NM Activity II–D3

Making Sense of the SPT of Gas Pressure

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Introduction: In this on-line sample activity, clicking on links to the “simulators” will open snapshots of simulator setups in a separate window. In these setups, if you click on Run, you’ll see the setup at the end of the simulation the activity text asks students to run. Clicking on Stop returns the student to the original setup.

In addition, in Act II-D3 Sim 1, students need to open the gas tank so that it fills the container. To open the gas tank (in both the real simulator and this on-line sample, you need to click on the blue dot indicated to the right.

	In Activity II-D2 you added several details to the 4th SPT rule (when gas particles collide with walls, they push on the walls). As mentioned earlier, to test whether a mental model makes sense, we ask three questions: • Does the model help us understand and explain our observations? • Does the model contradict other laws or observations we accept? • Does the model predict new phenomena that we can then observe? In this activity, you will apply the first two criteria to some of the phenomena you investigated in Cycle I. You will determine whether or not the added details to the 4th SPT basic rule contradict or enhance your understanding of some of the phenomena you investigated in Cycle I.

	Part I: An Example — Pumping Air into a Bicycle Tire

	In Cycle I you learned that when air is slowly pumped into (out of) a closed container with rigid walls (so the temperature remains constant) the • volume stays constant; • air density increases (decreases); • air pressure increases (decreases). 1. Suppose you were given the following problem to solve. Problem: You are helping your friend check the pressure and pump air into her bicycle tires. As you watch and help, you start thinking about the small-particle theory you are learning in class. You decide to try to explain the increase in pressure using the SPT.

	Scientists usually follow similar steps in solving problems. An example is given below. Study the problem-solving steps and example solution carefully.

	Problem Solving Steps	Example Solution

	Identify: • the type of container (open or closed) • the type of container walls [e.g. rigid and fixed, rigid and brittle (breakable), rigid and moveable, stretchy (elastic) and moveable, squishy (non-elastic) and moveable]; and • the type of change (e.g., compression, expansion, adding air, removing air). Determine whether the given change will cause an increase or decrease in the *mass* and/or *volume* of the gas inside or outside the container.	A bicycle tire is a closed container. Assume for simplicity that the walls of the tire are fixed and rigid. Pumping up a bicycle tire is adding air to the closed container. The volume of the air stays the same because the tire is a closed container and the walls are rigid -- the total push of the air particles on the tire walls is not enough to stretch or break the walls. The mass of the air in the tire increases as we add air to the tire.

	Use the basic rules of the SPT to determine what happens to the *density* of the gas -- at least initially.	The air density increases because the number of air particles in the tire increases. The tire is rigid and does not leak air, so as more particles are pumped into the tire, the particles are crowded closer together.

	Determine how any changes in the particle variables (e.g., number of particles in a unit volume, and average speed of the particles) affect the number of particle collisions with the wall each second and/or the average impulse (force x collision time) per collision.	The average impulse (force exerted by the air particles on the rigid tire walls x collision time) per collision stays the same because the particles are identical. The average number of collisions with the wall each second increases because there are more particles in the tire hitting the wall each second.

	Use the relationship between total force, number of particle collisions with the wall each second and the average impulse (force x collision time) per collision to determine what happens to the pressure.	The total force of the air particles on a unit area of tire wall (pressure) is (# collisions per second) x (impulse per collision). Since the number of collisions per second increases, the pressure increases.

	If the problem is very complex, you may need to divide the problems into *subparts* and repeat Steps 1-4.

	2. It is often helpful to visualize what is happening to the particles. Suppose BEFORE you pump air into the bicycle tire, an Ultrascope snapshot of the air in the tire looked like the one below.



	What will the Ultrascope picture look like after a lot of air has been pumped into the tire? Draw your visualization below.



	3. Use the Ideal Gas Simulator to check the example particle explanation. Open Act_II-D3_Sim 1. The rigid walls of the container represent the bicycle tire. The tank of gas represents the bicycle pump (adding gas to the closed container).



