Multiple paths to learning include learning with the body, yet kinesthetic movement, one of the most powerful paths to embedding learning, is generally restricted to earlier grades. Working with 8th graders in Hands On Molecular Science (HOMS), we found that molecular models gained salience as students worked out the ideas in movement first, and then modeled their motions on the computer. The following is an example of a physical simulation that students can enact to illustrate the properties of a gas. These activities complement computer simulations using StarLogo or Molecular Workbench as well as investigations performed in the lab using probeware.

Activity Overview
How do molecules within a hot air balloon behave? How do droplets within a cloud stay up? How does a gas push on its container? For that matter, how does perfume get from me to you? Students can act as molecules in a container and make discoveries about how the properties of a gas emerge from the properties of its molecules.

Students carry a few batons, each representing an amount of kinetic energy, that is, energy of motion. They move in a straight line unless they collide with the walls of the "container" or with each other. Their speed is related to the number of batons they carry. If they collide with each other, then the student with more kinetic energy give one of his or her energy batons to the other "student-molecule." Several different starting scenarios can be set up to observe what happens to this simulated multiple molecule system over time. At certain points the whole class is asked to stop and reflect on what they are discovering.

Materials
Batons. You can use materials such as the cardboard tubing inside of paper towels, straws, or (more robust) pieces of wood. Make sure there are 3.5 times as many batons as kids. Each baton represents a unit of energy.

1. Make a container. Set aside the largest possible part of the room to be a "container" for the "gas." The walls can be defined by tables, desks, floor tiles, or tape on the floor. Draw a line down the middle of the container.

2. Go over the rules for this simulation.
   • Each student walks in a straight line unless they collide with a wall or with another student.
   • The speed a student walks depends on how many batons are carried. Students with more batons need to walk faster, but not run. It doesn't much matter the speed that each number of batons represents, but it is helpful if all agree. Have them practice a one-baton walk, a two-baton walk, etc.
   • If a student collides with a wall, he or she should "bounce" off it just as a ball would. Keep the same speed before and after. Have students practice.
   • If two students collide, then the student-molecule with more energy batons gives one baton to the other student-molecule and each goes off in a random direction.
   • If two student-molecules collide that have the same kinetic energy, then they play "rock-paper-scissors" to determine who gets the energy. On the count of three each student makes the symbol of a stone (fist), scissors (two fingers separated), or paper (hand held flat). Stone wins over scissors (it breaks it), scissors over paper (it cuts it), and paper over stone (it covers it). The one who wins takes one baton from the other. Try to do this quickly.

3. Run the simulation. Give students zero to six batons at random. Distribute everyone evenly in the container. Have students play the collision game for a while, and stop them periodically.

4. Reflect. When they stop, have the students think about what the simulation tells them about a gas. Use terms that apply to a gas. Whenever possible, refer to the students as molecules, the boundary as the container, and to the number of batons as their kinetic energy. Ask students: o Will they ever all be in one corner? This is possible, but highly unlikely. o Do they all have the same energy? What is the most likely energy? Least likely? The energy will be distributed around three or four per molecule, with much higher and lower values possible, but unlikely. o Does the total energy ever increase or decrease? No. The total energy (number of batons) in the gas will always be a constant each time you stop the simulation. This is the idea of conservation of energy as long as you have an isolated system. o Does the average energy per molecule change? No, because the average energy is the total energy divided by the number of molecules. Neither changes, so the average stays constant. This average is related to the absolute temperature of the gas.

By getting students thinking about this simple simulation, you can build their intuitions about energy conservation, energy distributions, pressure, randomness, entropy, and the measure of randomness. You can deepen and explore these topics through further kinesthetic experiments.

Experiments: What If?
The following experiments can be performed on the basic gas. You might suggest the overall question and have the students work out the details of performing the experiment.

1. If the molecules start in one place, will they spread out? Is there any way to keep the gas from spreading?

   One way to to answer these questions is to start all the students in one corner. Have them predict what will happen. After only a short time, the gas will appear random no matter how they start.

2. How evenly do molecules spread out?

   One way to answer this is to start with all the student-molecules in one half of the container. Run the experiment and count how many are in each half when you call "stop." Rarely will the numbers on the two halves be equal, but they will quickly be very similar. With 32 students, you would expect 16 in each half. Your results will cluster around that number, but almost as often the split will be 15-17, 14-18, and even 13-19. Statistically, you can be sure that two-thirds of the time the split will be no more uneven than 12-20.

3. How long does it take for molecules to spread evenly?

   No matter where the molecules start, they quickly randomize. You quickly lose track of the initial configuration. Identifying the exact time at which the molecules are randomized is impossible; it will happen over a range of times.

