Explaining the Color Change of Black Body Radiation from Coal

[bill nye scienceguy!]

taking a lump of coal as an approximation of a black body, what is the explanation for the phenomenon of the emitted light changing colour from red to white when it is heated, ie the emitted quanta themselves changing, rather than simply more being released.

 

[AstroRoyale]

Both effects happen when the temperature increases. The peak of the spectrum of radiation that is emitted by a blackbody shifts towards shorter wavelengths as the temperature is increased. Also, more photons are emitted from a hotter BB than a cooler one. As the temperature increases, the color will go from red to yellow to white eventually to blue.

 

[lbrits]

You can view the cavity full of electromagnetic radiation as being a collection of harmonic oscillators with various frequencies (rather, wavelengths), each one for every mode of oscillation. Statistical mechanics says that at higher temperatures you can excite the more energetic oscillators, and that is what you observe.

There's a technical issue as to whether BB radiation reflects the temperature distribution of a "gas of photons" as we take it to be, or whether it merely reflects the "oscillators in the walls of the cavity". Unfortunately for the particular case I don't think there is a distinction, so BB radiation isn't exactly a "proof of photons".

 

[Ken G]

A good way to think of thermal radiation is to look at each frequency independently. Then you can just ask, why does the intensity at a given frequency or wavelength always increase with temperature? The answer is, it costs less entropy to excite photons at that frequency if the temperature of the source is higher. If you're not comfortable with entropy, this just means when you take heat out of the reservoir it loses a fraction of the number of ways it can be realized given the constraints you are applying, but if the temperature is higher, it loses a smaller fraction of the ways it can be realized. That makes it more likely to happen that it will lose that energy to making photons.

Each photon generates less entropy than the one before, so eventually you get a marginal change in photon entropy that matches the marginal change in reservoir entropy, and that's the expected number of photons. That marginal balance occurs at a higher photon number for a higher reservoir temperature, because higher temperature means less entropy cost per photon created.

This is true frequency by frequency, so higher T brightens all radiation fields, but the marginal balance is most sensitive when the frequency in a sense "matches" the T, so those are always the frequencies whose intensity is rising the fastest and that makes the spectrum peak at frequencies that are tuned to T-- i.e., higher T, proportionally higher frequency at the peak. So you don't need to think of the quanta being changed, it is all about them increasing the number produced-- but the number produced rises most steeply for frequencies tuned to the temperature, ergo the shift in the peak.