Relationships Between Pressure, Volume, And Temperature

Purpose:  In this experiment, we will take a close look at the relationships between pressure, volume, and temperature. In the end, we intend to verify that every experiment obeys the ideal gas law.

Heating a Can With Liquid Inside

We start off by observing the behavior of a can, in which we heat and submerge into a small tank of water

The experiment astonishes everyone as we observe the can implode. The reason for this is because while the can is heated, vapor is formed within the can and this vapor occupies space within the can. When the can is submerged in water, the change in temperature is negative and the vapor condenses into liquid that occupies less volume. To make up for the volume not occupied by the liquid, the can implodes to occupy the space.

Professor Mason is showing the entire class the crushed can

Our group put together a visual model of what occurs when a can with liquid is heated and submerged into water.

Heating a Can Without Liquid Inside

We do the same experiment, without liquid inside the can, and observe the behavior of the can. This time, the can does not implode. This is understandable, as there is no vapor to occupy a large amount of space only to condense into liquid that occupies a small amount a space.

The picture above shows the can that does not do anything when submerged

Pressure Calculations

Our group wrote down some of the many other ways to express pressure. After, we calculated pressure at sea level.

Pressure vs. Volume

In the black ink, our group predicted how a pressure versus volume graph would look like and compared it to a plotted pressure versus volume. Both graphs seem to show the same behavior of an inverse function.

On Logger Pro, we are able to see a more realistic graph for pressure versus volume and we see that pressure is, in fact, inversely proportional to volume.

After looking at the Logger Pro graph, we created a fit equation that best described our inverse proportionality. We find that a traditional inverse function does not quite satisfy the behavior of the slope, so we add another constant B. In red, we derive what the units of A would be. which turns out to be Newton-meters.

We get a real look at the relationship between pressure and volume. As pressure is dropped, the volume of the un-inflated balloon increases. This is because the balloon is tied and as the pressure in the balloon's surroundings drop, the inside pressure of the balloon makes up for it by expanding the balloon from the inside. 

Pressure vs. Teperature

Professor Mason sets up an experiment that would allow us to see the relationship between pressure and temperature.

Our group anticipates that the pressure is proportional to temperature, and so the graph would be linear. We showed why pressure is proportional to temperature using ideal gas law.

It turns out that our hypothesis of proportionality was correct, as Logger Pro creates a linear line.

Volume vs. Temperature

Next, we look at the relationship between volume and temperature. Professor Mason sets up an experiment, similar to a piston inside an engine.

The experiment ultimately shows that there is a proportionality between volume and temperature, as volume increases as temperature rises and decreases as temperature drops.

The Boltzmann Constant

Using the relationship between pressure and temperature, pressure and volume, and volume and temperature, we were able to derive the Boltzmann Constant with the help of the "A" variable derived previously. A was measured in Newton-meters or Joules.

Application of Ideal Gas Laws

Our problem was to find the change in water in a bell when the bell is submerged with the opening pointed downward. Using Ideal Gas Law, we were able to relate volume in terms of height and this relationship allowed us to find the change in height of the water within the bell.

Marshmallow and Pressure

Our next experiment deals with marshmallows under reduced pressure. We hypothesized that the marshmallow would compress under reduced pressure and return to its original form under atmospheric pressure, just as the deflated balloon did.

The marshmallow, actually, expanded, just as the deflated balloon. We forgot that there are air bubbles within the marshmallow and these air bubbles expand as pressure is reduced. The next observation that surprises us all is that the marshmallow does not return into its original form. It is, actually, smaller than before. This is because the air bubbles that used to plump the marshmallow rupture during the process of expansion and this causes the marshmallow to close the gaps it used to have, making the marshmallow smaller.

Using ideal gas law, we found the mass of Helium inside a balloon.

Conclusion:  We have tested every case about pressure, volume, and temperature and found that these cases were consistent with Ideal Gas Law. What surprised us the most was the implosion of the can, partly because of the noise created. But, the science behind the implosion amazed us the most. It was an excellent demonstration of pressure, volume, and temperature at work with phase change. The entire experiment was full of surprises, but, ultimately, every experiment was able to be explain with some relationship between pressure, volume, and temperature.