Clarification of Kinetic Energy during Phase Change

This website states that:

During a change of phase the temperature does not change, but the internal energy does. The internal energy is the sum of the kinetic energy of the molecules and the chemical potential energy of the molecules. During a change of phase, the average kinetic energy of the molecules stays the same, but the average potential energy changes.

I'm confused as the two bolded statements seem to contradict each other.

My interpretation is that during a phase change, the temperature remains equal, but the kinetic energy of its particles increase/decrease.

Could this please be clarified and confirmed?

• In thermodynamics, temperature is essentially a measure of the average kinetic energy of a sample. See, for example, Wikipedia, especially section 2.1. – orthocresol Sep 4 '17 at 9:43
• As temperature reflects the average KE, wouldn't temperature still increase during phase change? – George Tian Sep 4 '17 at 10:02
• It requires energy to change the phase of a material. This energy (in most cases) is supplied through heat. When you heat the material, this will cause the temperature (or average kinetic energy) to increase. However, if you reach a certain temperature (at certain conditions), this added energy will cause the material to undergo a phase transition. Phase transitions cost energy. So for a while, the temperature will not change. The energy from the heat will be used to change the phase of the material. – CoffeeIsLife Sep 4 '17 at 10:11
• Once all of the material has changed its phase, then the added heat will continue to increase the temperature. So to answer your question, the temperature does not change during phase change. – CoffeeIsLife Sep 4 '17 at 10:12
• Well, the KE stays the same, so the temperature stays the same. Or the other way round, if you prefer to think of it that way. – orthocresol Sep 4 '17 at 10:57

In my view, temperature is just a number to describe how much a molecule is moving, i.e. its kinetic energy (KE).

I think of phase changes as a having-dinner analogy: when you eat, your KE is the same (i.e. you're not moving faster or slower like when you walk or run, so your KE isn't changing much), but your potential energy (PE) is changing since the food you're consuming can be thought of as potential energy to be stored and used up later.

Thus, when you're eating, your internal energy (which is the sum of PE and KE) is changing since the PE variable changes, but temperature as a number to describe your movement isn't since your movement (i.e. KE variable) isn't changing.

The temperature is not the average kinetic energy.

This is a bad habit which most chemists and physicists pick up because for an ideal gas, and for most systems at normal parts of the phase diagram, this is true. In thermodynamics, however, temperature is defined in terms of the thermodyanic beta as, $$\frac{1}{k_b}\frac{\partial S}{\partial E}=\beta$$ where $\beta=1/(k_bT)$.

That is to say that during a phase change, because the temperature is constant, the ratio of the change in entropy to the change in total energy (kinetic plus potential) is constant. This means that when the phase change just begins and just ends, the ratio of entropy and energy must be identical, and unless this is quite an unusual phase change, this means both need to have changed from their initial values. It wouldn't be a phase change if neither entropy nor energy changed. Because temperature is defined in this way and not as $T\propto\langle \text{KE}\rangle$, then it is perfectly reasonable for the kinetic energy to either increase or decrease during a phase change.

For instance, in normal systems one would expect that the entropy of the liquid would almost certainly be larger than the entropy of the solid. This means that the total energy must decrease by an amount $T_m\Delta S$, which makes sense as one would expect the potential energy (and perhaps the kinetic energy) to decrease when going to the liquid phase. In other words, the entropic gain allows the system to energetically relax. With this picture, it is not too surprising that the average kinetic energy can decrease during a phase change.