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I know charcoal can smoulder in an incomplete combustion to produce carbon monoxide so I assume diamond also can. If it's heated to a sufficiently high temperature, will the reaction produce enough heat to sustain the full combustion reaction all the way to carbon dioxide even in air that's only 21 °C. If so, does the reaction of carbon monoxide with oxygen occur fast enough to be perceived as smouldering or does it occur slowly enough to be perceived as flaming combustion?

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Yes, diamond will combust in air. Regardless of the ambient air temperature, e.g. your example of $21\ \mathrm{^\circ C}$, you of course have to heat it to it's ignition temperature somehow, whether in a furnace, a flame, etc. The autoignition temperature for diamond is around $900\ \mathrm{^\circ C}$ (source 1, source 2), compared to about $730\ \mathrm{^\circ C}$ for graphite. The autoignition temperature is described in this Wikipedia article as:

"...the lowest temperature at which it spontaneously ignites in normal atmosphere without an external source of ignition, such as a flame or spark. This temperature is required to supply the activation energy needed for combustion."

So, once you have initiated combustion by some means heating it to about $900\ \mathrm{^\circ C}$, it will continue to burn, primarily to $\ce{CO2}$. Note that combustion does not require that a flame be produced or maintained.

How efficiently diamond combusts in air, in other words how much of the carbon is converted to $\ce{CO2}$ vs. $\ce{CO}$ and other partially oxidized carbon species is a function of a few different things. The same is true when burning graphite, wood, or most anything else. Is it a single smooth "rock" or a finely ground powder? How much of what sort of impurities does it contain? How efficiently ventilated is the system? These issues and other conditions of the combustion will determine the degree to which $\ce{CO}$ and other partially combusted carbon species are produced.

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    $\begingroup$ LOL - I'm not sure about that. I'd be glad to test this experimentally for you. Could you send me a bushel basket of diamonds about the size of chicken eggs? $\endgroup$
    – MaxW
    Commented Jan 28, 2017 at 6:44
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    $\begingroup$ And I suppose you want them to be gem quality ;) Check out source 1 and internet search it a bit. Antoine Lavoisier did some neat experiments with it, though I believe they were all in 1 atm of pure oxygen. The most dramatic situation (see YouTube) is when you throw hot diamond into liquid oxygen! $\endgroup$
    – airhuff
    Commented Jan 28, 2017 at 6:52
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    $\begingroup$ @Mithoron, I cannot find any evidence to back up your claim and I gave evidence to back up mine (see source 2 and link at bottom here in particular). Of course a continuous air supply is required, what other conditions do we need to sustain? Here is another link on the topic:quora.com/Diamond-is-100-carbon-Why-does-it-not-burn, and I strongly recommend looking up some of Lavoisier's experiments, very interesting even if he generally used 1atm oxygen rather than .21 atm. But he had to ignite it with a 17th century magnifying glass! $\endgroup$
    – airhuff
    Commented Jan 28, 2017 at 20:32
  • $\begingroup$ @airhuff Is the point of ventilation included in your answer is just because more and more CO2 will accumulate and the reaction will slow down? $\endgroup$ Commented Feb 22, 2017 at 9:48
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    $\begingroup$ Lasers are used to drill holes in diamonds of very specific sizes for wire drawing and such. The diamonds do not burst into flames though what would happen under pure pressurised oxygen I do not know. $\endgroup$
    – KalleMP
    Commented Feb 2, 2018 at 7:45

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