What causes the fire to glow?

The first time I tried to understand something intuitively was “Fire”. It was just about an year ago. I’m quite confident that I can carry you along with no confusion.

Fire & Flame?

Just like each time, we go with the terminology. How can we define “Fire”? The process of something burning? Flammable materials combust to produce flame, smoke and especially heat? Let’s give it a proper definition that makes it look like it’s something science’ey. In our topic, it’s just an oxidation reaction where a substance gets oxidized (i.e) it reacts (spontaneously) with the oxygen in air and produces light and heat (chemists give a name to this reaction, “exothermic”). Smoke is just a by-product which is not necessary for us today. Now, you should’ve figured out why oxygen is necessary for fire. Because, it is oxidation.

The light produced “in” fire is very attractive (called out as “flame”) that most people believe it to be plasma. Just because it’s beautiful, it isn’t really true. While cold plasmas like candle flames do exist, our “flame” is not plasma. We’re done with the definition now. Let’s pause it here (before we define flame), and see what blackbody radiation is…

Glory of blackbody radiation…

Planck’s law:

In the 18th-19th century, a theory arose based on which an object at any temperature above absolute zero emits electromagnetic radiation. Though this “law” had the involvement of Wien, Rayleigh & Jeans, Boltzmann, Max Planck (Hey!!! recall the constant named after him), our modern view is based on Planck’s correction of Wien’s model based on the analysis of Boltzmann, which led to the development of the newly born quantum mechanics.
(It was quite a blow to Rayleigh & Jeans, that their classical view of the phenomenon failed to succeed).

Blackbody:

What is a blackbody? It’s an idealized physical body, that absorbs all electromagnetic radiation incident on it, regardless of the frequency. It’s the same definition from Wikipedia, because that’s the simple way of defining blackbody. Black bodies don’t really exist in nature (although closest approximated versions of it, such as blackholes do exist), as a consequence of the conservation of energy (or first law of thermodynamics). In other words, blackbodies in thermal equilibrium with the surrounding, emit electromagnetic radiation isotropically, regardless of the incident radiation. If something were a blackbody, then a common question would arise. Where did the energy go? This is definitely a violation. In everyday situations, we just approximate (as we always do) by comparing the observed spectrum with that of a theoretical blackbody, (if it were) at such a temperature.

Now, to Flame…

If you’ve read Feynman lectures, you would’ve definitely known that atoms always jiggle around here and there (even at absolute zero). It’s this jiggling motion which is observed as heat. Well, HTwins have made a wonderful simulation on this jiggle & jiggle motion. And, this is only for gas molecules.

Something should be noted here. In solids, the molecules aren’t free to move, as they’re held in crystal lattices. Instead, they jiggle chaotically around their positions, causing local oscillations in the electron density distribution. The oscillation of these charges produces EM radiation (yeah, the blackbody radiation). In case of liquids (and the relatively very dense gases), the molecules can jiggle. As they are not held in lattices, they can also freely move around, provided they’re always close to each other. This random motion can also lead to the blackbody radiating state. With these concepts in hand, we will now resume our discussion on “flame”.

Let’s go through the common example. Wood burns in air. In wood, the carbon atoms are linked to one another by covalent bonds. In air, (as you may have noticed in the simulation) the oxygen molecules are freely flying around, dashing carbon atoms in the lattice, here & there (being in the gaseous phase). Both have some jiggling based on the average temperature of the system. When you heat the wood, the jiggling of carbon atoms increases (this is more like a threshold barrier, and it really is). As this becomes sufficient enough, one of the carbon atoms break the bonds, there comes in one of the oxygen atoms, being very active and with a tremendous amount of kinetic energy, both snap together brutally, so fast like a long-time-no-see pair and BAMM..!!!

Moreover, the attraction between carbon and oxygen (being so large than individual pairs of each other) in CO or CO_2 molecule, that a marvelous amount of heat is generated. Now, there are still unburnt leftover particles called the soot (mostly carbon), which are largely agitated by this heat and these emit blackbody radiation. Somehow, we’ve managed to come across the definition of flame by now. Flame is the region where the temperature of these soot particles is sufficient enough, that they emit electromagnetic radiation in the “visible part” of the spectrum.

What’s with the gas molecules then?

Gas molecules always fill up space (i.e) they diffuse out (well, you’ve seen the simulation). So, they can’t have any lattices, nor any constructive motion that leads to the emission of blackbody radiation, unless they’re subjected to extreme pressures when the density is high enough for them to radiate. Thus, gas molecules help the solid (soot) particles attain threshold temperature required for blackbody radiation. They just transfer heat. And, there are a few more possibilities. For example, gaseous molecules like CO_2 can absorb and emit radiation (infrared, in this case) by a series of electronic transitions where the spectrum is not continuous like that obtained by Planck’s law.

Now Houston, we have a serious problem. I’ve neglected the fact that the energy of the excited molecules are distributed according to Maxwell-Boltzmann distribution. Sometimes, these energies can be luckily high enough to cause ionization of other molecules that may later emit visible light (by a few electronic transitions). But, that’s only a tiny fraction in the bulk. So, we don’t usually call it as plasma, like the way we do for lightning or sun. This here, is the characteristic emission spectra of materials. More generally, this is what you do in a flame test. Calcium shows brick red color, etc…                    (Old school Chemistry 101)

What’s the use of these, so-called “blackbodies”?

Well, look around you… Every single object you see, the electric bulb, your television, your car, refrigerator, the sun, planets and the stars (and the Cosmic Microwave Background radiation too), even “YOU” itself emit blackbody radiation. Our blackbody radiation is in the IR spectrum, provided our body temperature is around 37 ºC (that’s why some snakes can sense us, even in total darkness).

For example, everything can be approximated to a blackbody at the thing’s equivalent temperature and the emission spectra can be studied. This plot of temperature-spectra is useful in a lot of fields in Physics. Another interesting thing is by using Stefan-Boltzmann relationship (obtained from Planck’s law) \sigma T^4=P/A, that the flux (power per unit area) at a particular location from the source can be found, just by using its temperature (the reverse is also possible). How do you think the surface temperature, or the white color of sun (or some other star in the Andromeda) was determined precisely just from Earth?

Inspired by this post, written by John Rennie, a physicist, chemist & a chef at Physics Stack Exchange

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