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Pressure

The final variable to define lends itself nicely to an intuitive understanding as well. We commonly think of the pressure as the force per unit area in physics. While the units work out to be the same, we define pressure in a different manner altogether here:

p = -

The equation states that pressure is related to the way that the energy changes as the volume changes. We will explore how this correlates with our intuitive notion in the problems at the end of the section.

Intensive vs. Extensive Variables

A key distinction needs to be made here among the variables. Some of the variables we call extensive, if they obey the following property - upon the doubling of the system, they too double. We can quickly see that the volume V doubles if the system doubles, as do the number of particles N and the entropy σ. If a variable remains constant upon the doubling of the system, then we call that variable intensive. The temperature τ, the pressure p and the chemical potential μ are all intensive. We will decide upon which category to put the energy in the problems at the end of the section.

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