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A different approach to introducing statistical mechanics

 

作者: Thomas A. Moore,   Daniel V. Schroeder,  

 

期刊: American Journal of Physics  (AIP Available online 1997)
卷期: Volume 65, issue 1  

页码: 26-36

 

ISSN:0002-9505

 

年代: 1997

 

DOI:10.1119/1.18490

 

出版商: American Association of Physics Teachers

 

关键词: 05.20;05.70;01.50.H

 

数据来源: AIP

 

摘要:

The basic notions of statistical mechanics (microstates, multiplicities) are quite simple, but understanding how the second law arises from these ideas requires working with cumbersomely large numbers. To avoid getting bogged down in mathematics, one can compute multiplicities numerically for a simple model system such as an Einstein solid—a collection of identical quantum harmonic oscillators. A computer spreadsheet program or comparable software can compute the required combinatoric functions for systems containing a few hundred oscillators and units of energy. When two such systems can exchange energy, one immediately sees that some configurations are overwhelmingly more probable than others. Graphs of entropy vs. energy for the two systems can be used to motivate the theoretical definition of temperature,T=(∂S/∂U)−1, thus bridging the gap between the classical and statistical approaches to entropy. Further spreadsheet exercises can be used to compute the heat capacity of an Einstein solid, study the Boltzmann distribution, and explore the properties of a two-state paramagnetic system.

 

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