Extensive and Intensive Properties; State Functions and Path Functions

Every measurable property of a thermodynamic system can be classified along two independent axes: whether it depends on the amount of matter present, and whether its value depends on the path taken to reach the current state.

Extensive properties depend on the quantity of matter in the system — they add up when two identical systems are combined. Mass, volume, total internal energy, total enthalpy, and total entropy are all extensive: if you double the amount of a substance, each of these doubles too. Intensive properties, in contrast, do not depend on the amount of matter present — they remain the same value regardless of how much of the system you have. Temperature, pressure, density, molar volume, and molar concentration are all intensive: the temperature of a cup of tea does not change if you pour out half of it, and the density of a substance is the same for a gram of it as for a kilogram. A useful test is to imagine dividing a homogeneous system exactly in half: extensive properties are also halved, while intensive properties are unchanged in each half. It is also worth noting that the ratio of two extensive properties is always an intensive property — for instance, density (mass/volume) and molar volume (volume/moles) are both intensive, even though mass, volume, and moles are each individually extensive. …