This guy, the top answerer, says that fire is not plasma because it's not ionized
I think the deviation of the flame due to the imposed electric field created by the parallel plates in the link by BMS (i.e., http://www.askamathematician.com/2013/05/q-is-fire-a-plasma-what-is-plasma/) indicates flame must be at least plasma-like. I was recently at a plasma physics workshop and I was discussing with a colleague whether fire constitutes a plasma. The conclusion was basically it can be considered a very weakly ionized plasma, akin to a very dusty plasma (e.g., see also Paul Bellan's webpage and associated links) in a way.
I hear arguments saying that plasma is ionized gas, but how can a flare not be ionized at such high temperature(and why isn't ionized, very hot flames considered plasma)?
While both fire and lightning have relatively low black-body radiation temperatures (i.e., compared to, say, the solar corona), this does not mean there cannot ionize gases. There is always a tail to the distribution, and that tail is energetic enough to exceed the ionization energies of some molecules/atoms.
Fire is gas, but some say it's plasma if you can see it (check the link the poster added below in the first comment), so when does it become a full-on plasma if it's not normally one?
Part of the reason people say that fire is not a plasma is that 1 eV corresponds to ~11,604 K, which is less than the typical ionization energies of most molecules/atoms but hotter than most fires. For instance, the lowest ionization energy of any of the monatomic elements is ~358 kJ/mol for caesium, which corresponds to ~3.89 eV or >45,000 K.
Not too surprisingly, and very thankfully, Earth's atmosphere is not made of caesium but mostly diatomic nitrogen and oxygen and monatomic argon. Thus, one needs to first dissociate the diatomic molecules then ionize the constituent atoms (i.e., ~1402 kJ/mol or ~14.5 eV for nitrogen, ~1314 kJ/mol or ~13.6 eV for oxygen, and ~1520.6 kJ/mol or ~15.8 eV for argon ionization). Of course, it takes much less energy to break many chemical bonds, but chemical dissociation typically does not result in free charged particles. Further, it generally takes more energy to ionize molecules than atoms (e.g., see https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Atomic_Theory/Ionization_Energies_of_Diatomic_Molecule or look up tables at NIST). For instance, it takes ~13.8 eV (~160,135 K) to ionize carbon dioxide compared to ~13.6 eV (~157,814 K) for atomic oxygen and ~14 eV (~162,456 K) for carbon monoxide.
Another issue is that even if a small fraction of particles are ionized, they will likely quickly neutralize due the much larger fraction of lower energy atoms/molecules with which they interact.
Wood is mostly made of lignin, cellulose, and/or hemicellulose. The bond dissociation energies are very complicated for these compounds, as the compounds are not simple monatomic or diatomic molecules, but they range from a few 10s of kJ/mol to ~400 kJ/mol or less than 1 eV to ~4 eV (less than 11,000 K to >46,000 K). The constituents are then CO2 and H2O for complete combustion. Then the ionization energies of CO2 and H2O are ~13.8 eV (~160,135 K) and ~12.6 eV (~146,210 K), respectively.
I was wondering why a lightning bolt is coined as "plasma", or a "spark" from an electrical wire/device is as well, yet flares, molten lava, and burning buildings are not(flares are pyrotechnic, exothermic, and very much like flames).
In contrast to most fires, lightning has a much higher black-body temperature (i.e., at least ~8000 K up to ~50,000 K or ~0.7-4.3 eV, though average temperatures are lower). Thus, the peak of the spectrum is already near the first ionization energy of some atoms so there will be a higher flux of photons in any tail of the distribution, i.e., more ionizing radiation. This is ignoring the fact that a huge amount of static charge builds up prior to a lightning strike, producing kilovolt electric potentials. Such large electric fields directly break down the dielectric that is the atmosphere, causing the electrostatic discharge (i.e., sudden/spontaneous current flow that acts to eliminate the electric potential) that ultimately produces what we call lightning.
Further, lightning is known to generate electromagnetic radiation in addition to its black-body emission from radio waves (e.g., ELF) to X-rays and gamma rays (called terrestrial gamma-ray flashes or TGFs).
Thus, the processes involved in generating lightning directly and indirectly result in the generation of electromagnetic (i.e., UV to gamma rays) and particle (i.e., the free electrons responsible for the kiloamp currents) ionizing radiation. In summary, lightning is a very different beast than fire, which is just a chemical reaction.
Useful Lightning Links