Intensive and Extensive Properties

Intensive properties are those that do not change as the size of an object changes. Extensive properties are those that change as the size of an object changes. The extensive properties scale directly with size, i.e. if the size of a system doubles, the value of an extensive property simply doubles as well. Intensive properties, on the other hand, would simply remain constant, whether the system size is doubled, tripled, or changed in any way. This distinction and the relationships between extensive and intensive properties are very important for mechanics, especially in the study of fluids. In general, all of the basic properties we think about using to describe a system (mass, volume, density, pressure, temperature, viscosity, color, etc.) can be divided into these two categories. Let's see what that looks like.

Intensive properties do not change as the amount or size of a substance changes.

Examples:

• Color

• Hardness

• Density

• Freezing/boiling point

The freezing point of 1 kg water is 273 K. What is the freezing point of 2 kg of water?

Solution: Since freezing point is intensive, it does not change as the amount of a substance changes. Therefore, the freezing point of any quantity of water is 273 K.

Extensive properties scale with the amount or size of a substance. They must exhibit and additive property when changing the amount of a substance.

Examples:

• Mass

• Volume

An uncut diamond is found to have a mass of 2.2 kg. If 0.7 kg of the diamond are cut away, what is the mass of the remaining piece?

Solution: Since mass is extensive, it must be additive. This means the mass of the cut away piece and the remaining piece must add up to the original mass.

2.2 kg - 0.7 kg = 1.5 kg

The ratio of any two extensive properties is an intensive property. The most common example is density, which is the ratio of mass and volume (both extensive) but is itself intensive, since it does not change as the amount of a substance changes.

$\rho=\dfrac{m}{V}$

Any intensive property defined as a ratio of an extensive property to mass is called a specific property. The most common example is specific heat capacity.