Or would the small size of the marble prevent the heat from spreading?
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5 Answers
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The heat transfer limit wouldn't be what prevents this; it would be the negative energy balance of oxidizing nitrogen that prevents igniting the atmosphere.
There was actually a serious concern among the scientists who designed the first nuclear fission bombs that detonating one would ignite the atmosphere and result in the destruction of all land life, but it didn't happen -- and although high temperatures can cause nitrogen to oxidize, the reaction doesn't release enough net energy to push more air over the activation threshold, with the result that such a reaction dies out as soon as outside energy is no longer supplied.
As suggested in comments, we should probably explicitly deny actually melting or vaporizing some or all of the Earth itself as being applicable here. "Ignition" as a concept implies starting a self-sustaining reaction (usually chemical) -- you can ignited gasoline vapor mixed with the correct ratio of oxygen or air with a pretty modest spark, but that's not the same as converting both gasoline and air to plasma from a level of radiation that makes a supernova look tame.
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5$\begingroup$ +1. Correct me if I'm mistaken, but it's probably worth explicitly mentioning that the marble (through radiation, as opposed to convection or conduction) would still be able to completely vaporize the planet if heated to a sufficiently high temperature. $\endgroup$– QamiJun 7 at 14:24
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3$\begingroup$ @Qami Sure. That's a lot different from anything we'd commonly call "igniting" the atmosphere. The concept of ignition typically refers to starting a self-sustaining chemical (or in some contexts nuclear) reaction. $\endgroup$ Jun 7 at 16:23
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$\begingroup$ Thanks! I just wanted it to be clear to the OP that his marble is capable of destroying the atmosphere (and more), in case that's relevant. $\endgroup$– QamiJun 7 at 17:27
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2$\begingroup$ The concern when the first atomic bomb was detonated was not about chemical combustion, but nuclear fusion, fusing nitrogen nuclei. See worldbuilding.stackexchange.com/questions/47424/… $\endgroup$ Jun 7 at 22:36
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On a chemical scale, you can't ignite the atmosphere because reacting oxygen gas with nitrogen gas consumes energy, it doesn't produce it. You can't get the self-sustaining reaction that defines combustion if you need to keep adding energy to it.
On a nuclear scale, it turns out the same thing is true: as part of the Manhattan Project, a paper entitled Ignition of the Atmosphere with Nuclear Bombs studied the possibility, and found that no matter how hot you made the air, nitrogen-nitrogen fusion did not produce enough energy to become self-sustaining*. Even at the optimum temperature of $1.16*10^{12}$K, energy escapes more than seven times too fast for a sustainable reaction.
* Stars get around this by packing the nitrogen atoms far more tightly, which keeps energy from escaping as fast.
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The marble would radiate. It would also expand.
Raising the temperature of the marble is equivalent to adding energy. You've added a finite-but-arbitrarily-large amount of energy to the atoms that make it up. So now you have a large number of subatomic particles that used to comprise it, moving at near light speed in an expanding shell. You also have a wave of emitted "blackbody" radiation as some of that energy converts to photons, as well as from the collisions from the particles with the atmosphere.
It doesn't so much ignite the atmosphere as flash it into plasma. A lot like the relativistic baseball. https://what-if.xkcd.com/1/
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1$\begingroup$ I like this answer that doesn't fixate on the word "ignite" and try to explain what would happen to the atmosphere with an extremely hot marble in it. $\endgroup$– EchoxJun 8 at 12:18
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$\begingroup$ Assuming a 1x1x1 m cube marble, another what-if article could apply: Hair Dryer. $\endgroup$ Jun 8 at 19:46
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Ignition process
As told here
Ignition is the process of providing the energy that is required to initiate a combustion process. When hydrocarbons interact with molecular oxygen to combust, it requires what is known as activation energy to do so - the minimum energy needed to "activate" a chemical reaction.
Combustion of atmosphere
As told here
Air itself is not flammable so air will never spontaneously combust, nor can it be made to burn non-spontaneously.
Conclusion: Air will not combust so you cannot ignite it.
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E=MC² - Heat is energy, energy is mass, if you can create infinite heat, you can create infinite mass.
Which means, If you could heat something to any degree, to infinite temperatures, you couldn't just ignite the atmosphere, you could vaporize the entire solar system, and set in motion destruction that would obliterate the universe from that point outwards at the speed of light as the marble turns into a black hole of infinite mass, simply by heating it to infinite temperatures.
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$\begingroup$ Yeah, things get weird if you have things like arbitrarily high temperatures, if you set that value high enough you would end up destroying literally everything that the radiation can reach, which would of course radiate at the speed of light. It would be like setting off as many supernovae as you care to imagine. I don't know if you could call that "igniting the atmosphere", but the difference is immediately irrelevant $\endgroup$– KevinJun 8 at 16:11
select(egypt.Jozef3259.house["item1295_marble_phoenix"]); set_property("tmp", 3e22); apply(). Then he had a very awkward 1v1 with the boss later that day. $\endgroup$