Intensive and Extensive Properties
Imagine you have a cup of hot tea. You take a sip — it's hot. Now pour half of it into another cup. Is the tea in each cup still hot? Yes, it is. The temperature didn't change just because you split the tea. Now think about the volume: each cup now has less tea than the original. The volume did change.
That's the entire intuition in one sip.
Temperature is an intensive property — it doesn't care how much tea you have. Volume is an extensive property — it cares a lot.
The Precise Definition
An intensive property is independent of the amount of matter present. An extensive property depends on the amount of matter.
If you take a system and cut it into two equal halves, any property that stays the same in each half is intensive. Any property that gets halved is extensive.
| Intensive (stays same) | Extensive (gets halved) |
|---|
| Temperature | Mass |
| Pressure | Volume |
| Density | Energy |
| Concentration | Number of moles |
| Refractive index | Heat capacity |
| Viscosity | Entropy |
Notice something: density is mass divided by volume. Both mass and volume are extensive, but their ratio is intensive. That's a powerful pattern — ratios of extensive properties are always intensive.
Why This Matters
In thermodynamics, you cannot simply add intensive properties. If you mix two buckets of water at 30∘C and 50∘C, the final temperature is not 80∘C — it's somewhere in between. But you can add extensive properties: the total mass is the sum of the two masses, the total volume is the sum of the two volumes.
A common mistake: thinking that "intensive" means "always constant." Temperature is intensive but it can change — it just doesn't change because you change the amount.
The Decisive Test
Here's a foolproof way to classify any property. Ask yourself:
If I double the amount of substance, does this property double?
- Yes → Extensive (mass, volume, energy, charge)
- No → Intensive (temperature, pressure, density, colour) …