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course phy 122
This experiment has me a little confounded since it is not in the usual format i am used to seeing for lab write ups. It also seems to be a little complex for what we are doing at this level in the course, but perhaps this should not be so and I should have no problem with it. I have found it to be a difficult and frustrating task. I am somewhat familiar with the concept of entropy and I can appreciate the usefulness of such lab exercises, but isn't there a possibility that i could conclude entirely improper information as to the nature of the system based on my inability to interpret the lab? Whereas if you told me that entropy is the nature of particles, among other things, to move from a state of order to disorder, and provided me with a model depicting such, i feel comfortable i could infer as much as if i had figured it out for myself.
Watch the 'red' particle for a couple of minutes, estimating the average time between its collisions and its average speed (one of the speeds given near the top of the screen corresponds to that of the 'red' particle--which is it?).
-the dos program doesnt quite show the top of the screen, and the red particle moves very fast. The windows based program shows the red particle moving slowly compared to the green particles. It seems to make a collision perhaps once every second, but it is probably more on the average of 1 ever 0.5 or 0.25 of a second.
Watch the 'blue' particle, and speculate on what property of this particle is different from that of the other particles.
-the blue particle has an atomic mass of 4, which I would have said the green particles were protons, less an amu than 1 would imply electrons. Protons and neutrons have atomic masses of about 1, and electrons 0.0005 or something. Anything greater than 1 would have to be a combination of atoms, an element most likely a small and simple one in this case.
Watch as the 'red' particle sometimes turns yellow. What causes this? What property does the particle have when it is yellow?
- The dos and windows version must be for 2 separate things, I assumed they were the same program, in the dos program the red particle does occasionally turn yellow when it collides with a freely floating yellow particle. Some form of chemical reaction is a likely representation here. Perhaps it is of a different polarity, becoming some form of ion.
What might the graphs represented at the right of the screen represent?
-it is difficult me to speculate with the minimal amount of chemistry Ive had so far, but perhaps it is a representation of the amount of atoms, particles, gasses, or whatever at work, their relative position to each other, their polarity, or how they are reacting with one another. Also the speed at which they are moving, there are many possibilities to this question.
Strike the 'S' key to stop the simulation, and if you are done give the appropriate response to the prompt to quit the program. CTRL-ALT-DELETE will also stop the program, but if you're not careful it will reboot your computer so avoid that option if you can.
Experiment kinmodel_01: The Distribution of Atomic Speeds
When the speed of the simulation is moderate it is possible to watch a specific particle (the red particle or the blue particle in the default simulation) and obtain an intuitive feeling for the relative frequencies of various speeds.
Run the simulation kinmodel at the default settings--simply hit the 'Enter' key for each option presented.
Observe the simulation long enough to get a feel for the maximum velocity you are likely to see. Then estimate how much time it spends at slow (less than 1/3 of max vel.), medium (between 1/3 and 2/3 of max. vel.) and fast (more than 2/3 of max. vel.) velocities.
o This is a difficult observation to make, the information changes very quickly, and when I try to change the speed it crashes.. in any case, the particles appear to spend more time in the lower speeds at about 45 percent, 30 percent in the medium range, and 25 in the upper range.
Express your estimates in percents of the total time spent in the three different velocity ranges.
Draw a histogram (a bar graph) of your estimates. Describe your histogram in your writeup.
o My graph fluctuates rather chaotically and the information is difficult to interpret, but the bars only on occasion fluctuate towards the max end of the velocity spectrum, they stay more in the low to medium range.
Now suppose you had estimated the percent of time spent in each of 10 velocity ranges (i.e., from 0 to .1 of max. vel., .1 to .2 of max. vel., etc, up to max. vel.). From your previous estimates, without further viewing the simulation, make a reasonably consistent estimate of the proportion of time spent in each of these ranges.
