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Abstract Title: Conceptual Difficulties with Binomial Distributions in Statistical Physics
Abstract: As part of our continuing research on the teaching and learning of concepts in upper-division thermal physics at the University of Maine, we report on student responses to questions about binomial distributions and the changes in those distributions with an increasing number of trials (N).  We have administered questions before and after traditional instruction and guided-inquiry activities that probe understanding of multiplicities, probabilities, and their distributions over N, covering more than 6 orders of magnitude in N.  Preliminary results indicate some positive learning outcomes, along with some persistent problems; e.g., confusion over the dependence of macrostate probability on multiplicity, and whether the probability of a single (N/2) macrostate emerges at large N to dominate the distribution, or not.  Results are discussed in the context of the term "overwhelming probability," commonly used to describe the connections with equilibrium thermodynamic (very large N) systems.

Supported in part by NSF Grants #PHY-0406764, DRL-0633951 and DUE-0817282.
Abstract Type: Contributed Poster

Author/Organizer Information

Primary Contact: Donald B. Mountcastle
University of Maine
Department of Physics and Astronomy
5709 Bennett Hall
Orono, ME 04469-5709
Phone: 207-581-1039
Fax: 207-581-3410
and Co-Presenter(s)
John R. Thompson  and  Trevor I. Smith

University of Maine
Department of Physics and Astronomy
5709 Bennett Hall
Orono, Maine  04469-5709

phone: 207-581-1039
     fax: 207-581-3410