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Thermodynamics and Geothermal Systems 39

that are given explicit values at some reference condition, and all else is derived from that data.
Gibbs developed his concept on the basis of reversible processes. Hence, what we call the Gibbs
function represents the maximum energy a system possesses that can be used to do useful work.

The sTandard sTaTe
Note that Equation 3.15 is written in terms of the Δ’s for the thermodynamic properties. That reflects
the fact that we can only compare states and properties based on some arbitrary reference system
we define and studiously respect. For example, it is usually assumed that the free energy of forma-
tion of an element is zero at 0.1 MPa and 298K. Any measurements that are then made using those
reference materials as the starting materials will produce data (heats of reaction, for example) that
characterize the more complex compound. For example, consider the reaction

H + 1/2 O < = > H O,
2
2
2
where H is a pure gas, O is a pure gas, and H O is a liquid or vapor. If this chemical reaction took
2
2
2
place at standard conditions in a calorimeter, which is an instrument to measure the heat given off
or absorbed in a reaction, the amount of heat given off in the formation of the water molecule would
be, by definition, the energy of formation of water at standard state conditions (STP). In principle,
similar measurements could be made for all simple oxides or compounds of interest and the result-
ing data, along with Equation 3.15 would allow the thermodynamic properties for all minerals and
fluids to be deduced.
Conducting similar experiments at conditions other than those of our defined standard state
allows equations of state to be developed that define how the energy content of a material changes
with pressure and temperature. Equations of state can take many forms and are developed for
substances to varying degrees of accuracy. As with the standard state conditions, we can use these
relationships to determine the energy content of our systems at any set of conditions of interest.
The importance of this capability can be appreciated by considering the energy content of H O
2
as a function of pressure and temperature. From Equation 3.15 it is clear that if a substance such as
H O is heated at constant pressure, the change in the Gibbs energy will be equivalent to the enthalpy
2
contributed by the heating process minus the product of the temperature times the entropy change,
G – G = (H – H ) – T × (S – S ). (3.16)

P,T
P,T
stp
stp
stp
P,T
This relationship is plotted in Figure 3.5 for liquid and vapor H O at 0.1 MPa and 1.0 MPa. This
2
figure provides some important insights into the behavior of materials that are predicated on their
thermodynamic properties. One obvious fact is that, at constant pressure, changes in temperature
affect a vapor phase more severely than a liquid. This reflects the fact that the molecules in a fluid
are more tightly bound by local molecular forces than are gas molecules. As a consequence, more
thermal energy is required to affect the thermodynamic properties of a liquid material. The same
is true for a solid phase.
An additional point that is clear from Figure 3.5 is that pressure has minimal effect on changes
in the thermodynamic property of liquids (or solids) but can dramatically change the thermody-
namic properties of gases. This, too, reflects the molecular interactions that occur in the material as
pressure and temperature change. Liquid water is nearly incompressible at near-surface conditions,
while water vapor is highly compressible. Both of these effects imply that the energy content of
gases will be sensitive to the physical conditions they experience, which will become an important
point when we consider geothermal resources and how they can be used.
A third, critical aspect that emerges from Figure 3.5 is a simple explanation for why water changes
phase, from liquid to vapor. Recalling the fact that all systems are driven to achieve their minimum