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Free expansion quiz: Instructor's Guide

Main Ideas

Students struggle with understanding that entropy can be created. It's an extensive quantity, and is the only one that isn't normally conserved, so that makes it pretty weird. We (professors) don't always realize how very weird this is, and students don't have the vocabulary to explain it to us, and are often afraid to try.

Students' Task

Estimated Time: 15 min for quiz, 30-35 min for discussion following

Students will determine the change in entropy (positive, negative, or none) for both the system and surroundings in three different cases. They will then present their decisions to the class and have a discussion about their results.

Prerequisite Knowledge

  • Basic understanding of Entropy; $\Delta S = \int dQ/T$
  • Familiarity with the Second Law
  • Familiarity with the terms “fast process, slow process”
  • Familiarity with what makes a process reversible or irreversible


  • A handout for each student

Activity: Introduction

I always tell them that this quiz will only be graded on whether they did it, in hopes of reducing their level of fear. The “activity” really begins after they've finished the quiz. I put a table on the board of the various $\Delta S$ and ask them to share their answers to each question with their little white boards (but raising hands would be okay). I make someone volunteer to explain why they chose what they did in each case. Students naturally will start asking questions, and the challenge will be in getting them to stop… and in trying to provide answers that will satisfy them.

Activity: Student Conversations

One confusion that comes up is how to find $\Delta S$. Sometimes we use $\int dQ/T$ (for reversible processes), but sometimes we don't do so, and instead argue based on the initial and final states.

The main confusion, however, is where the entropy comes from in the case of the free expansion. One correct answer is to explain that entropy is simply created when something irreversible is done, which is a natural consequence of the Second Law. I also explain that entropy is *not* something that is conserved. This is troubling to them, and the same question repeats… which possibly means I don't have the best answer for it. Students wonder if entropy can be “real”, if it can be created willy-nilly like this, so I end up emphasizing that it *is* real, and that it can be measured.

One student asked if entropy could be measured *directly*, to which I answered that it can't be measured directly, but neither can energy. In both cases one is forced to measure other properties and infer the energy or entropy. But that this doesn't mean that we aren't actually measuring them.

Finally, after we've talked about the properties of entropy, students are liable to ask what entropy really *is*. Eventually I relent and give a preview of the statistical interpretation.

Activity: Wrap-up

Some groups of students will have many questions that will threaten to push the group past the time limit. At some point, it may be best to simply state what the answers actually are, and that if students are still confused as to why, they should contact you. During the discussion, students may have made compelling arguments for incorrect solutions, and it is important to point out where their logic was flawed, so as to ensure students end up with a solid understanding.


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