# System Properties Fixed Or Scaling > The core distinction between thermodynamic properties is their dependence on the system's size: intensive properties like temperature, pressure, density, and specific heat capacity ($$c\_V$$) remain absolutely constant regardless of whether $$1 cm^3$$ or $$1 dm^3$$ of air is considered, confirming they are independent of system size and fixed characteristics of the air's state. Conversely, extensive properties, such as mass and total heat capacity ($$C\_V$$), are additive and scale directly with the size of the system, increasing linearly in direct proportion to the volume. This relationship is mathematically formalised by defining the extensive property ($$C\_V$$) through the integration of the intensive property ($$c\_V$$) over the system's mass ($$d M$$), expressed as $$C\_V=\int c\_V d M$$, or over the volume ($$d V$$) using density ($$\rho$$), as $$C\_V=\int c\_V \rho d V$$. The visual demonstration of the linear increase of extensive properties directly validates this mathematical integral relationship. ### :paperclips:IllustraDemo {% embed url="" %} ### :paperclips:IllustraDemo hub {% embed url="" %}