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Student understanding of the ideal gas law, Part II: A microscopic perspective
1.In most of the courses in this study, the ideal gas law is expressed as , where is the number of moles. In a few cases, the law was expressed as , where is the number of molecules.
2.C. H. Kautz, P. R. L. Heron, M. E. Loverude, and L. C. McDermott, “Student understanding of the ideal gas law, Part I: A macroscopic perspective,” Am. J. Phys. 73, 1055–1063 (2005).
3.L. C. McDermott and P. S. Shaffer, and the Physics Education Group at the University of Washington, Tutorials in Introductory Physics (Prentice Hall, Upper Saddle River, NJ, 2002).
4.See M. E. Loverude, C. H. Kautz, and P. R. L. Heron, “Student understanding of the first law of thermodynamics: Relating work to the adiabatic compression of an ideal gas,” Am. J. Phys. 70, 137–148 (2002).
5.For a succinct description of this research method, see L. C. McDermott, “Millikan Lecture 1990: What we teach and what is learned—Closing the gap,” Am. J. Phys. 59, 301–315 (1991). This article includes references to papers that give specific examples.
6.Some of the course instructors state this qualitative model explicitly before or after going through the formal mathematical derivation of pressure in the microscopic model.
7.In some cases, the term incident particle flux or the symbol were explicitly used; in other cases, only a verbal description of the quantity was given. The results did not seem to differ.
8.Although inter-molecular collisions play no role in the derivation of the ideal gas equations of state, collisions between molecules are referred to in the postulates presented in many introductory textbooks, including those used in courses in which the tutorials described in this article were tested. (These texts stipulate that the collisions are elastic and of negligible duration.) Moreover, students clearly believe that such collisions are important. Therefore, we think it is appropriate to deal with them in the tutorial.
9.In one section of the algebra-based course, the problem was given before the relevant lectures. In an informal poll, almost all students indicated that they had previously studied the ideal gas law, usually in a college chemistry course. The results did not differ much from those obtained in other sections after standard instruction.
10.The tendency to treat vectors as scalars in finding the difference of two vectors is also discussed in the context of collisions in P. S. Shaffer and L. C. McDermott, “A research-based approach to improving student understanding of kinematical concepts,” Am. J. Phys. 73, 921–931 (2005).
11.For other examples of compensation reasoning, see R. A. Lawson and L. C. McDermott, “Student understanding of the work-energy and impulse-momentum theorems,” Am. J. Phys. 55, 811–817 (1987);
11.T. O’Brien Pride, S. Vokos, and L. C. McDermott, “The challenge of matching learning assessments to teaching goals: An example from the work-energy and impulse-momentum theorems,” Am. J. Phys. 66, 147–156 (1998);
11.M. E. Loverude, C. H. Kautz, and P. R. L. Heron, “Helping students develop an understanding of Archimedes’ principle, Part I: Research on student understanding,” Am. J. Phys. 71, 1178–1187 (2003).
12.A situation in which the temperature of a gas is changed as a result of processes in the interior of the gas is a chemical reaction between different substances. In that case, one form of internal energy (that is, chemical) is changed to another (that is, thermal). Students may fail to distinguish between the two cases and interpret an adiabatic compression as a process similar to a chemical reaction.
13.S. Novick and J. Nussbaum, “Junior high school pupils’ understanding of the particulate nature of matter: An interview study,” Sci. Educ. 62, 273–281 (1978);
13.S. Novick and J. Nussbaum, “Pupils’ understanding of the particulate nature of matter: A cross-age study,” Sci. Educ. 65, 187–196 (1981).
14.Difficulties with mass and volume are frequently seen at the pre-college level. At the college level, such difficulties still occur. See, for example, the last article in Ref. 11.
15.In a few instances, even the subscripts describing the stoichiometric composition of a given compound (as in ) were confused with the molar mass or the number of moles.
16.For a brief discussion of this instructional approach as implemented by the Physics Education Group, and a description of the tutorials and their implementation, see L. C. McDermott, Oersted Medal Lecture 2001: “Physics education research—The key to student learning,” Am. J. Phys. 69, 1127–1137 (2001).
17.For a description of interactive tutorial lectures, see P. R. L. Heron, M. E. Loverude, P. S. Shaffer, and L. C. McDermott, “Helping students develop an understanding of Archimedes’ Principle, Part II: Development of research-based instructional materials,” Am. J. Phys. 71, 1188–1195 (2003).
18.Reference 3, pp. 227–230.
19.We have found that students who incorrectly answer questions based on the ideal gas law are often misled by incorrect or incomplete microscopic models. Since the second post-test question starts from a microscopic perspective, we regard it as more difficult than the first.
20.Some physicists take a different instructional approach. They argue that introducing a microscopic model makes it easier for students to think about both macroscopic and microscopic phenomena. See, for example, R. W. Chabay and B. A. Sherwood, “Bringing atoms into first-year physics,” Am. J. Phys. 67, 1045–1050 (2001);
20.F. Reif, “Thermal physics in the introductory physics course: Why and how to teach it from a unified atomic perspective,” Am. J. Phys. 67, 1051–1062 (2001).
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