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.
Examples of intensive properties include temperature, T; refractive index, n; density, ρ; and hardness, η.
[4] Examples include mass, volume and Gibbs energy.
For example, the square root of the volume is neither intensive nor extensive.
An intensive property is a physical quantity whose value does not depend on the amount of substance which was measured.
If the system is divided by a wall that is permeable to heat or to matter, the temperature of each subsystem is identical.
Additionally, the boiling temperature of a substance is an intensive property.
For example, the mass of a sample is an extensive quantity; it depends on the amount of substance.
The related intensive quantity is the density which is independent of the amount.
For example, species of matter may be transferred through a semipermeable membrane.
On the other hand, some extensive quantities measure amounts that are not conserved in a thermodynamic process of transfer between a system and its surroundings.
In a thermodynamic process in which a quantity of energy is transferred from the surroundings into or out of a system as heat, a corresponding quantity of entropy in the system respectively increases or decreases, but, in general, not in the same amount as in the surroundings.
The two members of such respective specific pairs are mutually conjugate.
Either one, but not both, of a conjugate pair may be set up as an independent state variable of a thermodynamic system.
, (This is equivalent to saying that intensive composite properties are homogeneous functions of degree 0 with respect to
, (This is equivalent to saying that extensive composite properties are homogeneous functions of degree 1 with respect to
It follows from Euler's homogeneous function theorem that where the partial derivative is taken with all parameters constant except
For example, heat capacity is an extensive property of a system.
, by the mass of the system gives the specific heat capacity,
The symbol for molar quantities may be indicated by adding a subscript "m" to the corresponding extensive property.
[5] Molar Gibbs free energy is commonly referred to as chemical potential, symbolized by
, particularly when discussing a partial molar Gibbs free energy
For the characterization of substances or reactions, tables usually report the molar properties referred to a standard state.
Examples: The general validity of the division of physical properties into extensive and intensive kinds has been addressed in the course of science.
[15] Redlich noted that, although physical properties and especially thermodynamic properties are most conveniently defined as either intensive or extensive, these two categories are not all-inclusive and some well-defined concepts like the square-root of a volume conform to neither definition.
Redlich pointed out that the assignment of some properties as intensive or extensive may depend on the way subsystems are arranged.
For example, if two identical galvanic cells are connected in parallel, the voltage of the system is equal to the voltage of each cell, while the electric charge transferred (or the electric current) is extensive.
However, if the same cells are connected in series, the charge becomes intensive and the voltage extensive.
For example, viscosity is a macroscopic quantity and is not relevant for extremely small systems.