An intensive property is a property whose value does not depend on the size or amount of the material being described. Cut the sample in half, and the value of an intensive property is unchanged.
The test is simple, and it is the cleanest way to feel the distinction in your hands. Pour a glass of water from a pitcher. The pitcher had some mass; the glass has less. The pitcher had some volume; the glass has less. But the temperature of the water in the glass is the same as the temperature of the water in the pitcher. The density is the same. The color is the same. None of these moved when the water moved. They belong to the water as a kind of stuff, not to the particular amount of it that happens to be in your container.
That is what makes intensive properties so useful for telling materials apart. If two samples have the same density, the same melting point, the same color, the same response to a flame, we have grounds to suspect they are the same kind of stuff. We could never conclude this from mass or volume; any material can have any mass, depending on how much of it is in front of us. Identity hides in the intensive properties; amount lives in the extensive ones.
A material has many features and therefore many properties, and a clean way to begin sorting them is to ask, of each one: does its value depend on how much I have? If yes, the property is extensive. If no, it is intensive. The same question, asked of every property in turn, builds the basic discipline of macroscopic description.
Question
Why does the temperature of a cup of boiling water equal the temperature of the whole pot it came from?
Reveal Merrill's answer →Hide answer
Because temperature is intensive. It does not divide when the water is divided. The cup and the pot are the same kind of stuff at the same condition, so they share the same value of every intensive property. Mass and volume divided when you poured the cup; temperature, pressure, density, and color did not. That is the whole distinction.