# Phase Diagram of Water

The characteristic properties of any substance, not just those of water, are determined according to the prevailing pressure, temperature, as well as the volume and amount of material present. Indeed, physicists say that these latter quantities determine the state of the material. In a few cases the relationship between the pressure, temperature, and volume can be written down as a simple formula, and the ideal gas equation is one such example.

Now, while the properties of a warm water-vapor gas can be determined according to a specific equation, the properties of water ice and liquid water cannot; indeed, they have their own distinct equations of state. Rather than write down the formulae for H2O in its various states, it is more convenient to look at the so-called phase diagram. Within such a diagram one can draw three loci: the fusion locus, which indicates where the phase transition from a solid to a liquid occurs; the vaporization locus, which shows where the phase transition from a liquid to a gas takes place; and finally the sublimation locus, which indicates the conditions under which a solid undergoes a phase transition straight to a gas with no intervening liquid phase. Figure 5.7 shows the phase diagram for water.

Pressure (Pa)

Pressure (Pa)

200 400 600

Temperature (K)

Figure 5.7. The pressure-temperature phase diagram for water. The sublimation, fusion, and vaporization curves indicate where phase changes occur. The location corresponding to the surface pressure and temperature of Earth, Mars, and Venus are indicated.

200 400 600

Temperature (K)

Figure 5.7. The pressure-temperature phase diagram for water. The sublimation, fusion, and vaporization curves indicate where phase changes occur. The location corresponding to the surface pressure and temperature of Earth, Mars, and Venus are indicated.

The three-phase change loci meet at the triple point, and this indicates the temperature and pressure at which liquid water, water ice, and water vapor can exist simultaneously. For H2O, the triple point occurs at a temperature of 273.16 K (or, 0.01°C) and a pressure of 611.73 Pa. The critical point (see Figure 5.7) corresponds to the end point of the vaporization curve, and for temperatures and pressures beyond this point, H2O vapor will change (upon cooling) into a liquid gradually, without an abrupt phase change. The critical point for water is located at a temperature of 647.4 K (or 374.3°C) and a pressure of 2.21 x 107 Pa.

The great utility of the phase diagram for water is that it provides a clear indication of what must be achieved through terra-forming so that liquid water can exist on the surface of a planet or a moon. As indicated schematically in Figure 5.8, the atmosphere of Mars must be increased in mass (since this will increase the surface pressure; see also Figure 5.5), and it must also be warmed. The increase in the surface pressure that might be aimed for on Mars

Temperature (K)

Figure 5.8. Schematic phase diagram for water, indicating possible paths by which the atmospheres of Venus and Mars might be changed so that liquid water can exist upon their surfaces.

Temperature (K)

Figure 5.8. Schematic phase diagram for water, indicating possible paths by which the atmospheres of Venus and Mars might be changed so that liquid water can exist upon their surfaces.

through terraforming corresponds to about a factor of 10-100 times greater than its present value. In addition, the average surface temperature will have to be warmed by perhaps as much as 15-20 K through terraforming.

For Venus, the problem is almost the exact reverse to that of the Martian situation, with both the atmospheric mass and the surface temperature requiring reduction. To make the surface conditions similar to that of the Earth, the surface pressure will have to be reduced by a factor of about 100, and the surface temperature will have to be reduced by some 440 K. To allow liquid water to exist on the surface of Titan, its surface temperature will have to be increased by about 200 K by terraforming.

The phase diagram for water shows that terraforming must typically control or modify both the surface pressure and the surface temperature of a planet or moon. Before we move on to consider how these two ends might be achieved, let us have a brief look at the circumstances under which a range of doppelganger Earths might allow liquid water to exist upon their surfaces.