Sketch a histogram of your estimates and describe the graph in your writeup.
o The closest I can come with this one is to say what I have said previously, the system changes every few seconds, and the values for velocity change more rapidly than I can detail them for a set of time quantities, Im not sure what to do with this one.
Watch the red particle for long enough to estimate the percent of time it spends colored yellow.
o The red particle is yellow only for a very small fraction of the time, maybe 5 percent.
Watch the whole simulation to see what average percent of the particles are yellow at a given time (there are 30 particles, including the blue one).
o There are only 1 or 2, sometimes no yellow particles
How would you expect the answers to these two questions to compare?
o Less yellow particles mean less collisions between yellow and red particles, so a smaller percentage of the two combined.
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Good.
Also, if a single particle spends 5% of its time in the 'yellow' range, then you would expect that 5% of the particles would be yellow at any given instant. If there are 30 particles, that translates to an average of 1.5 yellow particles, so your answer '1 or 2' is completely consistent with your percent estimate.
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Watch the number corresponding to the speed of the 'red' particle.
o It isnt clearly denoted what the speed of the red particle is, I will assume it is the only instance of speed that we see, which is the speed of the last two particles
Close your eyes for a few seconds at a time and open them suddenly, and each time write down the velocity of the 'red' particle immediately when your eyes open. Record about 100 velocities in this manner.
Tally your velocities to see how many of the 100 velocities were 0, how many were 1, how many were 2, etc.
Construct a histogram of your results and compare to the histograms you predicted earlier.
o The graphs continue to show that we have more occurrences in the lower values of velocity and less occurrences in the higher ranges of velocity.
Observe the 'blue' particle for at least 5 minutes, monitoring its speed to see if it ever reaches 3 or more.
Based on your observations and your experience with other distributions, sketch a histogram of the speed distribution for the 'blue' particle, 'rounding' your results to the nearest .25 (i.e., use 0, .25, .5, .75, etc. for your velocities).
o The blue particle remains in the 0-3 area for a vast majority of the time, only rarely does it touch 3.
Stop the simulation and quit it. Then run it again and watch the 'blue' graph at the right. Sketch this graph every minute or so, for about five minutes. Describe how the graph develops, and describe what you think it will look like after a long time.
o The graph appears to go from scattered points to a more uniform shape, the points come closer together and they start at an increasing curve and then level off. The final points do not tend to change much.
What do you think this 'blue' graph represents?
o Perhaps the speed of the blue particle but Im quite stumped.
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The graph could represent the relative frequencies of different velocities of either a red or a blue particle. It turns out that it represents a red particle. Every second or so red particle velocities are tallied. A running tally is maintained. The graph represents the frequency distribution as it develops.
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What do you think the 'yellow' rectangle is for, and what does the graph tell you in relation to this rectangle?
o I really cant tell
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The 'yellow' region of the graph shows the frequencies of velocities within the 'yellow' range.
I would expect that about 5% of the area beneath the graph would be in the 'yellow' range, consistent with your previous 5% estimate.
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Experiment kinmodel_02: Mean free path; mean time between collisions
It is possible to observe a chosen particle (the red or the blue particle in the default simulation) for its mean free path between collisions. This observation becomes more involving if, for example, the observer is 'rooting' for the red particle (in the default simulation) to collide with the blue particle. The tracks left by these particles also provide a record of the path between collisions.
First observe the 'red' particle for a few minutes and try to get a feel for how the distances traveled between collisions with other particles are distributed. Make your best estimate of what percent of the time the particle travels less than 1/2 inch between collisions, the percent of the time the distance rounds off to 1 inch, the percent of the time the distance rounds to 2 inches, etc.. When the particle collides with a 'wall', it doesn't count as a collision and distance keeps accumulating until it collides with another particle.
o The simulation appears to be constantly resetting and I cant infer as much about this data as Id like, the red particle appears to move only ½ inch and hit a particle 65 percent of the time, 1 inch maybe 30 percent, and 2 inches at 5 percent.
