Intensive and extensive properties

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Physical or chemical properties of materials and systems can often be categorized as being either intensive or extensive, according to how the property changes when the size (or extent) of the system changes. The terms "intensive and extensive quantities" were introduced into physics by German mathematician Georg Helm in 1898, and by American physicist and chemist Richard C. Tolman in 1917.^[1][2]

According to International Union of Pure and Applied Chemistry (IUPAC), an intensive property or intensive quantity is one whose magnitude is independent of the size of the system.^[3] An intensive property is not necessarily homogeneously distributed in space; it can vary from place to place in a body of matter and radiation. Examples of intensive properties include temperature, T; refractive index, n; density, ρ; and hardness, η.

By contrast, an extensive property or extensive quantity is one whose magnitude is additive for subsystems.^[4] Examples include mass, volume and entropy.^[5]

Not all properties of matter fall into these two categories. For example, the square root of the volume is neither intensive nor extensive.^[1] If a system is doubled in size by juxtaposing a second identical system, the value of an intensive property equals the value for each subsystem and the value of an extensive property is twice the value for each subsystem. However the property √V is instead multiplied by √2 .