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ERIC Number: EJ1028599
Record Type: Journal
Publication Date: 2013-Dec
Pages: 6
Abstractor: As Provided
Reference Count: N/A
ISSN: ISSN-0021-9584
Dependence of the Population on the Temperature in the Boltzmann Distribution: A Simple Relation Involving the Average Energy
Angeli, Celestino; Cimiraglia, Renzo; Dallo, Federico; Guareschi, Riccardo; Tenti, Lorenzo
Journal of Chemical Education, v90 n12 p1639-1644 Dec 2013
The dependence on the temperature of the population of the "i"th state, "P"[subscript "i"], in the Boltzmann distribution is analyzed by studying its derivative with respect to the temperature, "T." A simple expression is found, involving "P"[subscript "i"], the energy of the state, "E"[subscript "i"], and the average energy, <"E">. This relation is completely general (it has the same form in all the thermodynamic ensembles), and it has a relevant didactic content, given that it predicts the qualitative variation of "P"[subscript "i"] with "T" even in complex systems. The derivation of this relation, the discussion of its properties, and its application to simple problems is appropriate for a statistical thermodynamics course in the chemistry curriculum.
Division of Chemical Education, Inc and ACS Publications Division of the American Chemical Society. 1155 Sixteenth Street NW, Washington, DC 20036. Tel: 800-227-5558; Tel: 202-872-4600; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A