Sketch a histogram of your estimates, and also document the distance on your monitor between the 'walls' that confine the particles.
Now take some data.
Using the Pause/Break key on your computer, stop and start the particle motion as required in order to observe the distances traveled by the 'red' particle (the computer will stop when the key is depressed, and can be restarted using the 'Enter' key). Use a ruler to measure distances traveled. Don't leave any distances out, because this would bias the sample. Observe at least 100 distances.
Describe how you obtained your data and report your data as a frequency distribution (i.e., the number of observations for which the distance rounded to 0, 1, 2, 3, ..., inches).
Sketch a histogram of your results.
Sketch the histogram you would expect from a large number of observations.
Describe your histograms, and how they compare with your previous predictions.
o I was able to infer very little from this observation, but what I was able to see seems to support my previous predictions.
Experiment kinmodel_03: Equipartition of energy and the direction of disorder to (increasing or decreasing)
Observe the first several seconds of the simulation at the 'slow' default speed. You will see how the particles initially are all moving in or very close to the x direction, with little or no y component. Note the x and y kinetic energies, displayed near the top of the screen.
Observe what happens to the directions of motion of the particles as they start colliding.
o The move in very different directions, some vertical, horizontal, and diagonally.
Observe what happens to the x and y kinetic energies.
o The begin to fluctuate more, initially there was more energy in the x direction, when they start colliding we see more y energy.
Is the system more organized at the beginning of the simulation or after a couple of minutes?
o The system is more organized at the beginning
If the x and y kinetic energies were averaged for 100 years, starting a few minutes after the simulation began, which do you think would be greater?
o There seems to be more energy consistently in the x direction
Run the simulation in this manner several times, and each time determine how long it takes before the total y kinetic energy is first greater than the total x kinetic energy. Report your results.
-took about 4-5 seconds on slow for the y values to become greater.
Now take some data:
Running at the fastest default speed, stop the simulation with the pause/break key every few seconds, keeping your eyes closed for at least 2 seconds before stopping the motion.
Write down the x and y kinetic energies each time.
Do this at least 30 times.
Find the average of all your x and all your y kinetic energies.
Do you believe the difference in the averages is significant, in that the direction that has the higher average will always tend to have the higher average every time the simulation is run?
o I believe it is entirely random how the particles react and in which direction they move after collision. It at one point could have more y energy, more x energy, or an equal amount of both.
Experiment kinmodel_04: The improbability of all particles being segregated on one side of the viewing area (order vs. disorder)
Any selected region of the screen can be selected for viewing by masking the rest of the screen. The viewer can estimate the probability of this region being vacated within an hour, within a day, within a year, ..., within the age of the universe. Results will differ with the size of the region, the number of particles and the speed of the simulation.
Cut out a 1-inch square and watch the simulation for 2 minutes on the middle default speed. Observe how many times the square becomes 'empty' of particles. Estimate what percent of the time this square is empty.
Enlarge the square to a 1-inch by 2-inch rectangle and repeat.
Enlarge to a 2-inch by 2-inch square and repeat.
Enlarge this square to a 2-inch by 4-inch rectangle and repeat.
Enlarge to a 4-inch by 4-inch square and repeat.
Mask all but 1/4 of the screen and repeat.
How long do you think it would take, on the average, for 1/4 of the screen to become completely empty of particles?
How long do you think it would take, on the average, for 1/2 of the screen to become completely empty of particles?
A typical closet is about 100 million times as far across as the distance represented by the screen. Ignoring for the moment that the closet is three-dimensional and hence contains many more air molecules than would be represented by a 2-dimensional simulation, how long do you think you would have to wait for all the molecules to move to one side of the closet?
- The larger the square becomes the less likely an occurrence that all the particles will not be in that portion of the square. I wasnt sure what to use since I couldnt find anything transparent enough that I could hold to the screen and still see the particles. But a smaller section of square would occasionally be empty of particles, and as the section widened, it became less and less likely that the larger area would be free of particles. Im having a very hard time grasping the nature of the program, it could take 2s for the screen to be empty, or it could take 2 million years, it all appears to be entirely at random.
