An extensive variable is a variable whose value is proportional to the quantity of substance under study, for instance: total mass, volume, number of particles, energy, entropy, enthalpy, length, etc.
The complementary idea is that of an intensive variable.
Suppose there is one piece of substance whose quantity is n and another piece whose quantity is m. Let V be an extensive variable. Let the first piece have a value V(n) of the extensive variable. Let the second piece have a value V(m) of the extensive variable. Then, if the two pieces are put together to form a piece with mass n + m, then their corresponding variable is
- .
An extensive variable can be expressed as a function of the quantity of the substance, where the quantity is one of the factors of a product which equals the extensive variable.