This was really great. It's how I was taught entropy at college (biophysics and molecular biology) though without the sheep. "Statistical Mechanics" was the name our professor used.
The only tiny change I'd like to make is to add a line or two near the end, something along the following lines:
There's a lot fewer ways to arrange water molecules so that they form an ice cube than there are to arrange them as a liquid. Most arrangements of water molecules look like a liquid, and so that's the likely endpoint even if they start arranged as an ice cube.
The same is true of more or less any macroscopic object: the thing that we recognize and name ("chair", "table", "pen", "apple") requires the atoms to remain in one of a fairly small set of particular arrangements. Compared to the vast number of other arrangements of the same atoms ("dust"), the ones where the atoms form the "thing" are quite unlikely. Hence over time it's more likely that we'll find the atoms in one of the other ("random", or "dust-like") arrangements than the one we have a name for. The reason things "fall apart" isn't that there's some sort of preference for it - it's that there are vastly more ways for atoms to be in a "fallen apart" state than arranged as a "thing".
"Students who believe that spontaneous processes always yield greater disorder could be somewhat surprised when shown a demonstration of supercooled liquid water at many degrees below 00 C. The students have been taught that liquid water is disorderly compared to solid ice. When a seed of ice or a speck of dust is added, crystallization of some of the liquid is immediate. Orderly solid ice has spontaneously formed from the disorderly liquid.
"Of course, thermal energy is evolved in the process of this thermodynamically metastable state changing to one that is stable. Energy is dispersed from the crystals, as they form, to the solution and thus the final temperature of the crystals of ice and liquid water are higher than originally. This, the instructor ordinarily would point out as a system-surroundings energy transfer. However, the dramatic visible result of this spontaneous process is in conflict with what the student has learned about the trend toward disorder as a test of spontaneity.
"Such a picture might not take a thousand words of interpretation from an instructor to be correctly understood by a student, but they would not be needed at all if the misleading relation of disorder with entropy had not been mentioned."
> There's a lot fewer ways to arrange water molecules so that they form an ice cube than there are to arrange them as a liquid. Most arrangements of water molecules look like a liquid, and so that's the likely endpoint even if they start arranged as an ice cube.
Except this is, as an insight, obviously wrong. The arrangement you get is determined by temperature: cold water will spontaneously freeze, and hot ice will spontaneously melt. The model you state predicts that
In keeping with the level of explanation in the article, I was omitting the role of energy in describing the exploration of possible microstates by the system.
A system with zero energy is highly constrained in its exploration of possible microstates, and thus is unlikely to undergo a change in its macrostate.
A system with a lot of energy is much less constrained, and is more likely to undergo macrostate changes.
This wasn't really covered in the article, so I didn't want to put it into my (perhaps foolish) add on sentences.
This followup still predicts that cooling water cannot cause it to freeze. (And relatedly, it predicts that cold ice will take a long time to melt, but not that it won't melt. In fact, it won't melt.)
I don't see why either of those things follow, particulary the second.
Cold ice, in an environment that doesn't supply energy to the ice, will not explore microstates at any notable pace, and thus will not melt.
I don't think it makes any prediction about what will happen when cooling water, because the freezing reaction is related to the specific chemistry of water molecules. The only prediction is that any macrostate that gets newly entered into is less likely to change, because of the relatively low energy state of the system (compared to the energy required to break the newly formed bonds of the crystalline form.
1. Things tend to turn to dust rather than stay together, because the number of states where things are "together" are small, and the number of states where things are dust are high.
2. Ice has a few arrangements, and water has many. So water is "dust ice".
3. H2O will naturally tend towards "dust" form over time, so ice will eventually become water.
The only tiny change I'd like to make is to add a line or two near the end, something along the following lines: