Interactive Instruction on Ideal and “Real” GasesJames Ringlein Citation: The Physics Teacher 42, 92 (2004); doi: 10.1119/1.1646484 View online: http://dx.doi.org/10.1119/1.1646484 View Table of Contents: http://scitation.aip.org/content/aapt/journal/tpt/42/2?ver=pdfcov Published by the American Association of Physics Teachers Articles you may be interested in Oersted Medal Lecture 2007: Interactive simulations for teaching physics: What works, what doesn’t, and why Am. J. Phys. 76, 393 (2008); 10.1119/1.2815365 Comment on “Hot gases: The transition from the line spectra to thermal radiation” by M. Vollmer [Am. J.Phys.73 (3), 215–223 (2005)] Am. J. Phys. 75, 947 (2007); 10.1119/1.2735628 Electrostatics Activities, and a website for implementing Peer Instruction and Just-in-Time Teaching: TheInteractive Learning Toolkit Phys. Teach. 43, 398 (2005); 10.1119/1.2033539 Hot gases: The transition from line spectra to thermal radiation Am. J. Phys. 73, 215 (2005); 10.1119/1.1819931 Developments in interactive instruction for introductory physics AIP Conf. Proc. 399, 669 (1997); 10.1063/1.53160

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92 DOI: 10.1119/1.1646484 THE PHYSICS TEACHER ◆ Vol. 42, February 2004

This article explores efforts to use simulationsoftware in conjunction with peer instructiontechniques toward improving student com-

prehension of particle interactions in ideal and “real”gases. A series of Interactive Physics™ simulationsbuilds group student inquiry from small-scale idealgas cases through larger, more realistic particle simula-tions. The mathematics associated with the simula-tions is intentionally minimized in order to focus student attention on conceptual understanding. Ref-erences are made to other efforts in this educationaldirection, both in terms of rationale and applications.A website is cited in the Notes section containing bothmovie versions of the simulations, and includes thefiles available for download by IP users.

Background My first inclination toward a particle interaction

perspective on mechanics came from the Winter 2000Concord Consortium newsletter.1 Bob Tinker’s open-ing article advocated an emphasis on improving students’ understanding of particle interactions as afundamental goal of physics education. He made thepoint that an emphasis on particle interactions is cru-cial to the success of the “physics first” movement inhigh schools across the country. Only when physicstruly lays the groundwork for chemistry and biologywill we reap the maximum benefits from this change.Uri Wilensky followed up Tinker’s message in thissame newsletter with practical applications of StarLogoT programming toward this end. Amongother areas, he uses it to teach particle interactions in

an ideal gas.2

The inspiration of this newsletter started me think-ing that a true grasp of these phenomena had to beginwith really understanding the interactions of the parti-cles on a very small scale. I chose a pattern of instruc-tion that involved building up from small-scale idealgas type interactions, to larger ideal gas interactions,to “real” gas behavior on a small scale, and then pro-gressing to “real” gas behavior on a larger scale. Treat-ing these ideas visually and conceptually using an interactive lecture/discussion format and computersimulations was my goal.

I am a subscriber to the peer instruction techniqueof encouraging student interaction during lectures byperiodically focusing student-to-student discussion onwell-conceived questions that bring out the heart ofimportant physics concepts.3 The verbal exchange be-tween students on these questions really adds to theirunderstanding and enjoyment of the class. I use thisapproach to fully engage the students in discussing thesimulations.

The SimulationsSimulation #1—Two Ideal Gas ParticlesAt the point where students have completed a tradi-tional lab on conservation of momentum in colli-sions and explosions (I use the qualitative PASCOdynamics cart experiments), I introduce the first ofthe simulations meant to connect discrete particlebehavior to gases. It is simply two spheres in a two-dimensional box, both having the same initial veloci-ties and constrained to bounce off the walls. The

Interactive Instruction onIdeal and “Real” GasesJames Ringlein, Lancaster Country Day School, Lancaster, PA

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THE PHYSICS TEACHER ◆ Vol. 42, February 2004 93

only force of interaction between particles or wallsoccurs during the collisions. All collisions are per-fectly elastic.

Before the simulation is run in its initial state, thequestion asked is:

If both particles start with the same speed, willthe total kinetic energy of all the particlesremain the same? Will the speed of each parti-cle remain the same as the simulation runs?

After allowing time for students to formulate theirthoughts and share their ideas with each other, werun the simulation with the values of both totalkinetic energy and individual particle speed beingdisplayed. Our hope is that they realize that makingall collisions elastic will yield conservation of kineticenergy in the system as a whole, but that the speedand energy of individual particles will vary over time.

Simulation #2—Multiple Ideal Gas Particles The second simulation I used was a large number ofsimilar particles in a two-dimensional box, each withthe same initial speed, and interacting with eachother only during the impacts.

My question here is:

How will increasing the number of particles inthe box affect the results of the simulation interms of energy conservation and the speeds ofthe particles?

Of course, I hope they conclude that the totalkinetic energy of the system will remain constant,despite the wide variations in speed observedbetween the individual spheres. Depending on thelevel of the students addressed and their backgroundin chemistry, they may already be familiar with theMaxwell distribution of speeds in an ideal gas. If avisual and qualitative sense of this distribution pat-tern leads students to analyze the results in moredepth, Interactive Physics data can be transferred toa spreadsheet for more quantitative discussions.

From a concept-building perspective we may ask:

How would the range of speeds of the particleschange if, say, all were doubled in initial speed?How about if the initial speed were decreasedby half?

What we are really getting at here is an intuitivesense of the Maxwell distribution. Higher tempera-tures (initial speeds) should lead to a broader distribu-tion of velocities, and lower temperatures should leadto a narrower range of velocities. This concept can beverified with more experienced students by studyingthe Maxwell distribution in its mathematical formand using calculus (see Notes at the end of this paper).

Simulation #3—Two Particles Held bySprings While Electrostatically Repelledfrom Each Other

The third simulation I use is that of two spheresconnected by springs and having the same electrostat-ic charge. I do this next because students already havean intuitive sense of these two forces in action. Ofcourse, our ultimate goal is to model a system similarto that of a “real” (van der Waals) gas, where there is astrong short-range repulsive interaction and a relative-ly weak long-range attraction. The definition of a “real” gas in these systems is based on the Lennard-Jones potential, and we will eventually model a systemhaving this interaction between all of its particles.Starting with springs and electrostatic repulsion, how-ever, makes the simulation less foreign. Any collisionswith walls or between balls are again perfectly elastic.The first question related to this simulation is simply:

If the spheres start at rest, how will they moveover time?

We hope this generates discussions about the stiff-ness of the spring, the masses of the spheres, the quan-

1.0

The properties of the twospheres and spring may beadjusted to yield differenteffects.

The control below determinesthe initial y-velocity of the lower sphere as viewed at the start of the simulation.

Top Wall Elasticity

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94 THE PHYSICS TEACHER ◆ Vol. 42, February 2004

tity of charge on each, and the frequency of the vibra-tion. Even though I would not normally have coveredCoulomb’s law at this point in the course, studentsstill have an intuitive sense that “more charge means agreater force.” Again, it is very simple to both displayand change any of these variables as the students re-quest more information. In addition to requiring thestudents to discuss their ideas at this point, I alsoasked them to write a brief statement describing theirideas of how the different variables affect the motionof the connected spheres. They share these writtenstatements with each other as well. I am interested inhelping the students get an intuitive “feel” for thisphysical situation, not in burdening them with math-ematical complexity.

The second question explores the effect of initialvelocities on the motion of the particles:

If we vary the particles’ initial velocities, whateffect will this have on their motion over time?

We want to compare the results of the simulationbeginning at rest to this one. Hopefully, students willsee that the translational motion of the two spheresdepends on their initial velocities, but that they arestill influenced by the attractive force of the springand the repulsion of the like charges.

The last effect explored in this simulation is chang-ing the elasticity of the collisions with one of thewalls. We are, in effect, changing the coefficient ofrestitution between the top wall and the spheres.Again, we ask the students to

Predict the effect of taking energy out of thissystem by gradual cooling (making collisionswith the top wall no longer perfectly elastic).

Having the particles slow down because of energyloss in collisions with the walls is our analogy to re-moving heat by conduction to the walls of a container.The difference between this means of removing kineticenergy from the gas particles and what happens in realitymust be clearly explained to the students. There are onlyelastic collisions taking place between atoms/mole-cules in reality. The energy loss occurs for a real gasbecause of interactions with slow, relatively fixed wallatoms.

