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Let's say we have a one kilogram piece of rock. Now if we want to separate each molecule from the other molecules making this piece of rock, which method requires the least energy while neglecting energy losses ?

The first method I thought of is the complete mechanical breaking of all the molecules. I understand that this is not practically possible, but let's assume that we are able to mechanically break every bond between the molecules at room temperature. The energy required in this method will be the sum of all the mechanical work done to break the bonds between each molecule and the other molecules.

The second method is vaporizing the rock starting from room temperature until we end up with separated gaseous molecules. The energy required in this method will be the sum of energies to raise the temperature to the boiling point, plus the latent heat of fusion and the latent heat of vaporization.

So if we neglect energy losses in both methods, which one would require less energy ?

In other words: energy-wise speaking, is there a difference between mechanically breaking every bond and vaporizing the material ?

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No, there is no difference. It may be difficult to do the detailed energy accounting because we are making surface energy by breaking up the rock. When the particles become fines, we have free energy associated with radius. In principle it's the same.

One cannot neglect energy losses. If we raise the temperature, we suffer second law losses, even if the process is reversible. I will claim that the lower temperature process is theoretically lower energy, but it is a Master's thesis to make a really strong argument.

Good question.

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