left or right, or up and down. This is the same as going east-west or north-south.
On this map, we do not describe the motion in the third dimension.”
“However, there are phase diagrams in three dimensions—and even higher
dimensional spaces. These are used to describe systems with several components,
say water and ethanol. But now we are only interested in pure water,
and the phase diagram can be described in a two-dimensional space.”
The professor pointed at the phase diagram of water again.
“Likewise, in the phase diagram, we can imagine ourselves moving from a
cold to a hot region or from low to high pressures.”
“Imagine,” said the professor, aiming his laser pointer at the region denoted
‘vapor’ in the diagram, “that you are at point A in the diagram. This point is
characterized by low pressure, P, and high temperature, T” (Fig. 2.1).
“Walking within the phase diagram, up or down from point A is like treading
into nothingness. The water molecules are so dispersed that it almost seems
like you are walking in empty space. We shall, however, have a chance to ‘see’
the vapor phase from the microscopic point of view later on.”
“For instance, suppose we start at point A and walk either right or left
(i.e., increasing or decreasing the temperature), or up and down (increasing or
decreasing the pressure). In the real world, we shall not see much of a change—
but you will see quite a lot of changes on the microscopic level.”
“You should realize that the resemblance of the phase diagram to a real
map is not to be taken seriously. On a map, going to the right actually means
moving east, whereas there is no real movement in the phase diagram. Going to
the right signifies increasing the temperature of the system, not moving in the
real world. Likewise, going up means increasing the pressure on the system.”
Pointing to a point in A, in the ‘vapor’ region (Fig. 2.1), he continued:
“Scientists say that we have two degrees of freedom in this area. What this
means is that we can change both the temperature and the pressure, as we wish,
but we shall observe only one phase — in this case the vapor phase only.”
The professor pointed to a new region denoted ‘solid.’
“Similarly, in the region around this point, we can change both T and P —
remember T is the short-hand notation for temperature, and P for pressure —