Summary and Activities

This model simulates an isolated system of 1000 distinguishable and non-interacting molecules modeled as quantum harmonic oscillators, inspired by the article "A Computer Problem in Statistical Thermodynamics", P. Schettler, J. Chem. Education, 51, 250 (1974). Through successive random molecular jumps between the energy levels of the oscillators, the entropy of the system tends to a maximum and Boltzmann's distribution is approached. That is, the system evolves to the equilibrium state accordingly the 2º Law of thermodynamics. The model can be used as a complemental tool for teaching thermodynamics and statistical mechanics at undregraduate level, requiring only a browser to be executed.

(Note: The mouse over an output label or button displays a tooltip). The following activities are suggested:

1) Play the simulation by increments of 2000 jumps, clicking the first button. The running entropy is calculated by successive increments of 2000 jumps and plotted every 50 jumps. Keep clicking a few times. The running entropy (left display, blue circles) is tending to the entropy maximum (red line). The running number of particles/level (right display, blue circles) is changing its initial gaussian form and tending to Boltzmann's distribution (red curve)

2) Play the simulation continuosly, clicking the second button: the running entropy fluctuates around the entropy maximum, and the running number of particles/level fluctuates around Boltzmann's distribution. The Deviation, sooner or latter, sets around +- 2

3) When the simulation is running it can be paused, clicking again the second button

4) Reset the simulation clicking the third button and repeat the process at your will