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?
[Physics] Can paper burn without oxygen or air
combustion
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Much of the vapor you see at that stage is unburned material, not a true "smoke" which would be ashes or non-burnable material. A true solid is very difficult to burn. Most fuels instead volatilize as the temperature rises, increasing the surface area. This material coming from the heated fuel appears similar to smoke.
A visible flame is the burning of this material. When the flame is present, there is less unburned fuel and less smoke. There are several videos where you can see the process of relighting a candle by lighting the "smoke" from an extinguished candle. (The material is candle wax, not smoke).
Wouldn't it become more efficient as it got hotter, and the level of smoke decrease as the fire gets hotter, until the flames appear?
Efficient burning depends on more than temperature. You can have a very hot interior, and all that will do is produce a lot of unburned fuel (visible as smoke) due to lack of oxygen. Inside the bulk, it is too difficult for oxygen to arrive rapidly to support efficient burning. But outside much more is available and the process can proceed to completion.
Right after the wood is introduced, it's cold and there's nothing to see. As it heats, it produces some volatiles, but perhaps not rapidly enough to actually burn. If it caught at that point, it might sputter out. As the temperature rises, the fuel begins to appear at a faster rate until it supports a full flame and combusts.
Olin Lathrop captured something important, which is that the word "burn" does not always align to the chemistry definition of the word. But I did want to answer your question.
Chocolate will burn in a "naked" pan because the heat is not evenly spread. In cooking, it's desirable to have the top surface of the pan have an even temperature across the entire cooking surface. However, in practice, that can be difficult to achieve. Stoves often provide very uneven heating to the bottom of the pan, especially gas ranges which may only heat a circle! To spread the heat evenly, a pan must be very thick, and that is costly. Pan manufacturers try to strike a balance between a pan that's thick enough to spread the heat but thin enough to be affordable. High end pans will often have several layers of metal on the bottom to achieve a more even spread.
Chocolate is particularly demanding regarding temperatures. The science of chocolate is amazing, and I highly recommend looking into it some time. Chocolateers have to work with 5 different crystalline forms of chocolate that can form when it cools, of which one of them is "the right one." Accordingly, you must have a very even temperature within your pan of chocolate. Most pans just can't meet those criteria.
The "double boiler" solves this by heating water and then using that water to heat the container with the chocolate. First off, you can create a much larger thickness of material between the burner and your precious chocolate. Instead of having maybe a quarter inch of metal protecting the chocolate, you can have 2 inches of water or more! Second, water is a liquid so it can move. The water will form convection cells which are very effective at spreading heat out uniformly throughout the liquid.
Just be careful with the steam! Chocolate is quite hydrophilic, meaning it is attracted to water. If any of the steam condenses into your chocolate, the chocolate will immediately absorb the water, which causes the chocolate to "seize" into a useless lump which cannot be used unless you heat the chocolate hot enough to drive out all the water. This temperature is high enough that it will mess up all of the crystals you were trying to form, and you will have to re-temper the chocolate again!
Best Answer
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.