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One example of a line of reasoning that could lead to a reasonable estimate:
Let's say you mask all the screen except for a 2 x 2 square. You randomly stop the program 100 times, and observe that on 2 of the 100 times, that square is empty. So you estimate that the square is empty 2% of the time. You could stop the program 1000 times and see if the 2% estimate holds up, but that isn't necessary for a rough ballpark estimate.
Now let's say that your screen has dimensions 8 x 16, meaning that it contains sixteen 2 x 2 squares on each side.
To have all the particles on one side of the screen, all 16 of the 2 x 2 squares on the other side would have to be empty.
Now the probability that the first of the 16 squares is empty is .02. If it's not empty, then that side of the screen isn't empty. If it is, then the second of the 16 squares must also be empty. This will occur with probability .02.
So 2% of the time the first square will be empty, and when it is, 2% of the time the second square will be empty. So the probability that the first two squares will be empty is 2% of 2%, or .02 * .02.
Of course the third square must also be empty. The probability that this occurs when the first two are empty is .02 * .02 * .02, which we would write more compactly as .02^3.
This goes on for awhile, since there are 16 squares that all have to be empty. If we follow the reasoning all the way to the end, we see that the probability that all 16 squares on one side of the screen are empty is .02^16.
.02^16 is very rougly .00000000001, or 1 * 10^-11.
If there are 100 screens per second (there aren't that many, but let's be generous), then we would it to take about 1 * 10^9 seconds for half the screen to be empty. That's about 30 years.
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Experiment kinmodel_05: The probability that a particle's speed will occur in a given range
The default settings will not work with this experiment. This time when you run the program you need to choose to customize the settings. For everything but the numbers of different particles and their masses, and the 'yellow' marker, you may use the defaults.
For the number and masses of particles:
When asked for the number of particles of type 1, enter 28. When asked for the mass of this type give 1.
When asked for the number of particles of type 2, enter 1. When asked for the mass of this type give 10.
When asked for the number of particles of type 3, enter 1. When asked for the mass of this type give 1.
Regarding the 'yellow' marker:
You will choose the minimum and maximum speeds which will result in the particle being 'painted' yellow. This will allow you to observe the proportions of the particles in different velocity ranges.
If you wish you may also adjust the speed factor, which has default value 3. If you want the simulation to slow down to 1/3 the pace, you can enter 1 for the speed factor. If you want the simulation to go as fast as practical for the other default setting, you could use a speed factor up to 5. Only the pace of the simulation is affected by the speed factor; the speeds displayed on the screen are not affected.
Now try to observe the numbers of particles in various ranges:
Run the simulation and use a 'yellow' range of 3 to 6 and attempt to observe the proportion of the particles falling within this range. You will be able to get a fairly good idea of the proportion, but it will be hard to get a really good estimate unless you repeatedly pause the program and count the 'yellow' particles.
Run the simulation using a 'yellow' range of 4 to 4, which will give mark only particles whose velocity is 4. Determine to reasonable accuracy the average percent of particles with this velocity.
Repeat for velocities 0, 1, 2, 3, 5, 6, 7, 8, 9 and 10.
What are the percentages corresponding to each of these velocities?
What therefore do you think is the average particle velocity?
Experiment kinmodel_06: The connection between relative particle mass and average speed; equality of average kinetic energies
Using default settings, answer the following:
What percent of the time is the blue particle at each of the velocities 0, 1, 2, and 3?
What therefore do you think is the average velocity of the blue particle?
The blue particle is 10 times more massive than the other particles. How do you think its average KE therefore compares with the average KE of the other particles?
