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I am still trying to understand what are intensive and extensive properties. Possibly someone can give a pointer to a decent text (preferably on the web), as I am not too happy (to say the least) with what I found so far on the web. I already asked here one question on this, which I finally answered myself.

My new problem (among several others) is that density seems to be one of the first properties taken as example of an intensive property. While it seems a good approximation of what I know about solids and liquids, it seems to me a lot more problematic with gas, as they tend to occupy all the available space you give them.

But none of the documents I found seems to make any resriction regarding density of gas. It seems to me that my opinion (apparently contested) that velocity is an intensive property, may be easier to support than the intensiveness of density in the case of gas. Or to put it differently, I do not see why pressure should be more intensive than volume, while wikipedia lists pressure as intensive, but not volume. Ideal gas law states that $PV=nRT$, which apparently gives a pretty symmetrical role to $P$ and $V$. And density depends on pressure (actually using this same formula and molecular weight).

If it were not for the fact that some principles seem to be based on the concept, such as the state postulate which I found on wikipedia, I would start wondering whether these are real concept in physics.

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1 Answer 1

The definition I use are the following.

An extensive quantity is proportional to the number of components in the system it qualifies. If you double the number of components of the system (by doubling the number of atoms, the volume of liquid...), its extensive quantities will double too.

On the opposite, an intensive quantity is always in a way or another a quantity you can express as something "per component".

If you double the size of, say, an elephant, you will multiply the number of atoms by 8 = 2x2x2, but the number of atoms per cubic meter (the density) remains the same. The number of atoms is an extensive quantity while the density is intensive.

Does this help ?

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I know what you explained (thanks anyway). The issue is that, for a gas, I do not see that you have to change the volume when you double the number of molecules. It will simply double the density. I have, yet, no problem with liquids. –  babou Aug 20 at 0:48
I improved the question to make this clearer. –  babou Aug 20 at 1:07
@babou - I see your point. The thing is, there is an idea of "replication keeping every other property unchanged" when you increase an extensive quantity. If you double the number of gas molecules in the same volume, you can't consider that you replicate the system without changing anything else. Obviously you changed another property of the system that is density. –  Mathias Aug 20 at 1:07
Precisely, density and pressure which is related. –  babou Aug 20 at 1:09
That's it. Actually there is not much more to intensive/extensive that this, even if it might look like the contrary! –  Mathias Aug 20 at 7:58

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