Extensive variable

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, heat, work, momentum, electric charge.

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.

From equation (1) it can be deduced that

V(n) = n V(1)

and that

V(0) = 0.