Phase Diagrams

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© 1998-2008 by Glenn Elert -- A Work in Progress
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Discussion

phases & pressure

Increased pressure increases the range of temperatures over which a substance can exist as a liquid. Reduced pressure reduces this range. At a certain special pressure the boiling and melting points will equal, and the substance can no longer exist as a liquid. Below this pressure, the only possible phase transition is from solid to gas (and vice versa). This phase change is called sublimation (the reverse process is called deposition or desublimation) and the temperature at which it occurs is called the sublimation point (or sublimation temperature). That's the essence of the upcoming discussion. If this is enough info for you, stop reading and jump to the next section. If you want to understand what I'm talking about then keep reading. Knowing why some phenomena occurs is often more important than knowing that it occurs. (Of course, the reverse is also true, which is why I offer you the option to read on or jump ahead.)

To a certain extent, liquids are like a minimum security prison. (Solids are like a maximum security prison in permanent lock down, but that's another matter.) The molecules within have limited freedom and can only leave infrequently or with great effort. As long as a liquid has some surface area exposed to the atmosphere, here and there a molecule within the liquid near the surface will be moving fast enough to escape the liquid prison and enjoy the freedom of a vapor molecule in the surrounding atmosphere. But rather unlike a a prison, the reverse process is also possible. From time to time, a molecule in the atmosphere will be traveling fast enough to plow its way through the tightly guarded walls of the liquid only to find itself trapped within. Both events are happening simultaneously, but not necessarily with equal probability.

The thing that makes these processes different from inmates entering and leaving a prison is that they aren't so much governed by laws of good or bad behavior, but rather by physical laws describing energy and momentum. If a molecule of a liquid has sufficient momentum in the right direction, it will escape the liquid. Likewise, if a molecule of a vapor has sufficient momentum and is traveling in the wrong direction, it will join the liquid.

Given a droplet of water on the side of a glass; when more molecules of water escape the droplet than enter from the atmosphere the droplet is said to be evaporating. When more molecules enter than escape, the water in the atmosphere is said to be condensing on the glass. When the rate at which these two events are equal, the droplet is said to be in equilibrium — or more precisely dynamic equilibrium to distinguish it from the static equilibrium of a stationary bridge or level flying airplane.

All of this blah blah is a necessary set up for the remainder of the discussion, so be patient.

What is boiling and how is it different from evaporation? Both processes involve the same liquid to gas phase transition, but where evaporation can occur at any temperature boiling occurs only at a specific temperature. Let's return to the description of evaporation just discussed.

Evaporation occurs whenever more molecules leave a liquid than enter. Condensation occurs whenever more enter than leave. These changes are driven by the concentration of liquid molecules in the atmosphere. When their concentration is low, it's more likely that molecules will leave the liquid phase than enter it, so evaporation rules. When their concentration is high, it's more likely that molecules will enter the liquid phase than leave it. When neither process dominates it must be because the atmosphere has just the right concentration of liquid molecules floating around within it — no more, no less than what it can handle. Under these circumstances the atmosphere is said to be saturated.

The most energetic vapor molecules present in the atmosphere are fighting their way into the liquid. The most energetic liquid molecules are fighting their way out into the atmosphere. There's room in the atmosphere, but it has a limit. When that's reached, evaporation stops. What we have here is a war — a war of momentum on the microscopic scale or pressure on the macroscopic scale.

I lost track of where I was going. Here's some neat pictures.

A pressure cooker reduces cooking times by forcing water to remain a liquid at temperatures much higher than would be possible in an ordinary pot.

Homer sleep now.

[magnify]

