Physical properties of materials and systems can often be categorized
as being either intensive or extensive quantities, according
to how the property changes when the size (or extent) of the system
changes. According to IUPAC, an intensive property is one whose
magnitude is independent of the size of the system. An extensive
property is one whose magnitude is additive for subsystems.
An intensive property is a bulk property, meaning that it is a
physical property of a system that does not depend on the system size
or the amount of material in the system. Examples of intensive
properties include temperature, T, refractive index, n, density, ρ,
and hardness of an object, η (IUPAC symbols are used throughout
this article). When a diamond is cut, the pieces maintain their
intrinsic hardness (until their size reaches a few atoms thick), so
hardness is independent of the size of the system.
By contrast, an extensive property is additive for subsystems. This
means the system could be divided into any number of subsystems, and
the extensive property measured for each subsystem; the value of the
property for the system would be the sum of the property for each
subsystem. For example, both the mass, m, and the volume, V, of a
diamond are directly proportional to the amount that is left after
cutting it from the raw mineral. Mass and volume are extensive
properties, but hardness is intensive....
The terms intensive and extensive quantities were introduced by
Richard C. Tolman in 1917....
Examples of intensive properties include:
chemical potential, μ /
color / concentration, c / density, ρ (or specific gravity) / magnetic permeability, μ / melting point and boiling point / molality, m or b
/ pressure, p / specific heat capacity, cp / specific volume, v / standard
reduction potential, E° / temperature, T...
Examples of extensive properties include:
amount of substance, mol / energy, E / enthalpy, H / entropy, S / Gibbs
energy, G / heat capacity, Cp / Helmholtz energy, A or F / internal energy,
mass, m / volume, V
(bolding mine). 'Number of elements in a set' is obviously an extensive quantity.