Life science students develop a variety of resources for thinking about entropy and spontaneity in their biology, chemistry, and introductory physics courses. Helping students to develop a deeper and more coherent conceptual framework for organizing these varied ideas means attending carefully to the ways in which students interact with different disciplinary descriptions and to the ways in which these descriptions may be in tension. Canonical introductory physics treatments of the second law of thermodynamics, while useful in some contexts, may not be the most productive ones in authentic biological or chemical contexts. We draw on case-study interviews with introductory physics for life science students to argue that an approach to the second law of thermodynamics that emphasizes the interplay of energy and entropy in determining spontaneity (one that involves a central role for free energy) is one that draws on students' resources from biology and chemistry in particularly effective ways. We see the positioning of entropic arguments alongside energetic arguments in the determination of spontaneity as an important step toward making our life science students' biology, chemistry, and physics experiences more coherent.
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As noted earlier in the paper, it is a complicated business to determine the conditions under which oil and water spontaneously separate. Factors like the concentration and size of the oil molecules play a role in determining whether the oil will clump, as does the temperature at which the substances interact. Because the objective in our introductory physics course for life science students is not to explore in detail all the conditions under which oil and water might mix, but rather only to consider in a qualitative way the factors that contribute to the separation of oil and water under biologically relevant conditions when the separation is in fact spontaneous, we choose not to explore the dependence on oil concentration and size in any detail. Those dependences are discussed elsewhere (such as in Ref. 6).
