If you put a paper inside an oven vacuum packed and go beyond 250ºC, will it burn? There's no oxidizer. If not, what will happen?
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2If there's oxygen, stuff will burn. If not, then not. What's the question? – ACuriousMind Mar 17 '15 at 15:04
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Paper is mostly made of cellulose, which will decompose to water and carbon if heated in the absence of oxygen. – Solomon Slow Mar 17 '15 at 15:11
4 Answers
This is really chemistry rather than physics. Paper is mainly made from cellulose, and when heated in a vacuum cellulose undergoes a process called pyrolysis. The mechanisms involved are enormously complicated. Have a look at this paper to get some idea of how many different reaction pathways are involved. The end result of pyrolysis tends to be graphite (i.e. charcoal!), so your paper would probably end up as a graphite sheet, though that would take temperatures considerably higher than 250ºC.
Googling for pyrolysis of cellulose or some similar term will find you lots more on the subject. It's of commercial interest for turning biomass into fuel.

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I was about to write a very similar answer, but it offered nothing not seen here, so +1 – Harry Wilson Mar 17 '15 at 15:11
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In the fact of I also posted it on the stackexchange of chemistry. I comment to add the link because there are other interesting answers to the question: http://chemistry.stackexchange.com/questions/27465/can-paper-burn-without-oxygen-or-air – sospedra Mar 17 '15 at 16:39
It would not burn in the classical, combustion sense because as you noted, there is no oxygen present. Paper is a carbon-based material and so it requires oxygen to combust and form products like solid carbon, carbon dioxide, carbon monoxide, etc..
However, combustion is not the only thing that could happen here. In theory, if you heated it enough, you could add enough energy to the paper that the molecules begin to vibrate themselves loose from one another. And you could, in theory, add enough energy that they vibrate themselves apart and begin to decompose. And it's possible to add enough energy that electrons start popping off of them and the paper ionizes.
None of which is burning, but it would result in chemical changes in the paper.

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just out of curiosity, and in general terms, would any material containing an oxidant, following it's conversion to gas, have a slight chance of possessing tiny regions of short lived "ordinary" burning based on the maxell velocity distribution curves for gas particles. I realise that there are many variables, particularly the composition of the material and its response to temperature changes. The probability is minuscule that ordinary burning would occur, but in theory could it happen? hope my question is clear. just yes or no will be fine ...thanks and regards – Mar 17 '15 at 17:11
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@irishphysics Sure, and it doesn't require a Maxwellian velocity distribution or anything else particular. Just that enough molecules collide together with enough force to break apart the bonds in close enough proximity to one another to create new bonds with the fragments after the collision. But, if you do the math on the likelihood of that occurring, I think you would find it to be exceedingly rare for something like paper in a vacuum. Like it might only happen with 1 set of molecules 1 time in the history of the universe kind of rare. But I haven't done the math so that's just speculation. – tpg2114 Mar 17 '15 at 17:37
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thanks for that...I'm newbie to the site (self- study stage) and only now do I realise how far an "ordinary" question can really make you think, in some cases much more deeply about the issue, than say, a standard particle scattering problem in Q.M. appreciate the quick reply. – Mar 17 '15 at 17:49
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@irishphysics No problem. The other thing to think about with paper in particular -- the pyrolysis products are generally what would form from hydrocarbon combustion anyway, so even if they did manage to smash into each other they would just form back in their original, lowest energy states (if they happened to collide again, which is extremely unlikely in these conditions). – tpg2114 Mar 17 '15 at 18:47
My guess is that if in theory you gave it enough heat, then the molecules of the paper would vibrate so much they would produce a gas first, then if some of the molecules were oxidant agents you might get a burn. Almost certainly though depending on the paper material the molecules may be vibrating and moving so fast and being pushed away from each other they would be unable to combine so no burn. Great question
The title poses, "Can paper burn without oxygen or air?" A little sneaky pedantry here from a chemist - No Oxygen present, no air either, nor any mention of a vacuum. This allows us the presence of other strong oxidisers such as Chlorine and other halogens which will support combustion, which is what most people mean by "burn". As an aside, I well remember a chemistry practical demonstration where my teacher plunged a spoon of Phosphorus into a cylinder of pure chlorine to see a pale green flame spontaneusly appear, accompanied by copious white smoke (Phoshorus pentachloride) being emitted. So the answer is yes, but only in very uncommon enviroments, but which are found in the chemical industry where the Fire Service need to be aware of potential fire hazards.