Statistical Interpretation of Entropy
A set of interactive curricular materials for teaching the basic concepts of statistical mechancs and their relation to the Second Law of Thermodynamics.
This page contains a set of curricular materials and Open Source Physics Java programs that are designed to help introductory physics students understand the Second Law of Thermodynamics. The activities described in this package attempt to help students understand why one should expect the entropy of an isolated macroscopic
system (one consisting of a large number of particles) to always increase. The activities also illustrate the connection between this entropy increase and the fact that thermal energy flows from hot to cold (and not vice versa). A more detailed description of the
activities is given in a paper that was published in The Physics Teacher 48, 516-519 (November 2010).
The activities consist of two main parts. The first part is a description of a hands-on “experiment” which is intended to illustrate important concepts related to entropy and the Second Law of Thermodynamics. The second part is a sequence of computer simulations that allow students to explore the Second Law more deeply and in new contexts. The computer simulations and other curricular materials are all contained within an Open Source Physics Launcher package, which runs as a stand alone Java program. This program, as well as worksheets and other materials, are available below.
The materials you will need for these activities are:
- The Statistical Interpretation of Entropy Launcher Package (available below).
- The Statistical Interpretation of Entropy Worksheets (available below).
- A spreadsheet program, or other plotting program to create a plot of the data from the experiment. A pre-formatted Excel file is available below.
- Coins: each group of students who completes the activity will need 20 coins (preferably all identical). Twenty pennies will work just fine. Other tokens can be used as well as long as they have a clearly discernable “heads” side and “tails” side. It works best if the coins are arranged in four rows of five.
- 20-sided Dice: each group will also need one 20-sided die (d20). These dice can be found in a variety of hobby and gaming stores. They are generally made of plastic and have an icosahedral shape (see image below). At the time of this writing I have found packs of 10 d20’s for $4 plus shipping at http://www.hobbiesandgames.com.
Download the Statistical Interpretation of Entropy software by clicking on the links below. The simulations were built using the Easy Java Simulations (Ejs) program (see below). You can modify any of the simulations if you have Ejs installed by right-clicking within a plot and selecting “Open Ejs Model” from the pop-up menu.
- Launcher Package: ejs_StatisticalInterpretationOfEntropy
- Excel file formatted for use with the Coin Flip experiment: CoinData
Worksheets that guide students through the activities can be downloaded using the links below. The worksheets are available in pdf, LaTeX source, and html formats. (If someone would like to convert these into Word I would be happy to post the resulting files here – but I don’t use Word unless I am forced to do so.) The worksheets are released under the Creative Commons license (see below).
- Open Source Physics Library by Wolfgang Christian and collaborators (see http://www.compadre.org/osp/ for more details).
- Launcher and LaunchBuilder by Doug Brown.
- Easy Java Simulations (Ejs) by Francisco Esquembre (see http://www.um.es/fem/Ejs/ for more details).
- Ejs models (CoinFlip, IdealGasBox, HotColdBox, and MaxwellsDemon) by Todd Timberlake. Parts of CoinFlip are based on the MultipleCoinToss model by Wolfgang Christian and Mario Belloni. Parts of the other models are based on the PartitionedBox model by Wolfgang Christian.
- All Curricular Materials by Todd Timberlake.
The Java programs in the package are Open Source Physics (OSP) programs and are freely distributable under the GNU GPL license. For more information about the Open Source Physics project visit http://www.compadre.org/osp/.
All of the curricular materials (including the narratives in the Launcher package) are copyrighted by Todd Timberlake and are licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License. You may modify and redistribute these materials for non-commercial use as long as you clearly cite Todd Timberlake as the original author and release the materials under the same license.
Presentations Of This Material
- “The Statistical Interpretation of Entropy: An Activity,” The Physics Teacher 48, 516-519 (November 2010). Reprint: PTE000516
- “An active introduction to entropy and irreversibility for liberal arts students” poster presented at the 2009 Summer Meeting of the American Association of Physics Teachers, University of Michigan, July 2009. Poster: TimberlakeAAPT09_Ent