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.
Skip Nav Destination
Article navigation
January 1997
Papers|
January 01 1997
A different approach to introducing statistical mechanics
Thomas A. Moore;
Thomas A. Moore
Department of Physics and Astronomy, Pomona College, Claremont, California 91711
Search for other works by this author on:
Daniel V. Schroeder
Daniel V. Schroeder
Department of Physics, Weber State University, Ogden, Utah 84408-2508
Search for other works by this author on:
Am. J. Phys. 65, 26–36 (1997)
Article history
Received:
June 26 1996
Accepted:
August 21 1996
Citation
Thomas A. Moore, Daniel V. Schroeder; A different approach to introducing statistical mechanics. Am. J. Phys. 1 January 1997; 65 (1): 26–36. https://doi.org/10.1119/1.18490
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
All objects and some questions
Charles H. Lineweaver, Vihan M. Patel
Exact solutions for the inverse problem of the time-independent Schrödinger equation
Bhavika Bhalgamiya, Mark A. Novotny
In this issue: January 2025
Joanna Behrman, Pierre-François Cohadon, et al.
Introductory learning of quantum probability and quantum spin with physical models and observations
Anastasia Lonshakova, Kyla Adams, et al.
Erratum: “All objects and some questions” [Am. J. Phys. 91, 819–825 (2023)]
Charles H. Lineweaver, Vihan M. Patel
Quantum information science and technology high school outreach: Conceptual progression for introducing principles and programming skills
Dominik Schneble, Tzu-Chieh Wei, et al.
Related Content
Number of microstates and configurational entropy for steady-state two-phase flows in pore networks
AIP Conference Proceedings (January 2015)
The evolution of radiation toward thermal equilibrium: A soluble model that illustrates the foundations of statistical mechanics
American Journal of Physics (March 2004)
A statistical development of entropy for the introductory physics course
American Journal of Physics (February 2002)
A Simple Statistical Thermodynamics Experiment
The Physics Teacher (March 2010)
Enhancing the understanding of entropy through computation
Am. J. Phys. (November 2011)