Thermo PhET Labs

Phases of matter

1. Click Here to run the PhET "States of Matter"

2. Click on "States"

3. It starts with Neon as the element. Initially it is in the solid state. Notice that the atoms are vibrating, but are held in more or less the same position relative to each other.

4. Click the "Liquid" button to see the model of a liquid. Notice now the atoms stay close to each other, but are able to move around. This is a liquid. The volume is a constant, and not easily changed by pressure, but it can flow.

5. Now click "Gas" and see the model of a gas. Notice the space now between the atoms. This is why a gas does not have a firmly established volume, and just responds to the pressure present to determine the volume. Notice the gas particles are just moving in pretty much a straight line, until they encounter each other or the walls of the container, from which they recoil with perfectly elastic collisions.

6. While it is still a "Gas" click "Water" to see particles that are not points. Notice that now you also have rotational kinetic energy (The energy of the spin of the molecules). The Equipartition Theorem states that every mode of kinetic energy will contain an equal amount of energy, which means there is as much rotational KE in this system as there is for each degree of freedom of translational. (Translational means moving in a straight line - the normal KE) (For fun, click "Neon" and then back to "Water" and notice that to start out with initially, there is not very much RKE, but as the sim runs, it settles down and obeys the ET)

7. Now click Here (Links to an external site.)to look at atomic interactions.

8. Click "Argon Argon" in the menu on the right, and click the "+" to the right of the forces, and then the button at the bottom which lets you see the two forces. The purple force is the force of Coulombic repulsion between electrons. They are both negatively charged, so the electrons on the outside of the atom repel each other. This force is one of the most common forces - it's the contact force anything exerts by touching something else. The tan force is the van der Waals force - a force of attraction (That the Ideal Gas Law ignores btw) that has to do with a shift in the density of the electron cloud around the atom.

9. The Potential Energy graph shows the PE of the two atoms. Notice the asymmetry of the curve about the lowest point. It slopes gradually up to the right, and steeply up to the left. Grab the rightmost atom, and displace it to the right until it is above the pause button and release it. Notice that it oscillates back and forth now like a weird pendulum. Notice that it spends more time farther away (to the right of the lowest point in the PE Curve), and less time closer (to the left of the lowest point in the PE curve) because of the asymmetry of the PE curve.

10. This is a bit like the energetics of a solid (although not exactly the same). Because the PE curve is asymmetrical, the vibrating or oscillating atom spends more time farther apart than closer as it vibrates, the more it vibrates (i.e. the bigger the amplitude) the more the average spacing of the atoms. This is why most solids expand as you heat them. (The amplitude of the motion is directly related to the amount of thermal energy)

Ideal Gas

1. Click Here to run the Gas Properties PhET

2. Click on "Ideal". Initially there are no particles present, so below the pump click the left button, and drag the pump up and down twice to inject two pumpfulls of heavy particles. Then click the rightmost button below the pump and inject two pumpfulls of light particles. The light particles would be like Helium gas, and the heavy like Argon maybe. Notice that these particles are monatomic.

3. Notice that the lighter particles are on average moving faster than the heavy. Both populations have the same temperature, and therefore the same average kinetic energy, but the lighter particles have a greater velocity to compensate for their smaller mass. (i.e. ¹/₂mV² = ¹/₂Mv²)

4. Let's change the pressure. First let's do this by changing the volume. Grab the handle on the left side, and move the left side of the box left to increase the volume. Notice what happens to the pressure. Now slide it to the right to decrease the volume. Look at the pressure gauge. Move the left side to where it started out. This relationship is known as Boyle's Law. It really is just simple kinematics. Pressure is the aggregate force of the collisions with the walls of the container. In a smaller container there are more collisions because the particles (travelling at the same speed) have less distance to travel, so they collide more. If you double the distance, you get half the collisions per second, therefore half the pressure. Simple.

5. Now let's mess with the temperature. Note the pressure. Now grab the little slider on the bucket and drag it up to add heat to the sim. Watch the temperature rise. You started at 300 K, raise it to 600 K. What happened to the pressure? Cool it back down to 300 K, heat it back up to 600 K. What effect does this have on the pressure?

6. This Pressure-Temperature relationship is known as Gay-Lussac's law. As the temperature increases, the speed of the atoms increases, because temperature is directly proportional to the average kinetic energy. So doubling the temperature will increase the velocity by a factor of the square root of two. (KE = ¹/₂mv², so v = sqrt(2*KE/m) ) Now this affects the pressure two ways. Once factor is that the collision happen more frequently because they are going faster, covering the distance more quickly, so they occur more rapidly by a factor of root two. The other factor is that they hit harder - i.e. they have more momentum when they hit the walls, so each collision's force is increased by a factor of root two. Two factors of root two multiply to create a simple factor of two. Doubling the absolute temperature doubles the pressure.