Experiment kinmodel_07: The development of empirical frequency vs. speed and frequency vs. energy histograms (more about order vs. disorder, with statistical order emerging from the disordered system)
The frequency vs. speed, frequency vs. squart root of energy, and frequency vs. energy histograms (it is left up to the student to determine which is which) are normalized to have a consistent total area. These distributions develop over time, eventually reaching a smooth distribution analogous to the Maxwell-Boltzmann distribution. This development occurs much more quickly if the settings are customized to encourage a maximal number of collisions.
Experiment kinmodel_08: Images of 2-dimensional collisions
It is easy to customize the settings to obtain two large relatively slow particles. Any student who has watched air hockey pucks or billiard balls colliding will recognize the validity of the simulation.
If the particles leave 'tracks' then a 'snapshot' in which a single collision between the particles occurs will provide data sufficient to validate conservation of momentum.
Customized settings
The following parameters can be controlled by electing to customize settings:
The number of particles (default setting is 30, maximum is 1000, which shouldn't be much of a restriction in the near future of PC's).
The number of different particle types (more than 9 different particle types is not recommended because of restricted number of colors).
The speed factor that determines how fast the particles move across the screen. If the speed factor is too great, particles may occasionally (or frequently, depending on how great) miss collisions. This is not a big problem unless data is being taken that assumes no 'misses'.
The radius of a particle (default radius is 1% the width of the square viewing area).
The proximity of the centers of the particles within which collision will occur (default is 5 particle radii). A greater value here will result in more collisions, other parameters being equal.
The minimum and maximum speeds defining a speed 'window'. Any particle whose speed is in this 'window' will be colored bright yellow. This range of speeds will be indicated by a yellow rectangle on one of the graphs.
Whether all the particles leave 'tracks' or not. The last two particles usually leave 'tracks'.
The number of iterations before the screen is cleared and the various graphs are updated. An iteration consists of the calculation and display of the position of every particle. A fairly small number allows the viewer to observe the evolution of the graphs, while a somewhat greater number permits observation of a significant number and variety of particle 'tracks'. If the number is too great the particle 'tracks' will be obscured.
The last two particles specified will have velocities indicated onscreen; the last of these particles will be sampled to obtain the velocity distribution shown at the right of the screen.
'Research' questions
For which particle speeds is the time between collisions likely to be greatest, and for which will it be least?
Initial particle speeds are uniformly distributed. After a short time a specific nonuniform distribution of speeds takes over. How long does it take before the contribution of the initial uniform distribution to the graphs and histograms displayed on the screen become indistinguishable? How will the shape of the graph differ from the ideal distribution during the transition?
For the default settings, what is the 'peak' particle energy? What is the 'peak' velocity of the sampled particle?
A narrower speed range near the peak of the speed distribution can result in more instances of 'yellow' particles than a wider speed range away from the peak. At each possible integer speed v, it is possible to define a speed range (v0, vf) with v at the midpoint of that range, such that the average number of 'yellow' particles will be the same as for the 'unit' range around the peak of the distribution. The 'unit' range is a velocity range of width 1 unit centered at the 'peak' velocity.
What does it take to get a massive molecule surrounded by low-mass particles moving fast?
Does the presence of an even more massive particle give a medium-mass particle, surrounded by a greater number of low-mass particles, an advantage in achieving greater speeds? Does the presence of a more massive particle affect the energy distribution of the medium-mass particle?
At an advanced level: Derive Maxwell-Boltzmann distribution in 2 dimensions and compare the the empirical distribution.
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It appears that in revising the Assignments page for the recent review, some of the instructions for this experiment were missing, specifically the one that told you to do the preliminary observations, then ask me which part of the experiment was actually assigned.
The statement
'Before reading further email your instructor with your best answers to these questions. There are two good reasons for not reading ahead: If you get your answers by reading ahead your instructor will be able to tell, and if you read ahead you won't learn as much.'
was included in the experiment, but it would be easy to miss that.
In any case you did way more work here than was intended for your course. A lot of the things you did were more related to the University Physics course.
Of course you'll get generous additional credit for this.
In any case, check my notes for more insight and information.
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