Intensive and extensive properties

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 ratio of two extensive properties of the same object or system is an intensive property. For example, the ratio of an object's mass and volume, which are two extensive properties, is density, which is an intensive property.

The terms intensive and extensive quantities were introduced by Richard C. Tolman in 1917.

An intensive property is a physical quantity whose value does not depend on the amount of the substance for which it is measured. For example, the temperature of a system in thermal equilibrium is the same as the temperature of any part of it. If the system is divided the temperature of each subsystem is identical. The same applies to the density of a homogeneous system; if the system is divided in half, the mass and the volume change in the identical ratio and the density remains unchanged. Additionally, the boiling point of a substance is another example of an intensive property. For example, the boiling point of water is 100 °C at a pressure of one atmosphere, which remains true regardless of quantity.

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