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Extensive variables in thermodynamics are those which scale linearly with the system size. It is known that a ratio of two extensive variables is an intensive variable. Now, the number of particles (moles) is an extensive variable. Typically, measurable thermodynamic quantities are expressed in terms per mole. Then any such quantity, like energy (per mole) or entropy (per mole), must be an intensive variable. Is it true?

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You can express energy in Joules. Then it is extensive (it will scale with the system). You can also call it specific energy and express it in Joules per kg. Then it is intensive. Or you could consider "molar" energy and have Joules per mole and it would also be intensive.

Same goes for entropy, which is Joules per Kelvin (extensive), or enthalpy (Joules), or volume (cubic meters), etc. If you express them per unit of mass or mole or alike then it is intensive.

But usually just saying e.g. energy means Joules and therefor extensive. While other properties like density (kg per cubic meter) already are intensive.

Bottomline is, it can be seen from the units very easily.

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Yes, any molar quantity it is considered intensive. You can find a list at this wikipedia page: http://en.wikipedia.org/wiki/Intensive_and_extensive_properties

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  • $\begingroup$ But in statistical mechanics all the quantities are expressed in terms per particle. Does that mean that there are no extensive variables in statistical mechanics? $\endgroup$ – Enoch Arden Feb 15 '15 at 12:31
  • $\begingroup$ But you can still evaluate, for example, the energy of a system of many particles, that is (in classical thermodynamics) considered as extensive qunatity. The difference between extensive and instensive variables is done especially in classical thermodynamics where one does not investigate on the microscopic structure of his system but just notices that some quantities depend on the amount of material in the sysyem, while others don't. $\endgroup$ – NNec Feb 15 '15 at 14:53

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