I was recently drawn to an article published ASAP in *JCE* entitled Application of the Second Law of Thermodynamics To Explain the Working of Toys. Erick Castellon wrote the article highlighting the use of three toys that are used to help students develop an understanding of the second law of thermodynamics and entropy by having them observe the working of the toys and the energy transfers that occur while playing with them. I already had two of the toys, the radiometer and the drinking bird. I ordered the stirling engine from the link provided in the supporting information. As I waited for the stirling engine to arrive from Japan (which was only a few days) I attempted to write an activity to guide my students to conceptual understanding as they worked with the toys.

I wanted to strengthen my own understanding of the topics before I began writing, so I went back to *JCE* to find more related articles.

- Shuffled Cards, Messy Desks, and Disorderly Dorm Rooms - Examples of Entropy Increase? Nonsense! Frank L. Lambert 1999
- Disorder - A Cracked Crutch for Supporting Entropy Discussions, Frank L. Lambert 2002
- Entropy: Order or Information, Arieh Y. Ben-Naim 2011
- The Misinterpretation of Entropy as “Disorder”, Frank L. Lambert 2012
- Response to “The Misinterpretation of Entropy as ‘Disorder’” Arieh Y. Ben-Naim 2012

These are some of the articles that I read. There is some argument among authors about how best to teach the topic of entropy. I have used the term “disorder”. That word was used when I originally learned about entropy. And, of course, many of our text books still use that term along with analogies referencing messy bedrooms and similar situations. I have more reading to do. When I type “entropy” into the search box on the *JCE* Web site, there are many more articles on the topic!

## Comments 4

## Formality vs. Approachability

Hi Deanna:

You might want to check out the following article in the latest issue of the Journal:

http://pubs.acs.org/doi/abs/10.1021/ed4005563

I remember reading at least one of the articles you cited a few years ago. I bought Ben-Naim’s book (Entropy Demystified), which is mentioned in one of those articles and read through it. This booked helped me to increase my understanding of entropy. I am very interested not only in entropy, but also in how to present the concept of entropy to students.

It seems to me that presenting certain topics to students in an approachable manner often conflicts with making sure the topic is presented in a manner that is formally correct. A great example of this type of topic is atomic theory. I think students find it much easier to understand the Bohr model of the atom than the quantum model. When discussing certain ideas, I use the Bohr model simply because it’s easier to get my point across. I also find that entropy is a topic that falls into this category. That is to say when I teach about entropy, I often present ideas that aren’t rigorously correct but which allows students to better understand what I’m talking about. For example, I still use the “dispersion of matter” and “dispersion of energy” definitions of entropy (even though only the latter is rigorously correct) because it makes so much sense to my students. Frankly, this presentation is easier for me to understand also.

Of course we need to aspire to understand all the topics we teach in a formally correct way – in a way that experts in the field would describe as correct. However, it is my opinion that we shouldn’t always worry about presenting things in a formally correct way to our students. I think it is okay in some instances to present colloquial concepts and use familiar language. I think at times it is okay to tell my students “What I am saying isn’t entirely correct, but it’s a good way to think about things in many cases.”

For what it’s worth, my favorite definition of entropy is probability. High probability = high entropy. I even think that’s rigorously correct.

## Thanks Tom! Several times

Thanks Tom! Several times during the year, I point out to students that we (teachers) sometimes omit some of the truth behind our lessons in order to get things across more easily. The Bohr model is one of those times we tend to choose a model that we know is not the most rigorous, but it will be the easiest way to get the majority of students to a basic understanding. Those that need to develop a deeper understanding will figure it out soon enough (I hope that is true).

Section 17.3 in Chemistry A Molecular Approach 2nd Edition by Tro was recommend to me by a higher ed colleague. She said that she liked that it clearly lays out the statistical/microstate treatment of entropy in a way that is not too hard to understand. I use the 3rd edition of that text for my AP course, so I was happy to get that endorsement.

## Thermodynamics

Trying to teach entropy to students at high scool level using disorder leads them no where. Entropy must be taught at high school level using classical thermodynamics route: dS>=Q_rev/T (or dS_Univ>=0) where the equality sign applies to reversible processes and the inequality to irreversible processes. Q_rev is the heat exchanged between the system and surroundings reversibly. dS_Univ is the change in the entropy of the universe.

For processes AB involving no exchange of heat (adiabatic process), the system must be brought back to its original state through a reversible process. The entropy change for the process AB can now be obtained as follows.

The heat change suffered by a heat reservoir (HR) in the surroundings divided by its temperature gives the entropy change suffered by it. The sum of entropy changes suffered by all heat reservoirs gives the entropy change suffered by the system in the process AB. Note that during process AB the surroundings suffer no entropy change since no HR suffers any change (when AB is an adiabatic change). The process BA being reversible by design, there is no entropy change of the universe. Since the system has come to its original state the entropy change for the process AB is equal to the entropy change of the system in the process BA. This is calculated using the heat changes suffered by HRs and their temperatures. If no HR suffers a change of heat, the process AB is said to be reversible.

Trying to teach entropy using statistical thermodynamics as the starting point not only leads to difficulties but also puts them on a wrong track.

## Thanks

Thanks for your contribution. Appreciate your input.