# Intense size

An intensive variable is a state variable that does not change with different sizes of the system under consideration . A distinction is native intensive variables such as temperature and pressure , and material's intensive variables, like all molar and specific quantities of pure substances .

The counterpart to the intensive quantities are the extensive quantities , such as particle number , volume , energy and entropy , which change with the size of the system (scaling).

The dependency of a variable on the system under consideration can be traced, for example, using two identical systems that are separated by a partition. If one removes this separation and extends the consideration to the entire system, the difference between intensive and extensive quantities becomes clear: All quantities which now have the same value as before the removal of the partition are intensive quantities; on the other hand, all quantities which now have a different value are extensive quantities.

It is possible to convert extensive quantities into intensive quantities by relating them to a certain mass ( specific size ), to a certain volume (density of size) or to a certain amount of substance ( molar size ). The volume is an extensive quantity, but the molar volume is an intensive quantity.

The change in an intense quantity results in a change in the thermodynamic equilibrium .

Extensive and intense sizes
extensive intensive
Characteristic Sizes depend on the amount of fabric Sizes do not depend on the amount of fabric
property Changes with the size of the system under consideration. Extensive sizes are additive. If the amount of substance is multiplied, all extensive quantities multiply. Is not affected by the size of the system. Intense sizes are not additive.
Examples Amount of substance n , volume V , internal energy U , free energy F , free enthalpy G , mass m , electrical charge Q Temperature T , density ρ , pressure p , concentration c = n / V , viscosity , refractive index , electrical voltage U , permittivity ε , dipole moment ${\ displaystyle {\ vec {p}}}$
Specialty A state variable is also extensive if it is proportional to all other state variables known to be extensive. The proportionality only applies as long as all non-extensive state variables remain constant. The ratio of extensive quantities is an intensive quantity.
context The product of an extensive and an intensive quantity is an extensive quantity