GASLAB: ADIABATIC PISTON WHAT IS IT? ----------- This model is part of the GasLab
collection of models. See Gas-in-a-Box for an introduction to the GasLab
collection. This model simulates the behavior of gas molecules in a box with a
moveable piston. The piston has weights on it which push it down, and the gas
particles push upward against the piston.   The system is called "adiabatic"
because no heat energy (such as heat loss through the walls of the box) is added
to or removed from the system. Molecules are modeled as single particles, all
with the same mass and initial velocity. Collisions between molecules and against
the walls are elastic. The particles are colored according to speed -- blue for
slow, green for medium, and red for high speeds. Each particle bounces off the
sides and the bottom of the box without changing speed.  When it hits the piston,
however, its speed does change.  If the piston is moving upward at that moment,
the particle bounces off at a slightly smaller speed.  If the piston is moving
downward, it gives the particle a kick and the particle speeds up.  This is the
process by which the energy of the gas is changed by the motion of the piston.
This piston also changes speed with each collision.  The change is not large,
because the piston is much heavier than each particle; but the accumulated effect
of many particle collisions is enough to hold the piston up. Pressure is
calculated by adding up the momentum transferred to the walls of the box (but not
the piston) by the molecules when they bounce off.  This is averaged over all of
the walls to give the pressure.

HOW TO USE IT ------------- Initial settings: INITSPEED    initial speed of the
molecules. INITMASS   initial mass of the molecules. NUMBER     number of
molecules. BOX-HEIGHT height of the container. BOX-WIDTH  width of the container.
PISTON-MASS mass of the piston, in the same "units" as the molecular mass.

The model is unreliable at the boundaries. For optimum results, make sure the
settings are such that the piston doesn't get too close to the bottom or top of
the box.

Monitors: AVG-ENERGY: the average kinetic energy per molecule of the gas
PISTON-ENERGY: the sum of potential and kinetic energy of the piston.  The
piston's potential energy would be zero if it were at the bottom of the chamber. 
This energy is divided by the number of molecules, so that it's the piston energy
per molecule. TOTAL-ENERGY:  the sum of avg-energy and piston-energy. PISTON-VEL:
the speed of the piston (up is positive). PISTON-HEIGHT: the piston's height
above the bottom of the chamber. AVG-PRESSURE: average pressure of the gas.

The SETUP button will set the initial conditions.  The GO button will run the

Plotwindows: PISTON HEIGHT (1), measured up from the bottom of the box; PRESSURE
(2); ENERGY OF MOLECULES, PISTON, AND TOTAL ENERGY (3), in terms of energy per
particle.  This piston's energy is both kinetic (motion) and potential (it would
be zero at the bottom of the box).

RUNNING the MODEL -----------------

THINGS TO NOTICE ----------------

Watch all the graphs and notice how they change in relation to each other. You
can click on points in the graphs to display their coordinates.

Does the piston reach an equilibrium position?  What is the pattern of its motion
before that?  Why doesn't it keep oscillating, like a bouncing ball, if all of
the collisions are elastic?

Would you expect that the pressure would settle at a stable value?  What would
determine it?

The energy of the gas changes as the piston moves up and down.  How are the two
related?   Where does the energy come from and where does it go?

Can you infer what is happening to the temperature of the gas as the piston

Explain in physical terms and in terms of the model's rules how the piston heats
up the gas by pushing downward and cools it down when moving upward.

A familiar physical situation which is like this model is a bicycle pump.  Can
you think of others?  Does the model's behavior match your experience?

THINGS TO TRY -------------

Change the initial particle mass and particle speed.  How do these variables
affect the piston's motion and its equilibrium position?  Adjust the piston's
mass to keep it inside the box.

Change the piston mass, leaving the gas alone.  What happens to all of the
volume, pressure, and energy?  Note: if you do this while the model is running,
the piston energy changes suddenly.  Why is this?

In this simulation, the piston and the particles exchange energy on every
collision.  The model treats the wall collisions differently. Is this legitimate?
 How is a piston different from a wall?

In this adiabatic system, neither pressure, volume, nor temperature are constant,
so pressure and volume are not simply inversely proportional. In fact it turns
out that for two different states,

(P'/P) = (V/V')^gamma,

where gamma depends on the number of degrees of freedom of the molecules.   In
this two-dimensional case, gamma = 2.  Confirm that this is roughly true by
changing piston-mass (hence pressure) and noticing its effect on piston height
(hence volume).

EXTENDING THE MODEL -------------------

Add a heater in the box that changes the temperature of the gas.  What would
happen if the gas were heated and nothing else were changed?

Combine this with the "Two Gas" model such that there are gases pushing on both
sides of a piston, instead of gravity against a single gas.

Give the piston the ability to store thermal energy, so that it heats up instead
of moving when the particles hit it.

The total energy of the system is still not stable over a large number of
iterations.  How could it be improved?

STARLOGOT FEATURES ------------------

REFERENCES ----------- See  U. Wilensky, E. Hazzard, and R. Froemke, "GasLab --
an Extensible Modeling Toolkit for Exploring Statistical Mechanics", in the
Proceedings of Eurologo 99,  Sofia, August 1999.

RELATED MODELS -------------- Look at the other GasLab models, especially
Isothermal Piston.