DEMOCRITUS

Pressure and Density


State variables

Pressure, density and temperature are examples of "state variables". These are properties of the system that we can measure experimentally without knowing anything about the composition of the system or its internal structure and dynamics. They are "state" variables because they define the state of the system, in fact for the model system we have used in Democritus knowledge of any two of these variables is sufficient to determine the physical state of the system. Equations that define the relationship between these three variables are called "equations of state". A simple example of this is the universal gas law for an ideal gas which is

PV = nRT

The van der Waals equation for a non-ideal gas (which is applicable to all real gases) has the form

(P + an2 / V2) (V-nb) = nRT

which contains corrections to both the pressure and the volume and therefore recognises both intermolecular forces and finite molecular volume. Both of these are very important in the Democritus model.
The van der Waals equation is very important theoretically because it reveals the presence of "critical points" in the equation of state, which mark changes of state between liquids and gases.