The disorder metaphor for entropy – friend or foe?
Jesper Haglund
Department of Physics and Astronomy, Uppsala University, Sweden
GIREP 2017, Dublin
Entropy as disorder
• Entropy as disorder is a common metaphor in teaching
– Often elaborated as the messy room analogy
• Originates from descriptions of molecular interaction in the
development of statistical mechanics (e.g. von Helmholtz, 1883, Boltzmann, 1896)
• Captures certain aspects of entropy:
– Entropy of mixing
– Entropy increase during phase changes: solid -> liquid -> gas – Helps make endothermic reactions plausible
• Then again, all metaphors “break down” at some point (Glynn,
1989)
Criticism of the disorder metaphor
• “ A most inessential visualization which has probably done much more harm than good” (Dingle, 1959)
• “A cracked crutch” (Lambert, 2002)
• “Ultimately, however, it is the pervasive yet inappropriate use of the disorder metaphor for entropy that has
prevented more widespread incorporation of the second
law into student thinking” (Wei et al., 2014)
Drawbacks with the disorder metaphor
• Disorder is vague (Styer, 2000)
• Emphasises spatial configuration, but neglects energy (Lambert, 2002)
• The messy room analogy only gives a snap-shot view, and neglects multiplicity of microstates (Styer, 2000)
• Increase in entropy may be accompanied by increase in visual order, e.g. liquid crystals (Lambert, 2002)
• Does not convey the extensive character of entropy (Lambert, 2002)
• Leads students to intuit that adiabatic, reversible expansion of an ideal gas result in an entropy increase (Brosseau & Viard, 1992;
Haglund & Jeppsson, 2012)
In defense of the metaphor
• “Disorder is a metaphor for entropy, not a definition for entropy. Metaphors are valuable only when they are not identical in all respects to their targets. /…/ The metaphor of disorder for entropy is valuable and thus imperfect” (Styer 2008).
• “…our goal is to refine student ideas about disorder and build on them to develop a deeper and more
coherent framework, one that increases the likelihood that students will use the metaphor productively”
(Geller et al., 2014, building on the resources
framework, Hammer, 2000).
Questionnaire study
• Questionnaire filled out by second-year university students (N = 73) before and after a course in chemical thermodynamics (Haglund, Andersson, & Elmgren, 2015)
• Open-ended questionnaire items:
– Which are the most important other scientific concepts that relate to entropy, according to you?
– What is entropy? Give a brief explanation that reflects your understanding.
– (After the course:) How has the course influenced your understanding of the entropy concept? Please give concrete examples.
• Data analysis
– Categorisation of answers against background of previous research
Explanations of entropy
• Majority of students relate entropy to disorder (67% before the course / 77% after). Some of the students come to
problematise their previous understanding:
– “In the beginning of the course I saw entropy as ‘disorder’. Now I have a more nuanced view on entropy [in terms of the possibility for molecules to move and spread out].”
• Microscopic interpretations (38% / 68%)
– “Entropy is the molecules’ possibility to move freely. E.g. gas has high
entropy, solids have lower.”
Changes in students’ explanations
• Progress towards microscopic and more complex explanations has a systematic pattern
– Different levels of chemistry experience at different engineering programmes
• Disorder as a productive stepping stone?
No correlations with exam results
• Correlations with exam results were calculated for students who filled in both questionnaires and wrote the exam after the course
• No significant correlations were established between:
– Exam results, and…
– …concepts related to entropy, or categories of explanations, before or after the course
• “Entropy as disorder” was not entirely destructive, bot not very
useful, either…
Pair-interview study
• Interviews with pairs of students (N = 6) one year after the course in chemical thermodynamics (Haglund, Andersson, & Elmgren, 2016)
• Video/audio recording
Pair-interview study tasks
1. Does it sound reasonable? A system at higher temperature has…:
– …higher entropy, or… more entropy?
2. Rank the following notions (heat, internal energy, disorder, 2 nd law of thermodynamics, freedom, Gibbs free energy, etc.)
– By how closely they are related to entropy – By how scientific they are
– By how useful they are for explaining what entropy is
3. Problem solving
– Reflecting on given exam question relating to entropy change in chemical reaction – What happens to the entropy in reversible, adiabatic expansion of an ideal gas?
4. Reflect on how your learning about entropy has evolved
Pair-interview study – results
• “More entropy” sounds odd…
– …but not quite as odd as “more temperature”
• Substance metaphor use is not consistent in relation to intensive/extensive quantities. Consider:
– He has a lot of pressure on his shoulders – * There is a lot of heat capacity in the system
• Ranking pattern of disorder:
• Intuit entropy increase at adiabatic, reversible expansion
• The disorder metaphor applicable “in 2000 cases against one”
Related Scientific Useful
disorder … disorder
… … …
… disorder …
How to address the disorder metaphor?
• Glynn’s “Teaching With Analogies” approach (1989):
– Introduce the target concept – Recall the analogue concept
– Identify similar features of the concepts – Map similar features
– Draw conclusions about the concepts
– Indicate where the analogy breaks down
How to address the disorder metaphor?
• Incorporate energy aspect
– ‘Disco disorder’ vs. ‘desktop disorder’ (Pflug, 1983) – Adiabatic, reversible expansion
• Give examples of analogy break-down
– Liquid crystals as books in box
• Multiple complementary analogies/metaphors (Spiro, et al., 1989)
– Spreading (Leff, 1996; Lambert, 2002)
– Entropy as everyday idea of heat, extensive substance-like entity (Herrmann, 2000; Fuchs, 2010; contributions at this seminar by Fuchs, Dumont, and Corni)
• The disorder metaphor can give students an early flavour of what entropy means (Haglund, 2017)
– “There is usually nothing wrong with referring to entropy as a measure of
disorder. The phrase however, does not take one very far. To gain precision and something quantitative, one needs to connect disorder with ‘absence of
correlations’ and then with multiplicity” (Baierlein, 1994).
Thanks for listening!
jesper.haglund@physics.uu.se
References
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