7. Now let's mess with moles. (Not the mammalian kind) Return the sim to more or less the original volume (square) and temperature (300 K) and note what the pressure is. Grab the pump handle and pump it up and down a few times watching the pressure. Notice the effect this has on the pressure. (It's like pumping up a bike tire...) Grab the handle on the top near the thermometer, and drag it to the left to let air out of the sim. Watch the pressure gauge.

8. This Mole-Pressure relationship is known as Murray's Law. It's easy peasy - the more particles in the container, the more the collisions, and the more the pressure. Twice the particles, twice the collisions per second, and twice the pressure. Maybe it isn't called Murray's law. I feel that would be a good name though.

Absolute Zero Lab

The rationale for this lab is that as you decrease temperature. the pressure will decrease. Absolute zero is the temperature at which the gas exerts no pressure on the walls of its container. We will determine this by extrapolating from some data points.

1. Click Here to run the Gas Properties PhET

2. Click on "Ideal". Above the thermometer pull the menu down to make it read ^oC. Below the pressure gauge, pull it down to read kPa.

3. Initially there are no particles present, so below the pump click the right button, and drag the pump up and down three times to inject three pumpfulls of light particles.

4. Cool it to about 0 ^oC by sliding the slider on the bucket below the sim down. Record the temperature in a data table. Notice how the pressure jumps around a bit. This is because there are only about 145 particles in the whole sim. If there were a mole of particles, it would be rock steady. This is OK, let's use these natural fluctuations in pressure to generate trial to trial uncertainty.

5. To take a data point of pressure, hit the pause button in the lower left, record the pressure, un-pause for a second, and pause again, record the pressure. Do this to create data for five trials. If this were an IA, we might want more trials, but five is enough for now.

6. Now you have one temperature, and five pressure data points. Click the play button, and use the slider below the sim to heat it up to about 30 ^oC. Gather five trials of pressure the same way we did before. Then do the same for about 60 ^oC, 90 ^oC, and 120 ^oC. You now have five temperatures and for each temperature you have five trials of pressure. The temperatures don't have to be exact, just within maybe 5 ^oC of the target temperature. (I.e. 32 ^oC is fine for the 30 ^oC data point.) Whatever the temperature actually is, record it in your data table.

7. In your data table, create a column that contains the average of the trials, and the uncertainty of the trials. ((high-low)/2) Left to right, the columns could be "Temperature ^oC", "Average Pressure kPa", "Pressure Uncertainty kPa", "Trial 1", "Trial 2", "Trial 3", "Trial 4", "Trial 5" - as long as you indicate somewhere that the trials are pressures in kPa.

8. Notice that the uncertainty bubbles about, but there is no real trend. Because Google Sheets does not make it easy to make different sized error bars for each point, let's just average the uncertainties (no real basis for doing this, we just need error bars, and I don't want you to hate me too much)

9. Create a scatter graph of pressure vs temperature. Make the x axis go from -350 ^oC to 150 ^oC with major gridlines every 25 ^oC and minor every 5 ^oC. Add a trendline to the points. (The X-intercept is what?) Make the points 1 point in size, and give them error bars that are constant and the size of the average uncertainties in the trials.

10. Copy and paste your data table into the Google Doc you are going to submit, and resize your graph to take up the whole area of the spreadsheet, covering up the numbers. (Make it as big as possible, leaving room for the edit menu on the right...) Make sure at this point that it has a title, and the axes are labeled with units and quantities.

11. Add a steepest line to your graph using the draw tool. The steepest line is the steepest a line can be, but stay inside all the error bars. It needs to go entirely across the plot frame, intersecting the X axis. Then do a least steep line. Screenshot this into your Goooogle Doc that you are turning in. Keep in mind that if you click on the graph behind the lines, it will move the graph in front of the lines and they will be hidden. For this reason it is prudent to have the lines stick over the edge of the graph somewhere, so you can bring them to the foreground again. This is why we screenshot them. Someday, Google sheets will let you directly order layers, but it doesn't yet as I write this.

12. Read where the trendline meets the X-axis, and where the highest extrapolation (steepest line) hits the X-axis, and the lowest extrapolation (least steep line) hits the X-axis. Estimate these down to the nearest degree. It helps to Zoom in on the picture or the graph by changing the Zoom% to 200%

13. Answer these questions in your own words: What were your results. Cite your best fit line's X-intercept, and the highest and lowest extrapolations. Cite what absolute zero is in ^oC, and do two things, 1. Compare it to the value you got for the best fit line, and 2. State whether it falls within your max and min extrapolations.