Phase changes

Answer the following questions in your head:

1. A pot of water on the stove is getting hotter and hotter. At what temperature will it begin to boil?
2. You walk into a kitchen and find a pot of boiling water on the stove. What is the temperature of the water?
3. Sketch a graph of the temperature of a pot of water on the stove as it is heated. 

It is common to answer these questions in this way:

1. 100^oC (or 212^oF), 
2. 100^oC, 
3. a graph that looks like the following:

If those were the answers you gave, you may begin to realize that they can’t all be correct. If the temperature continues to rise (as the graph shows) then there is no way to predict what the temperature of the boiling water in question B would be. The truth is that the graph for question C should look like this.

In fact, the temperature stays the same during any phase change. Thus, melting ice stays at 0^oC until all of the ice has melted, just like boiling water stays at 100^oC until all of the water has boiled away.

This leads to a simple question—why? Why doesn’t the temperature change during a phase change?

The answer, unfortunately, is not as simple. We need to remember several things.

• there are two types of energy, kinetic (energy of movement) and potential (energy of attraction and position). 
• temperature is a measure of how fast particles are moving. 
• not all particles are moving at the same speed (like cars on the highway) 
• attraction decreases with speed (The South Street Effect).

Consider water at 100^oC and steam at 100^oC. Both have the same temperature and therefore, both have molecules moving at the same average speed, and therefore the same kinetic energy.

The difference between them is ONLY the spacing of the molecules. In water, the particles are densely packed, while in steam, the particles are separated by large relative distances. This means that steam has much more potential energy that water at the same temperature.

That means that the difference between liquid and gas (actually between any two phases at the same temperature) is potential energy.

So to turn liquid water at 100^oC into water vapor at 100^oC requires energy to be added (the potential energy difference). Let’s look at two different situations in which water undergoes the phase change from liquid to gas.

Sweating
The first example is sweating. When we sweat, water (and some ions) leave our body through pores in the skin. When the water leaves our body it is the same temperature as our skin. This makes sense since that is where the water was moments earlier. As the water molecules begin to evaporate, they take energy with them.

One way to imagine this is to remember that all collections of molecules have a range of speeds. Some molecules are moving quite fast while others are going very slowly (Boltzmann distribution). The molecules that are moving the fastest, feel the least attraction for the other molecules and are therefore the most likely to break away and leave (South Street Effect).

That means that the molecules left behind are the slower ones. The average speed of those left behind will, therefore, be slower. Since the temperature is a measure of the average kinetic energy, decreasing the average speed is the same as decreasing the temperature. Thus the water left behind on your skin is cooler than it was (and cooler than your skin). Heat then transfers from your hotter skin to the cooler water and, as a result, you are cooled down.

Another way to think about this it that as the water molecules undergo the phase change from liquid to gas they require energy (the potential energy difference between liquid and gas). The only source of this energy is the other molecules around them and your skin, so in the process of undergoing the phase change, they take energy with them. With less energy, the molecules left behind will move more slowly. Again, this means that their temperature is lower, and a loss of heat from your body.

Boiling
Now, let’s think about boiling. Part of the process is just like the evaporation of sweat. Hot water molecules leave taking heat with them resulting in the cooling of those molecules left behind.

However, when we boil water on the stove there is another, rather important, factor—the heat source. A pot on a stove is being heated from underneath by an electric coil or a flame. This influx of heat makes the molecules move faster, resulting in a higher temperature.

What is happening in the pot then is a combination of two different processes: the evaporation (boiling) of the water, removing heat and pushing temperature down, and the addition of heat from the stove pushing the temperature up.

These two factors balance and the temperature will remain constant.

Of course, there is also some math that we can do involving phase changes.