The Boltzmann Distribution From A Microcanonical Ensemble Model allows students and instructors to explore why the Boltzmann distribution has its characteristic exponential shape.  In this model, particles have only one degree of freedom–the energy to move in one dimension. Further, the density of accessible states is chosen to be uniform –i.e. each state is equally probable.  Starting with a system of N=2 particles, you are able to generate simple empirical results for the distribution of energies among the individual particles.  Then you can observe how this distribution changes with increasing N, gradually approaching the Boltzmann distribution.  

The Boltzmann Distribution From A Microcanonical Ensemble Model was developed using the Easy Java Simulations (EJS) modeling tool.  It is distributed as a ready-to-run (compiled) Java archive.   Double clicking the ejs_fmu_BoltzmannDistribution_PartitioningEnergy.jar file will run the program if Java is installed.  You can modify this simulation if you have EJS installed by right-clicking within the map and selecting "Open Ejs Model" from the pop-up menu item.

Please note that this resource requires at least version 1.5 of Java.