Intensive and extensive properties

Intensive properties do not depend on the amount of matter in a system; extensive properties scale with it. Dividing an extensive property by system size can produce an intensive property.

Thermodynamic system: A defined quantity of matter or region of space studied using thermodynamic principles. The chosen system determines which matter counts when judging whether a property scales with size.
Additive quantity: A quantity whose value for a combined system equals the sum of its values for the component systems. Extensive properties are additive when subsystems are combined without significant interaction effects.
Temperature: A physical quantity that indicates thermal state and determines the direction of spontaneous heat transfer. Temperature remains unchanged when an equilibrium system is divided into similar parts.
Surface area: The measure of the extent of a surface bounding an object or region. Unlike bulk extensive quantities, surface area need not scale linearly with volume or mass.
Equation of state: A relation connecting thermodynamic state variables such as pressure, volume, and temperature. Equations of state connect intensive variables with extensive measures of system size.
Thermodynamic state: The condition of a thermodynamic system described by its macroscopic properties. Properties classify a state, while their intensive or extensive character concerns system size.
Homogeneous function: A function that scales by a fixed power when all its inputs are multiplied by the same factor. Extensive properties scale linearly with system size; intensive properties scale with power zero.
Pressure: Force exerted per unit area by a fluid or other material on a surface. Pressure is intensive in ordinary bulk thermodynamic systems.
Finite-size effect: A deviation in a system's behavior caused by its limited dimensions or particle count. Small systems can violate bulk scaling assumptions underlying the usual classification.
Gibbs free energy: A thermodynamic potential that measures useful work available at constant temperature and pressure. Its extensive character and derivatives connect directly to chemical potential and equilibrium.

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