Thermodynamic Variables

Intensive and extensive state variables: pressure, volume, temperature, and chemical composition.

General idea of the topic

Not all quantities of a thermodynamic system behave the same way when the system is divided into parts. This topic distinguishes variables that depend on the amount of matter from those that do not — a distinction essential for correctly combining systems.

What you will truly understand

• Why intensive variables (temperature, pressure, density) have the same value in each subsystem, regardless of size.
• Why extensive variables (mass, volume, internal energy, entropy) add up when subsystems are combined.
• How the ratio of two extensive variables always produces an intensive variable.

Recommended learning route

1. Intensive Variables: properties independent of the amount of matter.
2. Extensive Variables: properties proportional to the amount of matter.

Physical criterion you must acquire

Before adding or averaging a quantity across two subsystems, check whether it is intensive or extensive: extensive variables add up, intensive variables are never added directly without weighting.

Connection with real problems

Mixing fluids at different temperatures, calculating molar or specific properties, and normalizing quantities across systems of different sizes all depend on correctly classifying each variable.

Final goal of the topic

Confidently classify any thermodynamic variable as intensive or extensive and correctly apply that classification when combining or dividing systems.