A liquid can be made to boil …
- by increasing it's temperature to the boiling point under environmental pressure or
- by reducing the environmental pressure until boiling point equals the temperature of the liquid.
The bubbles that form during boiling contain vapor of the liquid. This phenomena is called nucleation. Bubbles form at nucleation sites; typically, small imperfections in the walls of the container or grains of solid material.
Cavitation is the formation of bubbles in a liquid by mechanical means; typically, rapid rotation or vibration of an immersed solid surface like a propeller or in the vortices behind an object immersed in a liquid with a high flow speed (v > 14m/s at 1 atm is sufficient). If submarines are to "run silent", they have to keep their propeller speeds low. Cavitation occurs whenever the local pressure in a fluid drops below its saturated vapor pressure.
Liquids can exist at negative pressures by keeping them under tension.
The sublimation temperature of water ice is 198 K under Martian atmospheric conditions.
The sublimation temperature of ice in a vacuum is 152 K (seems too small)
water from deep sea thermal vents can be as hot as 700 °F and yet not boil
the boiling point of water decreases 1 °F for every 500 foot increase in altitude
sublimation, freeze drying. lyophilization: λύω "to loosen or solve" + φίλος "friend", solvent-friendly? (Loose and solve have the same etymology. Amazing!) The modern greek word is κρυοαποξήρανση, which is literally "freeze from dry"+ing. condensed milk, freezer burns on food stored in the freezer for awhile, freeze drying is a controlled form of freezer burn. Originally introduced in 1813 by William Hyde Wallaston to the Royal Society in London.
1856 Gail Borden received first patent on condensed milk from the United States and England.
vapors can be condensed by compression alone, gases must also be cooled
anomalous behavior of water, expands upon freezing

Frozen carbon dioxide is also known as dry ice since it cannot exist as a liquid under normal pressures. Dry ice doesn't melt, it sublimates.

bridge text

material	T_s (°C)
Normal Sublimation Temperatures of Selected Materials
acetylene	-84
carbon	3652
carbon dioxide	-78.5
dye sublimation printer film	205~210
graphite	3825
naphthalene	48
phosphorous, red	416
silicon carbide	2700
sulfur hexafluoride	-63.8
uranium hexafluoride	56

phases & solutes

dissolved substances (solutes)

Salt depresses the melting point of water making it an effective deicer at moderately low temperatures.

unorganized thoughts

It has been known since the Sixteenth Century that salt lowers the freezing point of water, and the Eighteenth Century managed to reach -33 °C by exploiting this fact
antifreeze/coolant

Summary

Equilibrium can be used to describe two very different situations.
- Static equilibrium occurs whenever the components of forces and torques acting in one direction are balanced by the components of forces and torques acting in the opposite direction.
  - A system in static equilibrium will have a constant translational and angular velocity.
- Dynamic equilibrium occurs whenever a change in the statistical behavior of a large group of particles is balanced by an opposite change in the statistical behavior of a similarly large group of different particles.
  - A system in dynamic equilibrium will have a constant mass, pressure, temperature, and volume.
  - Dynamic equilibrium is a state where no macroscopic change is observed.
- Phase changes occur whenever a large group of particles is out of dynamic equilibrium.
The dynamic equilibrium phase plotted on a pressure-temperature graph is called a phase diagram.
- Each substance has its own characteristic phase diagram.
- The lines separating phases on a phase diagram are known as phase boundaries.
  - liquid-gas
    - The liquid-gas phase boundary is known as the vaporization curve or vapor pressure curve.
    - The value of the liquid-gas phase boundary at a given pressure is a boiling point.
    - The value of the liquid-gas phase boundary at atmospheric pressure is the normal boiling point
    - The liquid-gas phase boundary terminates at a critical point with a critical pressure and critical temperature.
      - A gas cannot be liquefied by compression if it is hotter than its critical temperature. It will remain a gas.
  - solid-liquid
    - The solid-liquid phase boundary is known as the fusion curve or melting curve.
    - The value of the solid-liquid phase boundary at a given pressure is a melting point (or freezing point).
    - The value of the solid-liquid phase boundary at atmospheric pressure is the normal melting point (or normal freezing point).
  - solid-gas
    - The solid-gas phase boundary is known as the sublimation curve.
    - The value of the solid-gas phase boundary at a given pressure is a sublimation point.
    - The value of the solid-gas phase boundary at atmospheric pressure is the normal sublimation point.
- The point where three phase boundaries meet is a triple point.
  - All three phases exist in dynamic equilibrium when a substance is at its triple point.
  - A gas cannot be liquefied by cooling if the pressure is less than the triple point pressure. It will go directly to the solid phase.

Problems

practice

Write something.
- Answer it.
Write something else.
- Answer it.
Write something different.
- Answer it.
Write something completely different.
- Answer it.

numerical

problems

Resources

miscellaneous
- The Lower End of the Sublimation Curve. B. Diu, et al. European Journal of Physics. Vol. 23 No. 2 (March 2002): 205-212.

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