Wiggle Pressure

1. Place a 27-inch (69 cm) piece of 2 x 4 hanging off the edge of the table. Drill two holes using the drill bit approximately 3/4 inch (2 cm) from the end of the board and approximately two inches (5 cm) apart. Repeat on the other side of the board. Do the same thing to the other 27-inch board.

2. Using all but the short 11 1/2-inch (29 cm) length of wood, make a rectangular “arena” for the balls as shown in the picture above. The two 27-inch pieces should be on the outside and the shorter 12-inch pieces should be on the inside so that the interior dimensions are 24 inches by 12 inches (61 cm x 30 cm). (You’ll use the short length of wood later, in the To Do and Notice section.) Use the clamp to hold together the two long pieces against a short piece. Place a washer over each screw, and screw the sides together and repeat on the other side.

Turn on one of the balls, place it inside the arena, and watch as it runs into the walls. Does the ball apply a force to the wall with each collision? How might that force relate to pressure?

Count the number of collisions the ball makes against each wall of the arena over 10 minutes. Inside the arena, the long walls are twice the length of the short walls. How does the number of collisions with the long walls compare to the number of collisions with the short walls?

Turn on a second ball and add it to the arena. What happens to the number of collisions that occur each second? How might that relate to the pressure inside the container?

Place the 11 1/2-inch (29 cm) length of wood inside the arena so it divides the interior into two uneven sections, one twice the size of the other. It should be able to slide freely, changing the sizes of the two rectangular sections as it does. Turn on two balls and place one inside each section. The moving balls will hit the divider. Will the divider mostly stay in the same place or will it move? If you think the divider will move, can you predict where it will move to over time?

Move the divider to the center. Place two turned-on balls in one section and one turned-on ball in the other section, as shown in the animation below. After a long time (roughly 20 minutes), where do you predict the divider will be? Wait and see if your prediction is correct.

In this model, the motions of the self-rolling balls are analogous to the motions of gas molecules: both move around in random ways. Pressure in contained gases arises from the force produced when gas molecules collide with the walls of the container.

In general, the pressure on a surface is equal to the total force on the surface divided by the area of that surface. A longer wall experiences more collisions, and thus greater forces, but since it also has a larger area, the ratio of force per area is maintained, and all the walls of an irregular container end up with the same pressure.

Over longer periods of time, the longer walls will be hit about twice as often as the shorter walls. Since each collision applies a force to the wall, the longer walls will have a larger aggregate force applied to them than will the shorter walls. Still, the number of collisions per length of wall is about the same for all the walls, since the longer walls get hit twice as often, and they are also twice as long.

When you place a divider into the arena, creating two uneven sections with a single ball in each section, the divider will slowly move toward the center and eventually reach equilibrium there. The ball in the smaller section hits the divider more often because it has less distance to travel between collisions. Over time, this tends to nudge the divider toward the middle, until the sections are of equal size.

The situation is quite different, however, when one section has two balls and the other section has only one. The two balls will strike the divider twice as often as the single ball, creating a net force on the divider that tends to expand the two-ball section and compress the one-ball section. The two-ball section expands until the number of collisions on each side of the divider is the same, or when the two-ball section is roughly doubled in size.

The expansion of the chamber you witness here is a demonstration of Boyle’s Law: For a gas at a constant temperature, the product of a gas’s pressure and volume remain constant. In other words, if you double the volume occupied by a gas, the pressure drops in half.

This Snack can help students make a mental model of what’s happening with air molecules at the microscopic level. But like all models, this one has its limitations. For instance, in this model, the balls always move at the same speed, and so can’t demonstrate how temperature affects air molecules.

Your choice and order of activities here will likely vary depending on your students’ needs. If they’re just beginning to develop a mental model of what molecules are doing, you might start with the simplest arrangement. If you’re introducing students to the laws of physics that affect the molecular motion of gases, however, you might start with the final arrangement—two balls in one section and one ball in the other—which makes for a more interesting phenomenon.