Simulation #4—Two Particles with anAttractive and Repulsive Force FieldBetween Them

The next simulation involves introducing theLennard-Jones interaction, an idea that would nottypically be presented in high school but is crucial tothis presentation of the change of state in a “real” gasas it condenses and eventually freezes.

The standard form of the Lennard-Jones potentialis given as

V = 4� {(r0/r)12 – (r0/r)6},

where r0 is the separation at which V = 0, and � isthe minimum value of potential energy. 6

With my high school students I do not explore themathematics of this formula at all. I simply tell themthat the force field we defined would act in a similarfashion to the prior simulation, but without visiblesprings or charges. I suppose with some particularlycapable students a teacher could do some usefulspreadsheet modeling or numerical calculation exer-cises, but I have not as yet.

The concept is really the same as the previous mod-el, in that there exists an electrostatic repulsion whenthe particles are very close together, and a restoringforce (van der Waals attraction) similar to the springtension when the particles move apart beyond equilib-rium. So, instead of using springs and charges to cre-ate this effect, we now define the interaction using aformula in Interactive Physics. (Please note: more in-formation on using Interactive Physics to create thisforce field can be found in the Notes at the end of thispaper.) When the two-particles-in-a-box simulationruns, I ask the students to simply watch the simula-tion run first, then to

Predict the effect of reducing the elasticity (co-efficient of restitution) of one of the walls.

Hopefully, they conclude that the particles willtend to slow down and reach a stable equilibrium witheach other after most of their translational kinetic en-ergy is removed due to collision with the top wall.The effect is like the previous simulation in the sensethat the particles are electrostatically repelled fromeach other, held by a relatively weak spring, and al-

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THE PHYSICS TEACHER ◆ Vol. 42, February 2004 95

lowed to lose energy by inelastic collisions with a wall.It bears repeating that real atoms do not have this typeof inelastic interaction; it is only a trick we use in thesimulation to cause a reduction in the kinetic energyof the gas atoms after colliding with a wall. As far asthe gas atoms are concerned, the net result is the sameas if they collided with a cool wall.

Simulation #5 — Multiple “Real” Gas Particles

The final simulation in this series is the one that hasthe most dramatic effect. Up to this point in their highschool careers, most students are familiar with idealgases and the formulas for heat exchange and changesof state. But they have not seen a simulation that con-nects these ideas in a meaningful way. The simulationof a large number of Lennard-Jones particles in a boxseeks to help make this conceptual connection.

Once the students see the array of particles in thebox, they are asked to describe the motion they willsee in the box if the particles have random initial ve-locities and all interactions are defined by the forcefield they have seen previously, with all collisions be-ing elastic. This is, of course, very similar to an idealgas condition with the elasticity of all the walls set tothe maximum. The important conceptual point hereis that “real” gases will behave much like ideal gaseswhen their temperature is high enough to prevent theattractive forces from really taking effect.

However, as one wall is set to a lower elasticity, heatis removed from the system and cooling occurs. Stu-dents are again asked:

Predict the effect on the system of allowingheat removal to occur by introducing a lowercoefficient of restitution for the top wall.

All particles start with randominitial velocities between one and four m/sec.

They have the short rangerepulsion/long range attractionfor each other as defined by theLennard-Jones potential.

Top Wall Elasticity

.40

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96 THE PHYSICS TEACHER ◆ Vol. 42, February 2004

When the simulation runs, the system cools rapid-ly, transitioning between the ideal gas to formation ofdroplets in a primarily liquid system, to a crystallinesolid. The students have seen a phase transition simu-lated before their eyes!

I have used this sequence of simulations over sever-al class periods with my physics students, and it servedas a culminating activity to a study of situations in-volving conservation of momentum and energy. It al-so serves as a supplement to the knowledge of idealgases gained previously in chemistry.

Notes• Video for Windows movies of these simulations inaction can be seen on my webpage at: http://www. e-lcds.org/fac/ringlein/sims. Anyone using InternetExplorer as their browser should be able to viewthese. On the same page are the actual InteractivePhysics files available for download and use by usersof IP.

