# Extensive size

In physics, an extensive quantity is a state quantity that changes with the size of the system under consideration . Examples of this are mass , amount of substance , volume , entropy and the thermodynamic potentials ( internal energy , free energy , enthalpy and free enthalpy ). The counterpart of extensive size is intensive size .

The dependency of a variable on the system under consideration can be understood, 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.

If one forms the quotient from two extensive quantities of the same system, one obtains an intensive quantity:

• If one relates an extensive quantity to the volume , one obtains a density as an intensive quantity. Example: The intensive particle density belongs to the extensive number of particles .${\ displaystyle N}$ ${\ displaystyle n = {\ frac {N} {V}}}$
• If one relates an extensive quantity to the mass, then one gets a specific quantity as an intensive quantity . Example: The specific heat capacity belongs to the extensive heat capacity .${\ displaystyle C}$ ${\ displaystyle c = {\ frac {C} {m}}}$
• If one relates an extensive quantity to the amount of substance , the intensive quantity is a molar quantity . Example: The intensive molar mass belongs to the extensive mass .${\ displaystyle m}$ ${\ displaystyle M = {\ frac {m} {n}}}$

Many - but not all - extensive quantities are set- like quantities .

The change of an extensive quantity does not have to be followed by 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 , dielectric constant ε , dipole moment
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.
constitutive properties colligative properties
context The product of an extensive and an intensive quantity is an extensive quantity