CHED 201 |
| The Boltzmann distribution gives the most probable way that a limited amount of energy distributes itself among the available energy states in a system of a large number (N) of molecules. The mathematical derivation of the Boltzmann distribution makes use of Stirling's approximation for N! which is only accurate for very large N. To test the results of the Boltzmann distribution on smaller model systems requires one to work in a regime wherein the assumptions of large populations are no longer valid and Stirling's approximation is less accurate. The distribution may be corrected for smaller populations by re-examining the assumptions involved in its derivation. This paper describes such corrections to the Boltzmann distribution for small populations and tests this corrected distribution with hypothetical systems. The results are useful for teaching the Boltzmann distribution to undergraduate students and may also have implications to understanding energy distributions in nano-scale systems. |
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General Posters
7:30 PM-9:30 PM, Sunday, March 25, 2007 Hyatt Regency Chicago -- Riverside Center, Poster
Division of Chemical Education |