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Elementary Thermodynamics - Phase Diagrams and Critical Points

A comprehensive way of describing the relationship between pressure, temperature, and substance phase is with something called a phase diagram. With pressure shown on one axis, and temperature on the other, a phase diagram describes the various phases of a substance in possible equilibrium at certain pressure/temperature combinations.


This phase diagram (for water) illustrates some of the features common to all phase diagrams: curved lines define the boundaries between solid, liquid, and vapor phases; the point of intersection of these three curves is where the substance may exist in all three phases simultaneously (called the triple point of water); and points where a curve simply ends within the span of the graph indicate critical points, where the certain phases cease to exist.

The curved line from the triple point up and to the right defines the boundary between liquid water and water vapor. Each point on that line represents a set of unique pressure and temperature conditions for boiling (changing phase from liquid to vapor) or for condensation (changing phase from vapor to liquid). As you can see, increased pressure results in an increased boiling point (i.e. at higher pressures, water must be heated to greater temperatures before boiling may take place). In fact, the whole concept of a singular boiling point for water becomes quaint in the light of a phase diagram: boiling is seen to occur over a wide range of temperatures1, the exact temperature varying with pressure.


Something interesting happens when the temperature is raised above a certain value called the critical temperature. At this value (approximately 374 degrees Celsius for water), no amount of pressure will maintain it in a liquid state. Water heated to 374 degrees Celsius or above can only exist in a stable condition as a vapor.

The slightly curved line from the triple point up and to the left defines the boundary between solid ice and liquid water. As you can see, the near-vertical pitch of this curve suggests the freezing temperature of water is quite stable over a wide pressure range.

Below a certain pressure, called the critical pressure, the possibility of a stable liquid phase disappears. The substance may exist in solid or gaseous forms, but not liquid, if the pressure is below the critical pressure value.

Carbon dioxide exhibits a different set of curves than water on its phase diagram, with its own unique critical temperature and pressure values:

Note how the critical pressure of carbon dioxide is well above ambient conditions on Earth. This means carbon dioxide is not stable in its liquid state unless put under substantial pressure (at least 60.4 PSIG). This is why solid carbon dioxide is referred to as dry ice: it does not liquefy with the application of heat, rather it sublimates directly into its vapor phase.

Another interesting difference between the carbon dioxide and water phase diagrams is the slope of the solid/liquid boundary line. With water, this boundary drifts to the left (lower temperature) as pressure increases. With carbon dioxide, this boundary drifts to the right (higher temperature) as pressure increases. Whether the fusion temperature increases or decreases with increasing pressure marks whether that substance contracts or expands as it transitions from liquid to solid. Carbon dioxide, like most pure substances, contracts to a smaller volume when it goes from liquid to solid, and its fusion curve drifts to the right as pressure increases. Water is unusual in this regard, expanding to a larger volume when freezing, and its fusion curve drifts to the left as pressure increases.


1Anywhere between the triple-point temperature and the critical temperature, to be exact.

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