Students’ Reasoning Regarding Heat, Work, and the First Law of Thermodynamics

1. Students’ Reasoning Regarding Heat, Work, and the First Law of Thermodynamics David E. Meltzer Department of Physics and Astronomy Iowa State University Ames, Iowa Supported by National Science Foundation grants DUE #9981140 and REC #0206683

2. Introduction • There have been more than 200 investigations of pre-college students’ learning of thermodynamics concepts, all showing serious conceptual difficulties.

3. Introduction • There have been more than 200 investigations of pre-college students’ learning of thermodynamics concepts, all showing serious conceptual difficulties. • Recently published study of university students showed substantial difficulty with work concept and with the first law of thermodynamics.M.E. Loverude, C.H. Kautz, and P.R.L. Heron, Am. J. Phys. 70, 137 (2002).

4. Introduction • There have been more than 200 investigations of pre-college students’ learning of thermodynamics concepts, all showing serious conceptual difficulties. • Recently published study of university students showed substantial difficulty with work concept and with the first law of thermodynamics. M.E. Loverude, C.H. Kautz, and P.R.L. Heron, Am. J. Phys. 70, 137 (2002). • Until now there has been no detailed study of thermodynamics knowledge of students in introductory calculus-based general physics course.

5. Research Basis for Curriculum Development • To lay groundwork for NSF-sponsored curriculum development project in thermodynamics [Co-PI: T. J. Greenbowe], we undertook investigation of Iowa State’s second-semester calculus-based physics course populated mostly by engineering students.

6. Research Basis for Curriculum Development • To lay groundwork for NSF-sponsored curriculum development project in thermodynamics [Co-PI: T. J. Greenbowe], we undertook investigation of Iowa State’s second-semester calculus-based physics course populated mostly by engineering students. • Written diagnostic questions administered last week of class in 1999, 2000, and 2001 (Ntotal= 653).

7. Research Basis for Curriculum Development • To lay groundwork for NSF-sponsored curriculum development project in thermodynamics [Co-PI: T. J. Greenbowe], we undertook investigation of Iowa State’s second-semester calculus-based physics course populated mostly by engineering students. • Written diagnostic questions administered last week of class in 1999, 2000, and 2001 (Ntotal= 653). • Detailed interviews (avg. duration  one hour) carried out with 32 volunteers during 2002 (total class enrollment: 424).

8. Characterization of Interview Sample .

9. Characterization of Interview Sample • Represented 13 (out of 20 total) different recitation sections.

10. Characterization of Interview Sample • Represented 13 (out of 20 total) different recitation sections. • Represented 7 (out of 9 total) different recitation instructors.

11. Characterization of Interview Sample • Represented 13 (out of 20 total) different recitation sections. • Represented 7 (out of 9 total) different recitation instructors. • 66% were engineering majors.

12. Characterization of Interview Sample • Represented 13 (out of 20 total) different recitation sections. • Represented 7 (out of 9 total) different recitation instructors. • 66% were engineering majors. • 31 out of 32 had studied physics during high school.

13. Characterization of Interview Sample • Represented 13 (out of 20 total) different recitation sections. • Represented 7 (out of 9 total) different recitation instructors. • 66% were engineering majors. • 31 out of 32 had studied physics during high school. • Final grades well above class average.

14. Grade Distributions: Interview Sample vs. Full Class

15. Grade Distributions: Interview Sample vs. Full Class Interview Sample: 34% above 91st percentile; 50% above 81st percentile

16. Predominant Themes of Students’ Reasoning .

17. Predominant Themes of Students’ Reasoning • Understanding of concept of state function in the context of energy.

18. Predominant Themes of Students’ Reasoning • Understanding of concept of state function in the context of energy. • Failure to recognize “work” as a mechanism of energy transfer.

19. Predominant Themes of Students’ Reasoning • Understanding of concept of state function in the context of energy. • Failure to recognize “work” as a mechanism of energy transfer. • Confusion regarding relation between temperature and molecular kinetic energy.

