The glow of fire is actually microscopic particles of carbon soot and gasses glowing (incandescing) from the heat released by the break down of the thing on fire. It spreads upwards because hot air rises, and the microscopic soot particles are so small and light they are carried on the rising air as they glow from their heat. Similar to how metal glows when it is heated. Everything in the “system” creating a fire still has atoms with their electrons firmly attached. That’s not the case for plasma.
Plasma is a state of matter with so much energy that the electrons break free of their atoms. Think of the amount of energy a lightning bolt has, the bolt itself is the air turned to plasma. That’s the kind of energy we’re talking about, and those bolts only last a fraction of a second. Think of how much energy would be required to turn wood into plasma for even a whole minute. The heat would be so great you wouldn’t be able to stand anywhere near this hypothetical plasma “fire.”
Fire isn’t wholely unique to Earth. It’s just Earth is one of the few planets we know of with an oxygen atmosphere. It’s also the only planet we know of with substances that are stable until exposed to enough energy, then they decompose rapidly in oxygen. The actual chemical reaction that causes flames can happen anywhere. In fact if we define that reaction by what is happening at the atomic level with the combining of oxygen and other atoms with the release of energy, then we have what is known as an “oxidation reduction” reaction, and that kind of reaction is the same one that causes rust to form on exposed metals. That kind of reaction can happen almost anywhere, even in the vacuum of space if an oxygen containing molecule touches something that it can combine with.
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