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Confronting Conceptual Challenges in Thermodynamics by Use of Self-Generated Analogies

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Abstract

Use of self-generated analogies has been proposed as a method for students to learn about a new subject by reference to what they previously know, in line with a constructivist perspective on learning and a resource perspective on conceptual change. We report on a group exercise on using completion problems in combination with self-generated analogies to make sense of two thermodynamic processes. The participants (N = 8) were preservice physics teacher students at the fourth year of the teacher education program. The students experienced challenges in accounting for the constant entropy in reversible, adiabatic expansion of an ideal gas and the constant temperature in free, adiabatic expansion of an ideal gas. These challenges were found to be grounded in the students’ intuitive understanding of the phenomena. In order to come to terms with the constant entropy in the first process, the students developed idiosyncratic explanations, but these could by properly adjusted given suitable scaffolding. In contrast, the students by themselves managed to make sense of the constant temperature in free expansion, by use of microscopic explanatory models. As a conclusion, self-generated analogies were found to provide a useful approach to identifying challenges to understanding among students, but also for the students to come to terms with these challenges. The results are discussed against a background of different perspectives on the issue of conceptual change in science education.

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Notes

  1. See for example the debate initiated by Anderson et al. (1996) and Greeno (1997) in Educational Researcher.

  2. For a brief introduction of key thermodynamics concepts, please see “Appendix”.

  3. The rationale for this conclusion is that within the caloric theory of heat, heat in the form of caloric is assumed to be a self-repulsive fluid attracted to matter, implying a dependence on the density of the matter.

  4. The temperature decreases in free expansion of real gases, however, where attraction between particles cannot be neglected, since energy is required to separate the particles in the expansion. See e.g. Cheng (2006) for a quantitative treatment of the cooling of a van der Waals gas in free expansion.

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Acknowledgments

We would like to thank the participating teacher students and our colleagues within the Swedish National Graduate School in Science and Technology Education, in particular Konrad Schönborn, Roland Kjellander and Astrid Bulte for insightful suggestions at different stages of the study. We are also grateful for having had the possibility to discuss our ideas at the third Conceptual Change Modeling workshop, arranged by Ismo Koponen at the University of Helsinki. Finally, constructive suggestions from four anonymous reviewers helped strengthening the manuscript.

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  1. Swedish National Graduate School in Science and Technology Education, Linköping University, 60174, Norrköping, Sweden

    Jesper Haglund & Fredrik Jeppsson

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Correspondence to Jesper Haglund.

Appendix: Key Thermodynamics Concepts

Appendix: Key Thermodynamics Concepts

Introductory thermodynamics typically involves the study of different thermodynamic processes, where the state of a system, such as a box containing gas, changes. The system can exchange energy with the surrounding environment through the mechanisms of work, W, and heat, Q. Work refers to changes in macroscopic variables of the system, such as its volume, V, or amount of particles, N, and heat is typically due to a difference in temperature, T, between the system and its environment. The first law of thermodynamics may be stated in terms of: ΔU = W + Q, i.e. that the change of internal energy of a system is equal to the work and heat added to it.

Different thermodynamic processes are characterised by the mechanisms of energy exchange and changes to involved physical quantities. For instance, the present study focuses on the processes of reversible, adiabatic expansion and free, adiabatic expansion of an ideal gas. An ideal gas is assumed to consist of randomly-moving particles that interact exclusively through exchange of energy during collisions and occupy a negligible part of the system’s volume. Reversible processes are processes that can run backwards in time, while free expansion refers to allowing the gas to expand into a part of the volume that previously was inaccessible, and adiabatic means that no heat is exchanged with the environment. Equations of state, such as the ideal-gas law: pV = nRT, provide important information on the relation between the involved quantities, here, in addition to the temperature, the pressure, p, the volume, V, and the amount of substance, n, while R is the universal gas constant.

Entropy, S, is an extensive—i.e. depending on the size of a system—physical quantity, which was introduced as a macroscopic variable, through the relation: dS ≥ dQ/T, by Clausius, in order to account for equivalence values of work and heat in heat engines. Subsequently, Boltzmann gave entropy a microscopic interpretation in relation to the number of ways an isolated system’s energy and its constituent particles can be distributed, i.e. the number of microstates, Ω, according to: \( S = k_{B} \ln \Upomega \), where k B is Boltzmann’s constant. Subsequently, Gibbs introduced a microscopic interpretation of entropy in relation to the probability p i of the system being in microstate i: \( S = - k_{B} \sum\nolimits_{i}^{{}} {p_{i} \ln p_{i} } \), which could be generalised to systems that are allowed to exchange energy and particles with their surroundings.

Temperature, in turn, is an intensive quantity; if a system doubles in size, all other things equal, its temperature remains the same. Within the field of the kinetic theory of gases, a system’s temperature is often introduced as proportional to the average kinetic energy of its constituent particles. However, a more foundational definition depends on the system’s entropy:

$$ \frac{1}{T} = \left( {\frac{\partial S}{\partial U}} \right)_{V,N},$$

i.e. the temperature is the inverse of the partial derivative of the entropy with regards to the internal energy, given constant volume V and number of particles N.

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Haglund, J., Jeppsson, F. Confronting Conceptual Challenges in Thermodynamics by Use of Self-Generated Analogies. Sci & Educ 23, 1505–1529 (2014). https://doi.org/10.1007/s11191-013-9630-5

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