM radiation. For a system that does work by accepting one spectrum of electromagnetic radiation and shedding waste heat through a different spectrum (which would, I assume, be a blackbody spectrum) what fraction of the incoming spectrum is capturable as useful work? Can you sensibly speak of the "temperature" of an arbitrary spectrum of light, even if it's not a blackbody spectrum?
For example, a satellite in outer space without thrusters can only gain or lose energy through EM radiation - through solar panels accepting sunlight or beamed power from another installation, and through radiative cooling. I believe that if there's any portion of the sky that's truly, completely dark that the efficiency should be 1 - because a radiative cooler that can only see that region can continue to cool you to 0 and can use it as a sink for a Carnot engine.
- I assume that the portion of the "sky" that various spectra take up is irrelevant and only the "coldest" (however that works?) portion of the sky "counts" for restricting how you can shed waste heat, because you could use perfect mirrors to block the others from interacting with the radiator. I think it would affect the rate of transfer, but not the ideal efficiency. Is this correct?
- You don't have to use purely blackbody surfaces; you can construct surfaces with different emissivity at different wavelengths. This is part of what makes me confused about a "temperature" for non-blackbody light - if you are bathed in light of a few specific frequencies from all directions, can you still cool yourself to 0K with a radiator that has 0 emissivity in those wavelengths, and only interacts on the "missing" wavelengths? Would that mean that any distribution that's "missing" a wavelength band is 0K?
- How does the "stacking" of spectra work? If I'm receiving the sum of two spectra from the same direction, how is the exergy of the combined spectrum related to the individuals? I don't think it can possibly be additive, because of the previous bullet point.
The above musings give some context to where I'm coming from and what I do and don't know, but the actual question that I came here to ask is the one from paragraph 2:
For a system that does work by accepting one spectrum of electromagnetic radiation and shedding waste heat through a different spectrum (which would, I assume, be a blackbody spectrum) what fraction of the incoming spectrum is capturable as useful work? Can you sensibly speak of the "temperature" of an arbitrary spectrum of light, even if it's not a blackbody spectrum?
EDIT: At the behest of some folks in the comments, I'd like to clarify that I'm speaking of absolute zero and perfect reflection as limits. If it pleases you, you may find-replace the question with "0K" -> "the limit of the behavior as the temperature goes to 0 from above" and "perfect mirror" -> "The limiting behavior of a mirror as reflectivity goes to 1 from below"
