[Its.an.education.project] An example on statistical dynamics on XO

[Yoshiki Ohshima]

  Hello,

  We probably talk about what and how to teach in a bit more concrete
way.  I'll do a part by explaining an example in Etoys here.  If we
have thousands of similar examples, that would be pretty cool.

  So, here it goes:

  Open Etoys, click on Gallery of Projects cloud.  At the bottom row
and third from left (about right under "particles" in "You can play
with thousands of particles:"), there is an example of ideal gas
simulation.

  There are many red dots (molecule's turtleCount shows "2000" and
that is the number) moving in the confinement.  Each of molecules have
variables called "x", "y", "heading" and "speed".  The bottom, left,
and right walls of the space are solid and don't move, but the top
wall moves.

  At every step "molecule oneStep" script is executed.  In the script,
the first line makes all molecules moves their own heading direction
by their own "speed".  The next beige big tile represents a Test
statement and it is executed for all mocules.  If a molecules y
coordinate is less than a variable called "KedamaWorld's ceiling pos",
the "Yes" part is executed (meaning the molecule hits the green top
wall called "ceiling").  In the Yes part, the molecules makes 180
degrees turn (so there is some simplification done), adjust the y
coordinate so that it stays in the confinement, and increase another
variable called KedamaWorld's ceilingSpeed by the value of speed.

After doing the Test statement for all molecules, the ceiling pos
accumulated the "hits" in that step.  After the test, we offset the
accumulated value with a value called gravity, and and then make it
small enough by multiplying it by 0.01 (this kind of arbitrary
constant is always trouble to some students), and decide the new
position of the ceiling (the green line).

  Here, you can experiment various stuff:

  1) If you type "1000" over "2000" of "mulecules turtleCount", and
     hit the enter key, the number of molecules is reduced, and soon
     the volume settled at about the half of the original.
  2) You can then decrease the gravitiy value from 24.0 to 12 and the
     volume will be back to about the same as original.
  3) Click on the red square "tab" on the right edge, and drag out the
     assignment arrow for "molecule's speed" and drop it onto the
     desktop.  You should see a new script.  In the script and the
     right hand side of the assignment, type "1.4" in place of the
     number there.  Then, click on the yellow exclamation button in
     the script to execute it.  Now the volume should be twice as
     original.
  4) You can change the running script as much as you like.  Just
     break it to understand it^^;

So, what it is explaining?  It is trying to explain that

  PV = nRT

makes sense.  In science, you don't want to tell students to believe
what you teach.  Atoms and molecules are not visible, but if you say
"these are not visible, but they exist.  Believe.", that is rather
close to religion.  One thing we could do is to have students build a
simulation based on the model.  At the micro-level (if the student
relate himself to a molecule), the script should be almost simple
enough to high-school students, at lease who are familiar with Etoys
("own" variables and global variables need to be explained, though).
So, instead of showing the completed project, the students should
built their own.

  What the number of turtles mean?  It is "n" in the equation.  No
matter how many molecules we have, the interaction between them are
neligible (here is another simplification; the simulation can be
simplified but it *must* be honest).  The student should know that mv
= m'v' when two masses hit each other; the increase-by statement for
ceilingSpeed should make sense to them, too.

  And, the next three lines should be obvious to the students who did
the gravity project in the Powerful Ideas book.  To simulate the free
falling body in repeating script, you make a variable that holds speed
of body (in this case, the ceilingSpeed), change it with a constant
value and add it to the position.  The only difference is that it is
offset by the moving molecules.

  It is interesting to see that the gravity constant behaves as the
pressure "P".  Also, the "speed" is propotional to the square root of
temperature "T".  In the dimension analysis, that makes sense, and in
the script, the number of molecules that hits the ceiling in a given
step is propotional to the speed, and the momentum exchanged by a hit
is proportional to the speed.  This would be a nice a-ha moment even
for undergrads in phyisics major.

  Finally, you need to have some fun, right?  reset the gravity to the
original value (24), and set the molecules count to 500 (a quarter of
the original).  The volume is now a quarter of original.  There, you
can set the number of molecules to 2000 again.  It means that you cram
the 4 times more molecules in a space, and it results in an explosion!

  All in all, this project should be explainable to high school
students, and they can experiment their own ideas.

  Any feedback and comments are welcome!  And I hope that the
volunteers make such kind of examples (in any system they like) and
accessible to kids and teachers.

-- Yoshiki