4. Does energy get randomized, too?

   The simulation could start with half the students having all the batons. Any other unbalanced distribution would be fine, too. Experiment with stopping after different times and counting how many students have each number of batons.

5. What happens when you mix hot and cold gases?

   Half the students on one side might start with all the batons while the half on the other side have none. Other unbalanced energy starting conditions would be fine. After only a short time, students should see that the energy distribution is about the same, regardless of the starting condition.

6. What happens when the gas is compressed?

   Students might "shrink" the container while running the simulation by having one student be a piston that can push all students into half the space. The piston-person can hold out her hands and all the students could pretend that this defines a wall that cannot be crossed. The pressure is the collision rate on a fixed part of the container. This represents the outward force of the gas on the container. What happens to the pressure as the gas is compressed?

Background
The First Law of Thermodynamics says that the energy of an isolated system is constant or conserved. Since the energy of our gas is simply the number of batons, it should be obvious to kids that their total energy is constant. If it isn't obvious, have them add up the batons each time you stop the simulation. They should catch on that the sum is always the same. That's all there is to the "First Law."

Energy is only conserved in a system that is isolated and has no energy inputs from the outside. Students might notice that energy is not conserved in the fourth system (refer to page 9). This is because photons carry energy into the system from wherever they originated.

At some point, you can introduce the idea of the temperature of the gas. Temperature is related to the average kinetic energy of gas molecules. Here is a way to calculate the temperature of part or all of the gas when you "stop" it:

• Add up the total energy (number of batons) in the atoms selected. Multiply by 100. Divide by the number of atoms selected. This will be an "absolute" temperature like the Kelvin scale. To get the gas temperature in degrees Celsius, subtract 273.
• At a temperature of zero Kelvins (O K) the gas has no kinetic energy and is at rest. There is no way for it to go below O K because there is no negative kinetic energy.2
• The temperature of all the molecules will always become the same if the total energy stays the same and the number of molecules doesn't change. The only experiment that involves adding energy is when light brings in energy. Except in this case, the temperature will always become 77oC. This is because if you have 3.5 batons per student, the temperature will always become 3.5 * 100 = 350 K or (350-273) = 77oC. You can amaze your students by predicting this before they do the calculation!

The first four experiments illustrate that systems always get more random or disordered, but never spontaneously become more ordered. Starting with all the molecules on one side of the container or with some having all the energy is "ordered" or non-random. After running the experiment, these ordered starting conditions always disintegrate into similar disordered states. You can see that it is always possible that all the students will accidentally come back to the starting position, but it is so unlikely that you might as well say that it is impossible. They could play the simulation until the end of universe and still never assume exactly the starting position.

There is even a quantity, called entropy that can be calculated, that is a measure of the amount of disorder. If a system gets more disordered, entropy increases. The idea that systems become more disordered can be stated as entropy never decreases; it stays constant or increases. This is the Second Law of Thermodynamics, one of the most difficult physical principles to understand.

Assessment
Here are some challenging questions you can use to assess whether students have understood this lesson.

• Is it possible for a molecule in our simulation to have no energy?

  Yes. If two student-molecules each with one baton collide, one ends up with none. This is rare, but there is some chance that two student-molecules, each with one baton, will collide.

• If we run the simulation long enough, does everyone end up with the same number of batons?

  No. Energy is always being exchanged and a few molecules end up with lots of energy and some with little or none.

• What motion would they observe at zero Kelvin?

  All motion stops. No one has any batons.

• Is it possible to have a temperature below zero Kelvin?

  No, you cannot have negative batons and you cannot go slower than a dead stop.

For more variations of choreographed molecular science, visit the Hands on Molecular Science website.

Robert Tinker is president of The Concord Consortium (bob@concord.org). Barbara Tinker is the project manager for Molecular Workbench (barbara@concord.org).
Dan Damelin works with the Models and Data project.

Footnotes

1. There is an inaccuracy in this simulation that should be noted. The energy of a gas will increase when compressed. This happens because the compression requires a wall of the container to move inward. When atoms hit this moving wall, they leave with slightly more energy. This increases the energy in the gas; our simulation does not include this effect.

2. There are exceptions to these statements. In real gasses, there is a so-called "zero-point" motion at zero degrees. This motion cannot be extracted but is required by the uncertainty principle: we cannot know precisely where an object is and how much speed it has. If it had exactly zero speed, then it would have to be everywhere. Also, negative temperatures can be observed, in certain unusual conditions.

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Last Updated: April 21, 2001
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