20. Predominant Themes of Students’ Reasoning • Understanding of concept of state function in the context of energy. • Failure to recognize “work” as a mechanism of energy transfer. • Confusion regarding relation between temperature and molecular kinetic energy. • Confusion regarding isothermal processes and the thermal “reservoir.”

21. Predominant Themes of Students’ Reasoning • Understanding of concept of state function in the context of energy. • Failure to recognize “work” as a mechanism of energy transfer. • Confusion regarding relation between temperature and molecular kinetic energy. • Confusion regarding isothermal processes and the thermal “reservoir.” • Belief that work is a state function.

22. Predominant Themes of Students’ Reasoning • Understanding of concept of state function in the context of energy. • Failure to recognize “work” as a mechanism of energy transfer. • Confusion regarding relation between temperature and molecular kinetic energy. • Confusion regarding isothermal processes and the thermal “reservoir.” • Belief that work is a state function. • Belief that heat is a state function.

23. Predominant Themes of Students’ Reasoning • Understanding of concept of state function in the context of energy. • Failure to recognize “work” as a mechanism of energy transfer. • Confusion regarding relation between temperature and molecular kinetic energy. • Confusion regarding isothermal processes and the thermal “reservoir.” • Belief that work is a state function. • Belief that heat is a state function. • Belief that net work done and net heat transferred during a cyclic process are zero.

24. Predominant Themes of Students’ Reasoning • Understanding of concept of state function in the context of energy. • Failure to recognize “work” as a mechanism of energy transfer. • Confusion regarding relation between temperature and molecular kinetic energy. • Confusion regarding isothermal processes and the thermal “reservoir.” • Belief that work is a state function. • Belief that heat is a state function. • Belief that net work done and net heat transferred during a cyclic process are zero. • Inability to apply the first law of thermodynamics.

25. Predominant Themes of Students’ Reasoning • Understanding of concept of state function in the context of energy. • Failure to recognize “work” as a mechanism of energy transfer. • Confusion regarding relation between temperature and molecular kinetic energy. • Confusion regarding isothermal processes and the thermal “reservoir.” • Belief that work is a state function. • Belief that heat is a state function. • Belief that net work done and net heat transferred during a cyclic process are zero. • Inability to apply the first law of thermodynamics. • Difficulties regarding P-V diagrams.

26. Predominant Themes of Students’ Reasoning • Understanding of concept of state function in the context of energy. • Failure to recognize “work” as a mechanism of energy transfer. • Confusion regarding relation between temperature and molecular kinetic energy. • Confusion regarding isothermal processes and the thermal “reservoir.” • Belief that work is a state function. • Belief that heat is a state function. • Belief that net work done and net heat transferred during a cyclic process are zero. • Inability to apply the first law of thermodynamics. • Difficulties regarding P-V diagrams.

27. Understanding of Concept of State Function in the Context of Energy • Students’ understanding of state-function concept probed through questions concerning two different processes connecting identical initial and final states.

28. Understanding of Concept of State Function in the Context of Energy • Students’ understanding of state-function concept probed through questions concerning two different processes connecting identical initial and final states. • Do students realize that only initial and final states determine change in a state function, and that details of the transition process are irrelevant?

31. U1 = U2

32. Results on Diagnostic Question #3 • 2001 results: • 73% correct responses. • 2002 interview sample results: • 88% correct responses • 78% with acceptable explanation

33. Results on Diagnostic Question #3 • 2001 results: • 73% correct responses. • 2002 interview sample results: • 88% correct responses • 78% with acceptable explanation • 1999 results on similar question involving cyclic process: • 85% correct responses • 70% with acceptable explanation

34. Students seem to have adequate grasp of state-function concept • Consistently high percentage of correct responses on relevant questions. • Large proportion of correct explanations.

35. Students seem to have adequate grasp of state-function concept • Consistently high percentage of correct responses on relevant questions. • Large proportion of correct explanations. • Interview subjects displayed good understanding of state-function idea.

