Concept

# Intensive and extensive properties

Summary
Physical 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. According to IUPAC, an intensive quantity is one whose magnitude is independent of the size of the system, whereas an extensive quantity is one whose magnitude is additive for subsystems. The terms "intensive and extensive quantities" were introduced into physics by German writer Georg Helm in 1898, and by American physicist and chemist Richard C. Tolman in 1917. An intensive property does not depend on the system size or the amount of material in the system. It 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, extensive properties such as the mass, volume and entropy of systems are additive for subsystems. Not all properties of matter fall into these two categories. For example, the square root of the volume is neither intensive nor extensive. For example 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 . An intensive property is a physical quantity whose value does not depend on the amount of substance which was measured. The most obvious intensive quantities are ratios of extensive quantities. In a homogeneous system divided into two halves, all its extensive properties, in particular its volume and its mass, are divided into two halves. All its intensive properties, such as the mass per volume (mass density) or volume per mass (specific volume), must remain the same in each half. The temperature of a system in thermal equilibrium is the same as the temperature of any part of it, so temperature is an intensive quantity.