## Extensive and Intensive Properties

Read this text, which gives examples of each type of property.

If you think about the various observable properties of matter, it will become apparent that these fall into two classes. Some properties, such as mass and volume, depend on the quantity of matter in the sample we are studying. Clearly, these properties, as important as they may be, cannot by themselves be used to characterize a kind of matter; to say that “water has a mass of 2 kg” is nonsense, although it may be quite true in a particular instance. Properties of this kind are called extensive properties of matter.

This definition of the density illustrates an important general rule: the ratio of two extensive properties is always an intensive property.

Suppose we make further measurements, and find that the same quantity of water whose mass is 2.0 kg also occupies a volume of 2.0 liters. We have measured two extensive properties (mass and volume) of the same sample of matter. This allows us to define a new quantity, the quotient m/V which defines another property of water which we call the density.

Unlike the mass and the volume, which by themselves refer only to individual samples of water, the density (mass per unit volume) is a property of all samples of pure water at the same temperature. Density is an example of an intensive property of matter.

Intensive properties are extremely important, because every possible kind of matter possesses a unique set of intensive properties that distinguishes it from every other kind of matter.

Some intensive properties can be determined by simple observations: color (absorption spectrum), melting point, density, solubility, acidic or alkaline nature, and density are common examples. Even more fundamental, but less directly observable, is chemical composition.

The more intensive properties we know, the more precisely we can characterize a sample of matter.

Intensive properties are extremely important, because every possible kind of matter possesses a unique set of intensive properties that distinguishes it from every other kind of matter. In other words, intensive properties serve to characterize matter. Many of the intensive properties depend on such variables as the temperature and pressure, but the ways in which these properties change with such variables can themselves be regarded as intensive properties.

#### Problem Example

Classify each of the following as an extensive or intensive property.

 The volume of beer in a mug Extensive - depends on size of the mug The percentage of alcohol in the beer Intensive - same for any same-sized sample The number of calories of energy you derive from eating a banana Extensive - depends on size and sugar content of the banana The number of calories of energy made available to your body when you consume 10g of sugar Intensive - same for any 10g portion of sugar The mass of iron present in your blood Extensive - depends on volume of blood in the body The mass of iron present in 5mL of your blood Intensive - the same for any 5mL sample The electrical resistance of a piece of 22-gauge copper wire. Extensive; depends on length of the wire The electrical resistance of a 1km length of 22-gauge copper wire Intensive - same for any 1km length of the same wire The pressure of air in a bicycle tire Pressure itself is intensive, but is also dependent on the quantity of air in the tire

The last example shows that not everything is black or white!

But we often encounter matter that is not uniform throughout, whose different parts exhibit different sets of intensive properties. This brings up another distinction that we address immediately below.