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My book asks how can diamond ever be more stable than graphite, when it has less entropy. I have to explain how at high pressures the conversion of graphite to diamond can increase the total entropy of the carbon plus its environment.

So, I’m familiar the free-energy argument, but as my book is specifically asking to mention entropy, that is what I’m trying to do. As we’re talking about pressure, I’m guessing the answer would lie in the fact that the volume of diamond is smaller than that of graphite. It would seem then that, due to the high pressure, the increase in entropy due to the increase in volume of the environment will outdue the decrease in entropy of the diamond. Is there a formula to back this up? I would think that the energy of the environment is $-P\Delta V_{environment}$, so in increase in volume, would actually decrease its energy, so that isn't really helping my case. Any ideas?

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  • $\begingroup$ Note that every spontaneous process generates entropy, including the work that a high-pressure environment does to reduce the molar volume of carbon in the phase transition from graphite to diamond. $\endgroup$ – Chemomechanics Dec 18 '18 at 23:37

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