• The expression for the Maxwell distribution ofmolecular speeds in an ideal gas is given by

f (v) = 4� [M/(2�RT)]3/2 v2 e-Mv2/2RT,

where v is speed, M is molecular mass, T is Kelvintemperature, and R is the gas constant.5

• Recent physics education research has confirmedthe difficulties many students experience in fullycomprehending the ideal gas law, and the microscop-ic interactions at the heart of it. See “Research onStudent Understanding of the Ideal Gas Law” byKautz, Loverude, Heron and McDermott athttp://www.ipn.uni-kiel.de/projekte/esera/book/b027-kau.pdf and their listed references.

• Other researchers have developed laboratory/demonstration apparatus for teaching about molecu-lar interactions in a macroscopic and dramatic fash-ion. See “Motorized Molecules: From MolecularChaos to Thermal Order” by Prentis and Yuhasz inPhys. Teach. 39, 242–248 (April 2001).

• A significant number of ideal gas computer simula-tions can be seen online, allowing for a variety of

simulated experiments to be done. See http://www.phy.ntnu.edu.tw/java/idealGas/idealGas.html byphysicist Fu-Kwun Hwang and http://jersey.uoregon.edu/vlab/Piston/index.html at theUniversity of Oregon.

• Information on Interactive Physics software in general can be found at http://www.interactivephysics.com.

• Information on the Materials Research Science andEngineering Center at Johns Hopkins is availableonline at http://pha.jhu.edu/groups/mrsec.

• Feedback on this article is requested to be sent toringleij@e-lcds.org.

Special Notes for IP users• As noted above, the website http://www.e-lcds.org/fac/ringlein/sims contains both the movies of thesimulations and the files available for download.

• These are instructions on creating the Lennard-Jones interaction between particles for the van derWaals fluid:

With the box and spheres already created in the sim-ulation, we find under the “World” menu “ForceField” and a “Pair-Wise” field. In the top slot wewrite:

48 *((sqr( self.p – other.p )) ^ -6.5) – 24 * ((sqr( self.p – other.p )) ^ -3.5)

This defines the interaction forces between all theparticles in the simulation. In this code the term(self.p – other.p) is the displacement between thecenters of mass of any two particles in the simula-tion. The constants are essentially based on the sizeof the particles involved.4

• See a group of Interactive Physics simulations(available for download by IP users) dealing withchange of state in a fluid at http://www. interactivephysics.com/simulationlibrary/evaporation.html by Raymond Nackoney of LoyolaUniversity of Chicago.

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THE PHYSICS TEACHER ◆ Vol. 42, February 2004 97

AcknowledgmentsSpecial thanks to Mark Robbins of Johns HopkinsUniversity, Gang He, former graduate student atJHU, and Bob Cammarata, director of outreachactivities for the Materials Research Science andEngineering Center at JHU. This work was fundedby NSF grant # DMR0080031, administered by theMRSEC of Johns Hopkins University. The adminis-tration of the Lancaster Country Day School hasbeen an exceptional supporter of this professionaldevelopment work.

References1. Bob Tinker, “Atomic scale models —The key to science

education reform,” @CONCORD 4, No. 1 (Winter2000).

2. Uri Wilensky, “Monday’s lesson using StarLogoT,@CONCORD 4, No. 1 (Winter 2000).

3. Eric Mazur, Peer Instruction: A User’s Manual (PrenticeHall, Upper Saddle River, NJ, 1997).

4. Thanks to Mark Robbins of the Physics and Astrono-my Department at Johns Hopkins University for helpin deriving and applying this formula.

5. Peter Atkins, Physical Chemistry, 6th ed. (W.H. Free-man, New York, 1998), p. 26.

6 Ibid., p. 667.

PACS codes: 46.11, 01.40Eb, 05.20Dd

Jim Ringlein has been science department chair, physicsand physical science instructor at the Lancaster CountryDay School since 1996 and has taught high schoolphysics since 1986. He has been active in the RET pro-gram at Johns Hopkins University since 2000.

Lancaster Country Day School, 725 Hamilton RoadLancaster, PA 17603-2491; ringleij@e-lcds.org

What Do You Do After Majoring in Physics?1

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1. These are from the Physics & Astronomy Alumni Newsletter, Colgate University, Spring 2000.

2. Jonathan Rill (‘80)

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etcetera... Editor Albert A. Bartlett, Department of Physics,University of Colorado, Boulder, CO 80309-0390

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