Boyle's Law (Thomas Garcia)

Title:

Boyle's Law: The Proportional Relationship Between Volume and Pressure

Principle(s) Investigated:

Boyle's Law: P₁V₁=P₂V₂

Density = Mass/Volume

Standards:

HS-PS1-5

Constructing Explanations and Designing Solutions:

Apply scientific principles and evidence to provide an explanation of phenomena and solve design problems, taking into account possible unanticipated effects.

Materials:

Water bottle-From anywhere

Rectangular bottle- Listerine bottle

Disposable Pipettes- From Professor Herr's back room

Water- From the tap

Paperclips

Quickwrite!!!!!

Procedure:

• Fill both of the bottles with water mostly to the top.
• Fill a pipette with water until it is just barely buoyant and put it in the standard bottle.
• Fill a second pipette with water until it is just slightly too dense (sinks) and put it in the rectangular bottle.
  • for filling the pipettes, it may be easier to test their buoyancy in a separate container other than the bottles.
• Fill the remaining empty space in both bottles with water and then close them.
• Squeeze each bottle and you can start recording the results!

Student prior knowledge: What prior concepts do students need to understand this activity?

Students should have some knowledge of density, and that denser things will sink in a less dense medium, and less dense things will rise in a more dense medium. For example, bubbles of air float rise to the surface in water because they are less dense.

Students must also know that water, as a liquid, retains its constant volume. In addition, gases, have no constant volume and fill the space they are in.

Explanation:

This lesson demonstrates the inverse relationship between pressure and volume in gases. When pressure is applied to the water bottle, water will retain its volume, and that pressure will be directly translated to the air inside the pipette. The gas, as predicted through Boyle's Law, will decrease in volume. Using a lower volume, as seen in the density equation, will increase the density of the gas in the pipette. Thus the overall density of the pipette and its contents will be greater than the density of water and it will sink.

The discrepant event is seen in the Listerine bottle. When the smaller sides sides are squeezed together, the volume in the bottle actually increases; however, because the water cannot change its volume, the air in the pipette must expand to account for this. Therefore, following the same density equation logic, because the volume increases, the density decreases, and thus, the pipette and its contents rise to the surface.

Questions & Answers:

1. How can this experiment be described in terms of buoyancy? Hint: Buoyancy is related to the weight of the displaced fluid.
   • As the bottle is squeezed, water forces the air bubble smaller due to Boyle's law, and as the air bubble is now displacing less water, and the buoyant force is equal to the weight of the water displaced, the buoyant force is decreased and the pipette sinks.
2. Why does gas compress but liquids do not?
   • The particles of a gas move around freely and independently. As a gas is compressed, they do get closer to each other but still are not touching, and therefore can be compressed further. The particles of a liquid, however, are already in contact with each other. They are bonded and cannot be pushed closer to each other as they are already as close as they can be while still allowing for movement.
3. Can you apply pressure to either bottle and have no change to the pipette? Explain.
   • With the original bottle, if you apply pressure to the corners of the the bottle instead of the flat sides, you are essentially rounding out the bottle like with the rectangular one. This will have the same increased volume effect of the rectangular bottle but because the pipette is already at the top of the bottle and floating, no visible change will occur.
   • With the rectangular bottle, when you squeeze the long sides, the volume compresses as it did in the original experiment. Thus the pipette would sink; however with it already being on the bottom, no change occurs.

Applications to Everyday Life:

• These principles of Boyle's law not only apply to the Cartesian diver but to actual divers as well. Decompression sickness, or the bends, is caused by divers rising too quickly, and going from a high pressure zone, of deeper water, to a lower pressure zone of shallow water. The nitrogen gas that has been absorbed in there blood can rapidly increase in volume if the pressure they are experiencing rapidly decreases.
• Boyle's law also allows our lungs to take in air. As our diaphragm contracts, our lungs expand and increase their internal volume. This increase in volume creates a low pressure zone in our lungs. The air from outside, at a normal atmospheric pressure, rushes in to fill our lungs and bring the pressure differentials to equilibrium. Thanks to Boyle's Law, we can breathe.
• Our sodas explode due to Boyle's law as well. The carbon dioxide gas that gets put into the soda slowly escapes the liquid while inside the sealed bottle. As it cannot escape, the pressure inside builds up (you can sometimes feel the high pressure inside a soda bottle because you can't compress it). When the bottle is finally opened, the gas quickly escapes, going from the high pressure inside, to the relatively low pressure outside the bottle. This rapid decrease in pressure inside the bottle causes the remaining carbon dioxide gas in the soda to rapidly increase in volume. As the volume of gas increases rapidly, and the bottle only has a small fixed volume, this mixture of gas and soda come pouring out.

Photographs:

Cartesian Diver: Normal Circumstances Discrepant Circumstances

Visual of volume increase in the rectangular bottle and corresponding math proof

Videos: Include a video of your investigation

Standard Cartesian Diver

Discrepant Cartesian Diver