Gas Energies Plotted

	Energy Equipartition Evolution of a 2D Gas
Please click here for a full discussion of this subject.
This animation shows the evolution of the energy distributions of two gases that initially do not have the Boltzmann .  

There are two types of atoms (colored red and blue).  These are positioned randomly inside a container and are given random energies up to their respective maximum energy, Emax. When the Start button is pushed these atoms take on their normal thermal velocities.  They then may undergo two atom collisions either with the opposite color or the same color or they undergo one particle collisions with  the walls of the container.  The wall collisions in this animation do not change the speed of the atoms.  The two atom collisions can result in an energy increase for one of the atoms and the same energy loss for the other atom.  As is clearly shown in the link above, the more energetic atoms always tend to give up energy to the less energetic atoms.  These energy exchanges result in two distinctive effects
1. The distribution of number of atoms, N(E), Vs E becomes the same for both atom types.  This is equivalent to saying that both types assume the same temperature even though their average initial energies were quite different.
2. The distribution function of N(E) is an exponential
N(E)=N0 exp(-E/dE)
where N0 is a normalizing constant and dE is the energy at the 1/e point of the distribution.  dE is equivalent of kT where k is the Boltzmann constant and T is the temperature in degrees Kelvin.

Before the Start button is pressed, the learner is shown the starting energy distributions which are random up to the chosen maximum energy values.

When the animation is started, the number of atoms Vs energy of both types of atoms are sorted into energy bins.  From these number values four plots are made. 
1. Histograms of the number of red atoms Vs Energy and the number of blue atoms Vs Energy. Since the total number of atoms per energy bin is small, it is to be expected that there will be a lot of random variation of the heights of the histogram columns.  Both red and blue histogram energy scales extend to three times the maximum initial larger energy of the atom types.

2. The data from the N Vs E energy bins are used to perform a least squares fit to an exponential curve. These curves are plotted as continuous curves with green denoting the red atom fit and purple denoting the blue atom fit.  Just above the curves, the values determined for dE as well as the correlation coefficient, R, for the fit are given.  After starting the animation, it will take some time for R to approach 1.0 since many collisions are required to establish equilibrium (i.e. to "thermalize" the two gases).

The learner may (within limits) use the Sliders to change the following variables:
1. Mass of red atoms
2. Mass of blue atoms
3. Initial maximum energy of red atoms 
4. Initial maximum energy of blue atoms 
5. Number of red atoms
6. Number of blue atoms

The program is set up so that if any of the above values are changed, the animation is stopped and the energy bins are emptied and a new initial distribution is randomly chosen. When the Start button is pressed the energies start again to evolve toward their new final distributions.
Energy Distribution Details
Sliders
Disc Radius Blue Radius Total Discs Starting energy