We report on students’ thinking regarding entropy in an introductory calculus-based physics course. We analyzed students’ responses to a variety of questions on entropy changes of an arbitrarily defined system and its surroundings. In four offerings of the same course we found that before instruction, no more than 6% of all students could give completely correct responses to relevant questions posed in both general and concrete contexts. Nearly two-thirds of the students showed clear evidence of conservation-type reasoning regarding entropy. These outcomes were little changed even after instruction. Targeted instruction that guided students to recognize that entropy is not a conserved quantity appears to yield improved performance on qualitative questions related to this concept.
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20.
For practical purposes and to facilitate analysis, we ordinarily specify a particular system along with a separate region or reservoir referred to as the surroundings; both this system and the surroundings are then isolated from the rest of the universe. See discussion of the “concrete-context” question in Sec. III C.
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The instructor for the course in which this question was first used employed the terminology “isolated system,” so the question was written to include that language in version A. Student understanding of this terminology was not a focus of our research. We also discovered that the distracters in version A might not have fully represented students’ thinking on this question, and so we created version B. See discussion in Sec. IV B 3.
23.
See EPAPS Document No. E-AJPIAS-77-013909 for appendices. Appendix I contains detailed responses to all questions in each course. This document can be reached via a direct link in the online article's HTML reference section or via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html).
24.
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25.
After instruction in Spring 2005, this overlap proportion was almost unchanged at 41%. After use of specially designed curricular materials, this overlap proportion increased sharply; see Sec. VI A.
26.
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27.
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Student responses are consistent with the most general form of the entropy inequality and might be considered to be partially correct. However, the questions explicitly referred to irreversible processes, or process that can actually occur, for which the total entropy always increases. The patterns of student responses we have reported appear to be independent of the specific terminology used in a particular question. That is, whether one or another term is used, the proportion of correct responses remains essentially unchanged.
32.
The complete data are provided in Appendix V on EPAPS. See Ref. 23.
33.
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38.
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41.
See Appendix XI on EPAPS. See Ref. 23.
42.
In contrast, we and others have found that students’ conceptual difficulties regarding processes that do not involve heat transfer, for example, the free expansion of a gas, persist to some extent. See Refs. 8 and 12.
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