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Student understanding of the ideal gas law, Part I: A macroscopic perspective
1.In most of the physics 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 gas particles.
2.C. H. Kautz, P. R. L. Heron, P. S. Shaffer, and L. C. McDermott, “Student understanding of the ideal gas law, Part II: A microscopic perspective,” Am. J. Phys. 73, 1064–1071 (2005).
3.For a brief annotated bibliography that includes some studies among young students, as well as a few at the university level, see L. C. McDermott and E. F. Redish, “Resource letter: PER-1: Physics education research,” Am. J. Phys. 67, 755–767 (1999).
4.S. Rozier and L. Viennot, “Students’ reasonings in thermodynamics,” Int. J. Sci. Educ. 13, 159–170 (1991).
5.D. E. Meltzer, “Investigation of students’ reasoning regarding heat, work, and the first law of thermodynamics in an introductory calculus-based general physics course,” Am. J. Phys. 72, 1432–1446 (2004).
6.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).
7.C. H. Kautz, “Identifying and addressing student difficulties with the ideal gas law,” Ph.D. dissertation, Department of Physics, University of Washington, 1999 (unpublished).
8.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.
9.The quizzes are taken seriously by most students, as is discussed in L. G. Ortiz, P. R. L. Heron, and P. S. Shaffer, “Investigating student understanding of static equilibrium: Predicting and accounting for balancing,” Am. J. Phys. 73, 545–553 (2005).
10.See, for example, 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).
11.The students were asked to compare the initial and final equilibrium states to avoid the issue of whether the process itself could be considered quasistatic.
12.Note the similarity between this statement and the one made by a student in Ref. 5 in the context of an isothermal process. Meltzer, however, interprets this statement primarily as evidence for student difficulties with the microscopic model of temperature (rather than pressure).
13.Meltzer has observed a similar type of incorrect student reasoning in the context of an isothermal process, that is, that the absence of a temperature change implies that there is no heat transfer (Ref. 5). See also Ref. 6.
14.For these students, the insulation seems to assume the role of a thermal reservoir that supplies or absorbs heat in order to keep the system’s temperature constant.
15.See, for example, G. Erickson and A. Tiberghien, “Heat and temperature,” in Children’s Ideas in Science, edited by R. Driver, E. Guesne, and A. Tiberghien (Open University Press, Milton Keynes, 1985),
15.and the chapter on “Heating” in R. Driver, A. Squires, P. Rushworth, and V. Wood-Robinson, Making Sense of Secondary Science (Routledge, London, 1994).
16.M. L. Rosenquist, “Improving preparation for college physics of minority students aspiring to science-related careers: Investigation of student difficulties and development of appropriate curriculum,” Ph.D. dissertation, Department of Physics, University of Washington, 1982 (unpublished).
17.M. J. Cochran, “An investigation of student understanding of the second law of thermodynamics and the underlying concepts of heat, temperature and thermal equilibrium,” Ph.D. dissertation, Department of Physics, University of Washington, 2005 (unpublished).
18.P. H. van Roon, H. F. van Sprand, and A. H. Verdonk, “‘Work’ and ‘heat’: On a road towards thermodynamics,” Int. J. Sci. Educ. 16, 131–144 (1994). See also Refs. 2 and 4–6.
19.See, for example, K. C. de Berg, “Student understanding of the volume, mass, and pressure of air within a sealed syringe in different states of compression,” J. Res. Sci. Teach. 32, 871–884 (1995).
20.L. C. McDermott, L. K. Piternick, and M. L. Rosenquist, “Helping minority students succeed in science, Part I. Development of a curriculum in physics and biology,” J. Coll. Sci. Teach. 9, 136–140 (1980), and Refs. 10 and 16.
21.For examples, see the articles by L. C. McDermott and others in the Physics Education Group that have been published in Am. J. Phys., several of which are included in Ref. 3.
22.L. C. McDermott and the Physics Education Group at the University of Washington, Physics by Inquiry (Wiley, New York, 1996). See the Heat and Temperature module.
23.L. C. McDermott, P. S. Shaffer, and the Physics Education Group at the University of Washington, Tutorials in Introductory Physics (Prentice Hall, Upper Saddle River, NJ, 2002).
24.For a more complete 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).
25.See Ref. 23, pp. 227–230.
26.The conditions necessary for a movable piston to ensure constant pressure include the absence of friction and negligible acceleration of the piston at all times. In the tutorial, students assume that there is no friction between the piston and the container walls. The conditions for quasi-static changes are beyond the scope of the tutorial. All situations considered are therefore equilibrium states before and after any changes take place.
27.See Ref. 23, pp. 231–235.
28.For a more detailed description of an interactive tutorial lecture, 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).
29.The results for students who had participated in the interactive tutorial lectures and who had done the tutorial laboratory experiment were identical to those for students who had participated in the interactive tutorial lectures only.
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