Development and assessment of research-based tutorials on heat engines and the second law of thermodynamics

American Journal of Physics

Volumn 74, Issue 8, 2006, Pages 734-741

  Cochran, Matthew J ^a   Heron, Paula R L ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746868889     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.2198889     Document Type: Article

References (37)

1. See, for example, J. Tobochnik, H. Gould, and J. Machta, "Understanding temperature and chemical potential using computer simulations," Am. J. Phys. 73, 708-716 (2005);
2. D. F. Styer, "Insight into entropy," Am. J. Phys. ibid. 68, 1090-1096 (2000);
3. F. Reif, "Thermal physics in the introductory physics course; Why and how to teach it from a unified atomic perspective," Am. J. Phys. ibid. 67, 1051-1062 (1999);
4. T. A. Moore and D. V. Schroeder, "A different approach to introducing statistical mechanics," Am. J. Phys. ibid. 65, 26-36 (1997);
5. R. Baierlein, "Entropy and the second law: A pedagogical alternative," Am. J. Phys. ibid. 62, 15-26 (1994);
6. H. S. Leff, "A mixing route to thermodynamics," Am. J. Phys. ibid. 61, 667 (1993);
7. M. I. Sobel, "A model for introducing the concept of entropy," Am. J. Phys. ibid. 61, 941-942 (1993);
8. T. V. Marcella, "Entropy production and the second law of thermodynamics; An introduction to second law analysis," Am. J. Phys. ibid. 60, 888-895 (1992).
9. B. R. Bucy, J. R. Thompson, and D. B. Mountcastle, "What is entropy? Advanced undergraduate performance comparing ideal gas processes," in Proceedings of the 2005 Physics Education Research Conference, edited by P. Heron, J. Marx, and L. McCullough (AIP Conf. Proc. 2005), Vol. 818, pp. 81-84;
10. D. E. Meltzer, "Student learning in upper-level thermal physics: Comparisons and contrasts with students in introductory courses," in Proceedings of the 2004 Physics Education Research Conference, edited by J. Marx, P. Heron, and S. Franklin (AIP Conf. Proc. 2005), Vol. 790, pp. 31-34;
11. W. M. Christensen and D. E. Meltzer, "Students' ideas about entropy and the second law of thermodynamics," 2005 Winter Meeting of the AAPT, Albuquerque, NM, 2005,
12. AAPT Announcer 34 (4), 97 (2004).
13. See, for example, S. Kesidou and R. Duit, "Students' conceptions of the second law of thermodynamics: An interpretive study," J. Res. Sci. Teach. 30, 85-106 (1992). Kesidou and Duit report that at the precollege level, student understanding of the second law is limited by difficulties with more basic thermal physics concepts. Their study focused on student ability to recognize that the second law of thermodynamics accounts for the fact that certain processes proceed in one direction only, for example, that a cup of coffee cools spontaneously.
14. M. J. Cochran, "Student understanding of the second law of thermodynamics and the underlying concepts of heat, temperature, and thermal equilibrium," Ph. D. dissertation, Physics Department, University of Washington, 2005.
15. 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);
16. C. H. Kautz, P. R. L. Heron, M. E. Loverude, and L. C. McDermott, "Student understanding of the ideal gas law. I. A macroscopic perspective," Am. J. Phys. ibid. 73, 1055-1063 (2005);
17. C. H. Kautz, P. R. L. Heron, P. S. Shaffer, and L. C. McDermott, "Student understanding of the ideal gas law. II. A microscopic perspective," Am. J. Phys. ibid. 73, 1064-1071 (2005).
18. The second-year course usually adopts the same textbook as the introductory calculus-based course, supplemented with readings from more advanced books. During most of the investigation reported here, the text was R. Resnick, D. Halliday, and K. S. Krane, Physics (Wiley, New York, 1992), 4th ed. Our experience has been that the specific text does not appear to influence student performance on the type of questions discussed in this paper.
19. 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).
20. The course at UC used D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics (Wiley, New York, 2001), 6th ed. during most of the investigation described here.
21. The junior-level course at SPU used D. V. Schroeder, An Introduction to Thermal Physics (Addison-Wesley, San Francisco, 2000) during the investigation described here.
