Variables and Equations of State

The physical state of a pure substance is defined by volume V, pressure p, temperature T, and amount of a substance n.

These state variables are categorized as extensive, which decrease when a sample is divided, or intensive, which remain constant irrespective of sample size.

These variables are interconnected through an equation called the equation of state; any change in one of the physical quantities changes the others.

For instance, consider a gas cylinder having a certain initial pressure and volume at room temperature. Heating the gas cylinder increases the energy of the gas molecules, causing them to collide more frequently and with greater force. This increases the pressure on the container walls, potentially causing rupture at sufficiently high temperatures.

For ideal gases, this relationship is expressed by the ideal gas equation, where the molecular size and intermolecular interactions are neglected. For a given quantity of gas, fixing any two variables automatically sets the third.

However, real gases require more complex equations, like the van der Waals equation, to accommodate intermolecular forces and actual molecular sizes.