Variables and Equations of State

The physical state of a pure substance can be defined by certain state variables such as volume (V), pressure (p), temperature (T), and amount of substance (n). When two gases are separated by a movable wall, the gas with the higher pressure naturally compresses the gas with the lower pressure. This causes the high-pressure gas to expand and the low-pressure gas to compress until both gases achieve mechanical equilibrium. At this point, their pressures equalize, and the movement of the wall ceases.

A pressure gauge is utilized to measure the pressure of a gas sample within a container, while temperature is measured in kelvins on the thermodynamic scale. The state of bulk matter, on the other hand, is determined by variables such as mass, volume, and amount of substance, which is usually measured in moles to denote the number of specified entities in the sample.

These variables can be categorized as either extensive, such as mass and volume, which depend on the system size, or intensive, like temperature and pressure, which remain unchanged when the system is subdivided. An equation that links these physical variables for a thermodynamic system is called an equation of state.

For an ideal gas, this equation is represented by the ideal gas law. In this case, knowing any three of the four state variables—pressure, volume, temperature, and amount of substance—allows the fourth to be determined. Real gases, however, deviate from ideal behavior due to intermolecular forces and the finite size of molecules, and thus require more sophisticated equations of state, such as the van der Waals equation. The Virial equation of state is an empirical extension of the ideal gas equation that can describe the behavior of gases and liquids over a wider range of pressures and temperatures.