# Corey Hart’s Lessons In Thermodynamics

A good friend graciously transcribed the following from a recent class I was planning to audit called Corey Hart’s Lessons In Thermodynamics.

Corey Hart: Good morning, class. I am your instructor, Corey Hart, and this is Lessons in…

Awkward Young Woman (interrupting): Wait, you’re Corey Hart?

Corey Hart: Yes, and this is Lessons in Thermodynamics.

Awkward Young Woman: The Corey Hart?

Corey Hart: Yes.

Awkward Young Woman: The one from that video my mom loved in the 80’s?

Corey Hart: Yes. May I continue?

Awkward Young Woman: Um, yeah, it’s your class.

Corey Hart: Thank you. Now, as you may or may not recall, not only is heat required to raise the temperature of any solid to its melting point, but the melting itself requires heat and that’s called the heat of fusion.

(Corey heads to a large whiteboard and continues.)

From a thermodynamics point of view, at the melting point the change in Gibbs free energy (ΔG) of the material is zero, but the thermodynamic potential, enthalpy (H), and the entropy (S) of the material are increasing (ΔH, ΔS > 0). The melting phenomenon happens when the Gibbs free energy of the liquid becomes lower than the solid for that material. At various pressures this happens at a specific temperature. It can also be shown that:

$\Delta S = \frac {\Delta H} {T}$

Here T, ΔS and ΔH are respectively the temperature at the melting point, change of entropy of melting and the change of enthalpy of melting.

(Corey notices the blank stare on the Awkward Young Woman’s face but continues.)

The melting point is sensitive to extremely large changes in pressure, but generally this sensitivity is orders of magnitude less than that for the boiling point, because the solid-liquid transition represents only a small change in volume. If, as observed in most cases, a substance is more dense in the solid than in the liquid state, the melting point will increase with increases in pressure. Otherwise the reverse behavior occurs. Notably, this is the case of water, as illustrated graphically to the right, but also of Si, Ge, Ga, Bi. With extremely large changes in pressure, substantial changes to the melting point are observed. For example, the melting point of silicon at ambient pressure (0.1 MPa) is 1415 °C, but at pressures in excess of 10 GPa it decreases to 1000 °C.

(Corey notices the entire class seems lost, but since he’s on a roll, he continues.)

Melting points are often used to characterize organic and inorganic compounds and to ascertain their purity. The melting point of a pure substance is always higher and has a smaller range than the melting point of an impure substance or, more generally, of mixtures. The higher the quantity of other components, the lower the melting point and the broader will be the melting point range, often referred to as the “pasty range”. The temperature at which melting begins for a mixture is known as the “solidus” while the temperature where melting is complete is called the “liquidus”. Eutectics are special types of mixtures that behave like single phases. They melt sharply at a constant temperature to form a liquid of the same composition. Alternatively, on cooling a liquid with the eutectic composition will solidify as uniformly dispersed, small (fine-grained) mixed crystals with the same composition.

(Corey notices the drool hanging from each student’s mouth, but he’s in the home stretch, so he continues.)

In contrast to crystalline solids, glasses do not possess a melting point…

Awkward Young Woman (unable to take it anymore): Wait, glasses don’t possess a melting point? Not even under extreme heat, like, in a car on the hottest summer day on record?

Corey Hart: No, upon heating, they undergo a smooth glass transition into a viscous liquid. Upon further heating, they gradually soften, which can be characterized by certain softening points.

Awkward Young Woman: So, why did you wear your sunglasses at night?

Corey Hart: Class dismissed.

As you can tell, I missed this class. So, when I got in my car after work and put my sunglasses on, I looked like this.