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One very common way to show the equation of state is to focus on just the pressure and temperature (although we could also look at relationships between pressure and volume or temperature and volume, but these tend to be less interesting and give us less information). This depiction of the state of matter as a function of pressure and temperature is called a phase diagram. You can see a phase diagram for water in Figure 3.17.

Figure 3.17 A phase diagram for water. The axes are not drawn to a fixed scaling, but they are drawn to exaggerate values of important features of the diagram.

Let's examine some of the main features of this diagram. On the x axis is temperature and on the y axis pressure. Follow the horizontal line shown on the figure from the left to the right. This line shows the change in the form of water at a pressure of 1 atm (our usual experience).

At atmospheric pressure and low temperatures below 0 °C water is a solid. This is consistent with our experience of snow and ice on a cold winter's day. Or more trivially, the reason why we use a freezer to make ice. If we warm the ice, then at 0 °C it undergoes a phase change when it meets the melting curve. The melting curve defines when a substance transforms from a solid into a liquid (or vice versa) for any given combination of pressure and temperature. This is also an experience we are all familiar with when we see ice melting in a drink or on the roads. As we heat it up further, the water undergoes another phase change at 100 °C as it turns into gas when it reaches the vaporization curve. The vaporization curve defines when a substance transforms from a liquid into a gas (or vice versa) for any given combination of pressure and temperature. At this point, water boils. If we continue to heat it to very high temperatures (several thousand K), it would turn into a plasma as electrons are driven off the nuclei (this phase is not shown on the diagram).

There are two features of the diagram to point out. At high temperatures and pressures, there is a point called the critical point, at which gas and liquid become indistinguishable. Matter in this part of the phase diagram is called a supercritical fluid. This state of matter is not used in biological systems, although it has general importance for understanding the behavior of matter. Some exoplanets with high surface pressures and temperatures have been suggested to have atmospheres and surfaces with supercritical water (Chapter 20).

You will also notice that at pressures lower than atmospheric pressure, water boils at lower temperatures than 100 °C. This is consistent with the experience of mountaineers. The higher they go, the lower the temperature at which water boils (making it more difficult to cook vegetables). At the summit of Mount Everest (a height of 8848 m), the boiling point of water is 71 °C. If we continue to reduce the pressure, we hit a point on the graph called the triple point. The triple point is the point at which all three phases of matter can co-exist. You will see that at this point and at lower pressures, if we heat ice it turns directly into gas – it undergoes sublimation. The triple point of pure water is at 0.01 °C (273.16 K) and 611.2 Pa. There is no liquid phase in this region of the phase diagram.