36. Students seem to have adequate grasp of state-function concept • Consistently high percentage of correct responses on relevant questions. • Large proportion of correct explanations. • Interview subjects displayed good understanding of state-function idea. Students’ major conceptual difficulties stemmed from overgeneralization of state-function concept.

37. Students seem to have adequate grasp of state-function concept • Consistently high percentage of correct responses on relevant questions. • Large proportion of correct explanations. • Interview subjects displayed good understanding of state-function idea. Students’ major conceptual difficulties stemmed from overgeneralization of state-function concept.Details to follow .. .

38. Predominant Themes of Students’ Reasoning • Understanding of concept of state function in the context of energy. • Failure to recognize “work” as a mechanism of energy transfer. • Confusion regarding relation between temperature and molecular kinetic energy. • Confusion regarding isothermal processes and the thermal “reservoir.” • Belief that work is a state function. • Belief that heat is a state function. • Belief that net work done and net heat transferred during a cyclic process are zero. • Inability to apply the first law of thermodynamics. • Difficulties regarding P-V diagrams.

39. Failure to Recognize “Work” as a Mechanism of Energy Transfer .

40. Failure to Recognize “Work” as a Mechanism of Energy Transfer • Basic notion of thermodynamics: if part or all of system boundary is displaced, energy is transferred between system and surroundings in the form of “work.”

41. Failure to Recognize “Work” as a Mechanism of Energy Transfer • Basic notion of thermodynamics: if part or all of system boundary is displaced, energy is transferred between system and surroundings in the form of “work.” • Study of Loverude et al. (2002) showed that few students could spontaneously invoke concept of work in case of adiabatic compression.

42. Failure to Recognize “Work” as a Mechanism of Energy Transfer • Basic notion of thermodynamics: if part or all of system boundary is displaced, energy is transferred between system and surroundings in the form of “work.” • Study of Loverude et al. (2002) showed that few students could spontaneously invoke concept of work in case of adiabatic compression. • Present investigation probed student reasoning regarding work in case of isobaric expansion and isothermal compression.

43. Interview Questions A fixed quantity of ideal gas is contained within a metal cylinder that is sealed with a movable, frictionless, insulating piston. (The piston can move up or down without the slightest resistance from friction, but no gas can enter or leave the cylinder. The piston is heavy, but there can be no heat transfer to or from the piston itself.) The cylinder is surrounded by a large container of water with high walls as shown. We are going to describe two separate processes, Process #1 and Process #2.

44. [This diagram was not shown to students]

45. At initial time A, the gas, cylinder, and water have all been sitting in a room for a long period of time, and all of them are at room temperature movable piston water ideal gas Time A Entire system at room temperature.

46. Time B Piston in new position. Temperature of system has changed. Step 1. We now begin Process #1: The water container is gradually heated, and the piston very slowly moves upward. At time B the heating of the water stops, and the piston stops moving when it is in the position shown in the diagram below: Question #1: During the process that occurs from time A to time B, which of the following is true: (a) positive work is done on the gas by the environment, (b) positive work is done by the gas on the environment, (c) no net work is done on or by the gas.

47. Time B Piston in new position. Temperature of system has changed. Step 1. We now begin Process #1: The water container is gradually heated, and the piston very slowly moves upward. At time B the heating of the water stops, and the piston stops moving when it is in the position shown in the diagram below: Question #1: During the process that occurs from time A to time B, which of the following is true: (a) positive work is done on the gas by the environment, (b) positive work is done by the gas on the environment, (c) no net work is done on or by the gas.

48. [This diagram was not shown to students]

49. Results on Question #1 • positive work done on gas by environment: 31% • positive work done by gas on environment [correct]:69%

50. Results on Question #1 • positive work done on gas by environment: 31% • positive work done by gas on environment [correct]:69% Sample explanations for (a) answer: “The water transferred heat to the gas and expanded it, so work was being done to the gas to expand it.”