22. Experience with other topics suggests that most students take non-graded quizzes seriously. For an example, see L. G. Ortiz, P. S. Shaffer, and P. R. L. Heron, "Investigating student understanding of static equilibrium: Predicting and accounting for balancing," Am. J. Phys. 73, 545-553 (2005).
23. See also C. Henderson, "Common concerns about the Force Concept Inventory," Phys. Teach. 40, 542-547 (2002).
24. Reference 7, pp. 227-235.
25. Results from the two UW classes given all three device questions were similar and have been combined. In this and many other cases in which the same question has been given in several sections of the same course at similar stages in instruction, we find that the results typically do not vary by more than about 5% about the mean calculated over all sections. Because there are a great many variables that could account for differences from class to class, we typically base assessments of instructional significance on the typical distributions we observe, rather than on tests of statistical significance, which take into account only expected random variation. For a discussion in greater detail see P. R. L. Heron, M. E. Loverude, P. S. Shaffer, and L. C. McDermott, "Helping students develop an understanding of Archimedes' principle. II. Development of research-based instructional materials," Am. J. Phys. 71, 1188-1195 (2003).
26. Research on student understanding of the first law of thermodynamics among university students can be found in the first article in Ref. 5 as well as in 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).
27. Questions on other topics in thermal physics have been given in both the UW second-year course and the UC calculus-based course. In all such cases the UW students have performed somewhat better. Thus using the UW course for a comparison group provides a reasonable, and probably conservative, measure of the effectiveness of the tutorial at UC.
28. For an example, see the article mentioned in Ref. 12. We found that some versions of the tutorials had much greater impact than others for the same amount of time spent.
29. An example is: "... the most general statement of the second law of thermodynamics can be restated as: the total entropy, S, of any system plus that of its environment increases as a result of any natural process: ΔS>0." See D. C. Giancoli, Physics for Scientists and Engineers (Prentice Hall, Upper Saddle River, NJ, 2000), 3rd ed., p. 539.
30. Another example is "This law [the second law], which is an extension of the entropy postulate, states: If a process occurs in a closed system, the entropy of the system increases for irreversible processes. It never decreases. In equation form, ΔS≥=0." See D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics (Wiley, New York, 2001), 6th ed., p. 500.
31. A detailed discussion of this approach to entropy and the second law can be found in Ref. 4. For other examples in which the entropy inequality is identified as the second law, see D. G. Miller, "Thermodynamic theory of irreversible processes I. The basic macroscopic concepts," Am. J. Phys. 24, 434-444 (1956);
32. R. C. Tolman, The Principles of Statistical Mechanics (Oxford U.P., London, 1938), pp. 546, 558;
33. R. Clausius, The Mechanical Theory of Heat (Macmillan, London, 1879), pp. 110, 214.
34. It can be argued that the only truly isolated system is the universe itself, in which case ΔS≥0 concisely states that the total amount of entropy in the universe can either increase or remain the same in any natural process much as the corresponding equation ΔE=0 states that the total amount of energy in the universe is a constant.
35. We chose not to give an integral form of the entropy inequality in the tutorial. The use of a summation sign instead was an attempt to make the tutorial suitable for an algebra-based course.
36. Miller, in the first article in Ref. 17, explains that the quantity ∫dQ/T may be considered the entropy added to a system by heat transport across its boundaries. In a similar manner, Schroeder encourages students to think of the flow of entropy. See D. V. Schroeder, An Introduction to Thermal Physics (Addison-Wesley, San Francisco, 2000), p. 96.
37. A second edition of Tutorials in Introductory Physics, which will cover the second law of thermodynamics, is planned for release in 2007.