	The Ultrascope is showing the particles in a “slice” of space in the container. Attached to the Ultrascope window are two meters. The first meter is # of particles. This meter is a measure of the density of particles in the volume of space shown by the Ultrascope. You can STOP the simulation and count particles and you will come up with the same number as the meter. Try it below. The second meter is I/C, impulse per collision. This meter is measuring how hard the particles are colliding with the walls of the container.

	There are three graphs: Average Impulse per Collision versus Time, # Particles (density of particles) versus Time, and Pressure versus Density. Turn the gas tank on (so the switch is red). Run the simulation for 100-150 seconds. Make a sketch of the results on the graphs below.


	Did the pressure and density change as you expected (as you saw in Cycle I)?


	4. Making Sense. Use the simulator results to check the example particle explanation and your Ultrascope visualization.

	Did the particle variables stay the same or change in accordance with the example explanation? Was your visualization of the AFTER Ultrascope snapshot consistent with the simulator results? If not, correct your original drawing.

	Part II: Pulling Up on the Plunger of a Syringe

	Now it’s your turn to create and check a particle explanation for a phenomena you investigated in Cycle I. When a gas is compressed (expanded) slowly in a closed container with rigid walls (so the temperature remains constant), the • volume decreases (increases); • gas density increases (decreases); • gas pressure increases (decreases).

	1. Imagine sealing the end of a syringe and pulling the plunger up, as shown. What happens to the volume of gas inside the syringe? The gas density? The gas pressure?


	2. Particle Explanation: Complete the problem-solving steps of the particle explanation below. Fill in the blanks with decreases, stays the same, or increases. Write a particle explanation after each “because.”

	Problem Solving Steps	Your Solution

	Identify: • the type of container (open or closed) • the type of container walls [e.g. rigid and fixed, rigid and brittle (breakable), rigid and moveable, stretchy (elastic) and moveable, squishy (non-elastic) and moveable]; and • the type of change (e.g., compression, expansion, adding air, removing air). Determine whether the given change will cause an increase or decrease in the *mass* and/or *volume* of the gas inside or outside the container.	The volume of the air because
	Use the basic rules of the SPT to determine what happens to the *density* of the gas -- at least initially.	The air density because
	Determine how any changes in the particle variables (e.g., number of particles in a unit volume, and average speed of the particles) affect the number of particle collisions with the wall each second and/or the average impulse (force x collision time) per collision.	The average impulse (force exerted by the air particles on the rigid tire walls x collision time) per collision because The average number of collisions with the wall each second because
	Use the relationship between total force, number of particle collisions with the wall each second and the average impulse (force x collision time) per collision to determine what happens to the pressure.	The total force of the air particles on a unit area of tire wall (pressure) is (# collisions per second) x (impulse per collision). Since the number of collisions per second , the pressure .

	3. Suppose BEFORE you pull the plunger up, an Ultrascope snapshot of the air in the syringe looked like the one below.



	What will the Ultrascope snapshot look like after you seal the end and pull the plunger up? Draw your visualization below.



	4. Use the *Ideal Gas Simulator* to check your particle explanation and visualization. Open Act II-D3_Sim 2. The top of this container can be moved up and down like the plunger of the syringe. Select the piston, then RUN the simulation. Use the up arrow key (é) to slowly move the piston up at a steady rate. Once the piston is at the top of the container, STOP the simulation.

	There are three graphs: Average Impulse per Collision versus Time, # Particles (density of particles) versus Time, and Pressure versus Density, as shown below. Make a sketch of the results on the graphs below.



	5. Making Sense. Use the simulator results to check the example particle explanation and your Ultrascope visualization.

	Did the particle variables stay the same or change in accordance with the example explanation? Was your visualization of the AFTER Ultrascope snapshot consistent with the simulator results? If not, correct your original drawing.

	6. Go to your Idea Journal. Use the results of this activity to add details to the SPT basic rules.

NM Activity II–D3

Making Sense of the SPT of Gas Pressure

In this activity, you will apply the first two criteria to some of the phenomena you investigated in Cycle I. You will determine whether or not the added details to the 4th SPT basic rule contradict or enhance your understanding of some of the phenomena you investigated in Cycle I.