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.

📎IllustraDemo

A derivative illustration based on our specific text and creative direction

🏗️Structural clarification of Condensed Notes

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