Chapter 6 Lecture Notes
With this chapter we change the direction of the course from rather abstract concepts to
direct physical application of the ideas that we have learned. The simplest place to start
applying the laws of thermodynamics is with pure substances. In this chapter we will
consider the thermodynamic behavior of pure substances and specifically we will
consider changes in the phase of pure substances. Probably the one substance for which
everyone is familiar with all possible phases is water. We all know that water can exist
as a solid, liquid and gas. We have all frozen water in the freezer and we have all boiled
water on the stove. For this reason, I will often comment on the properties of this rather
amazing substance. Bear in mind, however, that water is indeed a rather amazing
substance and most other substances do not behave in the same way. I will point out
some of the differences as we go along.
The major question that we will address here is, how do we know what phase a substance
will be in at any particular temperature and pressure? The concept underlying the answer
to this is that of Gibbs free energy. We know that any spontaneous process has a
negative change in Gibbs free energy. What this means is that all things try to go to the
state of lowest Gibbs free energy. Thus, if you want to know what phase of water is most
stable for any particular temperature and pressure, all you need to do is to consider what
the Gibbs free energy of each of the phases is, compare them and pick the lowest one.
Since we do not want to worry for the moment about amounts of substances, we will
work with molar quantities. Since the chemical potential is the molar free energy, we can
restate the above rule as the phase with the lowest chemical potential will be more stable.
Remember that last chapter we came up with the equations:
 G 

 V
 P  T
 G 

  S
 T  P
It should be obvious from this and the definition of chemical potential that
  
  V
 P  T
  

  S
 T  P
This means that for a constant molar volume, the chemical potential is linearly related to
the pressure with a slope of the molar volume. It is also linearly related to temperature
and in this case the slope of the line is the negative molar entropy. Since both molar
entropy and molar volume change from one phase to another, the slopes of these lines
will be different depending on which phase is under consideration. For these reasons, at
any particular temperature and pressure, one of the phases will have the lowest chemical
potential and that one will dominate:
Here we see the effects of
temperature on the chemical
potential. The slope of the
chemical potential vs.
Temperature line is the negative
of the entropy. Thus, gases,
which have large entropies, will
have the steepest slopes and
solids, which have the least
entropies, will have the smalles
slopes. Because they have
different slopes, the lines cross.
At the crossing points, one phase
becomes more stable than
another. We can see that at high
temperature, the Gas has the
lowest chemical potential, but at
low temperature, the solid is
lowest. In between, the liquid is
lowest.
The effect of pressure is sort of
opposite that of temperature.
Here the slope of the dependence
of chemical potential on pressure
is the molar volume. The molar
volume of solids is low, but that
of gases is high. Again the slope
is greatest for the gas and least
for the solid and thus the various
lines cross. Where they cross,
the phase changes. At low
pressures, gases are favored. At
high pressures, solids are
favored.
This is a phase diagram. It
takes the information from
the last two diagrams and
combines it showing where
the phase boundaries are
between the solid, liquid and
gas phases. Notice that there
is a place on the diagram
where all three phases
coexist. This is a special
point called the triple point.
Finally, there is something
called the critical temperature
above which there is no
difference between liquids
and gases (they have the same
density at higher
temperatures).
Now let's consider several topics by way of tutorials:




Phase changes in a closed system with no atmosphere present.
Phase changes in a closed system with atmospheric gases present.
Phase changes in an open system.
What causes the phase of a substance to change?