Donald B. Mountcastle

Effects of cholesterol and temperature on the permeability of dimyristoylphosphatidylcholine bilayers near the chain melting phase transition.

The passive leakage of glucose across bilayers of dimyristoylphosphatidylcholine (DMPC), cholesterol (variable), and dicetyl phosphate (constant 5.9 mol%) has been measured as efflux over 30 min from multilamellar vesicles. Bilayer cholesterol was varied from 20 mol% to 40 mol%. Glucose permeation rates were measured from 10 degrees C to 36 degrees C, and showed a maximum in permeability at 24 degrees C, the DMPC phase transition temperature. Increasing the bilayer cholesterol content above 20 mol% reduced that permeability peak. These results are quite consistent with a large number of similar bilayer permeability studies over the past 25 years. However, they are not consistent with a previous study of these same systems, which reported increased glucose permeability with temperature, without any maximum at or near the lipid chain melting temperature (K. Inoue, Biochim. Biophys. Acta 339 (1974) 390-402).

Student Understanding Of The Physics And Mathematics Of Process Variables In P‐V Diagrams

Students in an upper‐level thermal physics course were asked to compare quantities related to the First Law of Thermodynamics along with similar mathematical questions devoid of all physical context. We report on a comparison of student responses to physics questions involving interpretation of ideal gas processes on P‐V diagrams and to analogous mathematical qualitative questions about the signs of and comparisons between the magnitudes of various integrals. Student performance on individual questions combined with performance on the paired questions shows evidence of isolated understanding of physics and mathematics. Some difficulties are addressed by instruction.

Assessing Student Understanding of Partial Derivatives in Thermodynamics

We are engaged in a research project to study teaching and learning in upper‐level thermal physics courses. We have begun to explore student functional understanding of mathematical concepts when applied in thermal physics contexts. We report here preliminary findings associated with partial differentiation and the Maxwell relations, which equate mixed second partial derivatives of various state functions. Our results suggest that students are often unable to apply the appropriate mathematical concepts and operations to the physical situations encountered in the course, despite having taken the prerequisite mathematics courses.

Student (Mis)application of Partial Differentiation to Material Properties

Students in upper‐level undergraduate thermodynamics courses were asked about the relationship between the complementary partial derivatives of the isothermal compressibility and the thermal expansivity of a substance. Both these material properties can be expressed with first partial derivatives of the system volume. Several of the responses implied difficulty with the notion of variables held fixed in a partial derivative. Specifically, when asked to find the partial derivative of one of these quantities with respect to a variable that was initially held fixed, a common response was that this (mixed second) partial derivative must be zero. We have previously reported other related difficulties in the context of the Maxwell relations, indicating persistent confusion applying partial differentiation to state functions. We present results from student homework and examination questions and briefly discuss an instructional strategy to address these issues.

What Is Entropy? Advanced Undergraduate Performance Comparing Ideal Gas Processes

We report data on upper‐level student understanding of entropy and the Second Law of Thermodynamics when comparing the isothermal and free expansions of an ideal gas. Data from pre‐ and post‐instruction written questions are presented, and several noteworthy features of student performance are identified and discussed. These features include ways students think about these topics prior to instruction as well as specific difficulties and other interesting aspects of student thought that persist after instruction. Implications for future research are also addressed.

Representations of partial derivatives in thermodynamics

One of the mathematical objects that students become familiar with in thermodynamics, often for the first time, is the partial derivative of a multivariable function. The symbolic representation of a partial derivative and related quantities present difficulties for students in both mathematical and physical contexts, most notably what it means to keep one or more variables fixed while taking the derivative with respect to a different variable. Material properties are themselves written as partial derivatives of various state functions (e.g., compressibility is a partial derivative of volume with respect to pressure). Research in courses at the University of Maine and Oregon State University yields findings related to the many ways that partial derivatives can be represented and interpreted in thermodynamics. Research has informed curricular development that elicits many of the difficulties using different representations (e.g., geometric) and different contexts (e.g., connecting partial derivatives to specific experiments).

Addressing Student Difficulties with Statistical Mechanics: The Boltzmann Factor

As part of research into student understanding of topics related to thermodynamics and statistical mechanics at the upper division, we have identified student difficulties in applying concepts related to the Boltzmann factor and the canonical partition function. With this in mind, we have developed a guided‐inquiry worksheet activity (tutorial) designed to help students develop a better understanding of where the Boltzmann factor comes from and why it is useful. The tutorial guides students through the derivation of both the Boltzmann factor and the canonical partition function. Preliminary results suggest that students who participated in the tutorial had a higher success rate on assessment items than students who had only received lecture instruction on the topic. We present results that motivate the need for this tutorial, the outline of the derivation used, and results from implementations of the tutorial.

Student Estimates of Probability and Uncertainty in Advanced Laboratory and Statistical Physics Courses

Equilibrium properties of macroscopic systems are highly predictable as n, the number of particles approaches and exceeds Avogadros number; theories of statistical physics depend on these results. Typical pedagogical devices used in statistical physics textbooks to introduce entropy (S) and multiplicity (ω) (where S = k ln(ω)) include flipping coins and/or other equivalent binary events, repeated n times. Prior to instruction, our statistical mechanics students usually gave reasonable answers about the probabilities, but not the relative uncertainties, of the predicted outcomes of such events. However, they reliably predicted that the uncertainty in a measured continuous quantity (e.g., the amount of rainfall) does decrease as the number of measurements increases. Typical textbook presentations assume that students understand that the relative uncertainty of binary outcomes will similarly decrease as the number of events increases. This is at odds with our findings, even though most of our students had previously completed mathematics courses in statistics, as well as an advanced electronics laboratory course that included statistical analysis of distributions of dart scores as n increased.

Upper‐Division Activities That Foster “Thinking Like A Physicist”

In this targeted poster session, curriculum developers presented their favorite upper‐division activity to small groups of session participants. The developers and participants were asked to identify hidden curriculum goals related to “thinking like a physicist” and discuss how the different styles of activities might help students achieve these goals.

Identifying student difficulties with conflicting ideas in statistical mechanics

In statistical mechanics there are two quantities that directly relate to the probability that a system at a temperature fixed by a thermal reservoir has a particular energy. The density of states function is related to the multiplicity of the system and indicates that occupation probability increases with energy. The Boltzmann factor is related to the multiplicity of the reservoir and indicates that occupation probability decreases with energy. This seems contradictory until one remembers that a complete probability distribution is determined by the total multiplicity of the system and its surroundings, requiring the product of these two functions. We present evidence from individual and group interviews that students knew how each of these functions relates to multiplicity but did not recognize the need to combine the two to characterize the physical scenario.