Magic 101

I’m mulling a potential project involving magic and chemistry for my G-Chem 2 class in the upcoming semester. G-Chem 2 is mainly about thermodynamics and equilibria. Smaller, but significant topics include kinetics and electrochemistry. In previous years, I have started the class thinking about energy, and this remains a strong theme throughout the semester. Last semester in my G-Chem 1 class we had one class discussion on the energy required to cast spells. Based on that discussion, it seemed we could group energy use into three categories.

Category #1: Moving matter. Provided you don’t have to move too many particles, this has the lowest energy cost. To lift a stationary solid 10 kg stone to a height of 1 m requires overcoming a potential energy of 100 Joules. To move water vapor molecules in the air to create a tablespoon’s worth of water in your hand might require less energy. Since gas molecules are already moving with plenty of their own energy, nudging them in a particular direction might not be too strenuous.

Category #2: Chemical reactions involving making and breaking chemical bonds. Turning a cup-full of liquid water into gas would require putting in sufficient energy to break the hydrogen bonds between molecules. We’re now approaching the 10-100 kiloJoule range. Stronger covalent, ionic or metallic bonds are typically in the 200-800 kiloJoule range per mole of bonds broken. This could be substantial, however for many chemical reactions to proceed, one does not need to fully break the chemical bonds of the reactants. Partially breaking them is sufficient; barriers to chemical reactions are typically a quarter to a third of the strength of the chemical bonds. All this is to say, that a spell requiring chemical reactions to take place might require more energy. A fireball requires starting a combustion reaction.

Category #3: Changing the identity of atoms. It might not be as difficult to transfigure sand into glass and vice versa since both are primarily made up of silica (SiO₂). However, turning copper into chalk (calcium carbonate) might not be so easy. Transmutation, changing one element into another element, requires changes to the nucleus. The energies required are likely to be in the MegaJoule range or higher.

There is however a fourth category that can be related to energy, although isn’t exactly an energetic quantity. This is the thermodynamic property known as entropy. Overcoming entropy would be a feature of many magical spells. Seeing a broken egg reassemble itself would seem like magic was at work. Creating a vacuum above an object to levitate it might be a subtler version of overcoming entropy. Thanks to the science of thermodynamics, we can calculate the energetic cost to overcome entropy for different physical and chemical manipulations.

Assuming that the energy involved in magic can be transmitted via electromagnetic (EM) radiation, we have a range of choices for different manipulations. Visible and ultraviolet light are well-suited to breaking chemical bonds. Microwaves are well suited to heating and therefore moving molecules around. Higher energy or lower energy EM waves may be called upon for different tasks. The advantage of EM radiation as an energy over other sources is that it can be tuned specifically depending on the energy requirements. Photochemistry is very specific with a laser-like focus (pun intended). Thermal energy, on the other hand, is undisciplined, inefficient and leads to plenty of waste. But it has its uses, especially if you’re trying to warm up.

I could come up with a variety of magical challenges and have the students figure out how to achieve their goals with the minimum amount of energy required. For example, what would it take to cast aguamenti to create a cup of water? (It’s a magical spell that creates water in the Harry Potter series.) It might depend on the humidity in the air, or how close you are to a water source. How might you actually cast fuego (the fireball spell in the Dresden Files)? What burnable material is around? How much energy would be required to combust it in an atmosphere of 21% oxygen?

This sort of thinking tickles my brain. I wonder if the students would find it interesting or merely irrelevant. I suppose I won’t know unless we try it.

P.S. I did make it past a hundred, and since this is #101 for the year, I’ve aptly titled this blog post.