Modern Engineering Thermodynamics

Pressure
Vapor
3.7 Phase Diagrams 67
S L
Pressure
Solid
S
V
Triple
point
Liquid
L
Vapor
V
Critical
point
Gas
Pressure
Solid
Solid−liquid
Liquid
Critical
point
Liquid−
vapor
Triple line
Solid−vapor
Gas
Vapor
Temperature
Volume
FIGURE 3.6
Pressure-temperature and pressure-volume diagrams for a substance that contracts on freezing (for example, carbon dioxide).
Solid
Solid−liquid
Liquid
Critical
Liquid−point
vapor
Triple
line
Gas
Solid−
vapor
Volume
Temperature
FIGURE 3.7
The p-v-T surface for a substance that contracts on freezing (for example, carbon dioxide).
of two-phase liquid-vapor equilibrium, and the sublimation line represents the region of two-phase solid-vapor
equilibrium. These three lines intersect at one point, called the triple point, which is the only point where all
three phases can be in equilibrium simultaneously. The triple point on the p-T diagram appears as a line on the
p-v diagram, with the triple point simply being an end view of this line. Table 3.3 gives the property values at
the solid-liquid-vapor triple point of various substances. At the triple point of a pure substance, C =1, p = 3, and
the number of degrees of freedom are f =1− 3 + 2 = 0; that is, there is no flexibility in the thermodynamic state
and none of the properties can be varied and still keep the system at the triple point. The properties can be varied
along the various two-phase boundary lines but not at the three-phase triple point. If a substance has more
than one solid phase, then it also has more than one triple point.
When pressurized, most liquids freeze at a higher temperature because the pressure forces the molecules together.
However, at pressures higher than 1 atmosphere, water remains liquid at a temperature below 0°C due to the
strong hydrogen bonds in water. This is why ice melts under an ice skater’s blades and lubricates her or his movement.
The melting of ice under high pressures is also thought to contribute to the movement of glaciers.
When subjected to high pressures, water can form at least 15 solid phases. These phases differ by their crystalline
structure, ordering, and density. In 2009, ice XV was found at extremely high pressures and −143°C. Figure 3.8