Student understanding of the first law of thermodynamics: Relating work to the adiabatic compression of an ideal gas

See, for example, the following articles in the theme issue on thermal and statistical physics in Am. J. Phys.: R. W. Chabay and B. A. Sherwood, “Bringing atoms into first-year physics,” 1045–1050;

F. Reif, “Thermal physics in the introductory physics course,” ibid. 67, 1051–1052 (1999);

A. B. Arons, “Development of energy concepts in introductory physics courses,” ibid. 67, 1063–1067 (1999).

In addition to the specific references below, see the summary in the chapter by G. Erickson and A. Tiberghien in Children’s Ideas in Science, edited by R. Driver (Open University Press, Philadelphia, 1985).

A list of additional research articles related to student understanding of heat and temperature can be found in

L. C.

McDermott

and

E. F.

Redish

, “,” , – ().

See, for example,

R.

Stavy

and

B.

Berkovitz

, “,” , – ();

S.

Kesidou

and

R.

Duit

, “,” , – ();

M.

Linn

and

N.

Songer

, “” , – ();

E.

Engel

,

E.

Clough

, and

R.

Driver

, “,” , – ().

The article mentioned in Ref. 3 contains an extensive list of articles on research on student understanding in introductory mechanics and on the development and assessment of curriculum based on research.

For examples of the development and assessment of curriculum by the Physics Education Group in topics other than mechanics (for example, electricity and magnetism, geometrical and physical optics, and modern physics) see Ref. 25 and articles in Ref. 3 by members of the Physics Education Group.

The research reported in this paper is described in greater detail in M. E. Loverude, “Investigation of student understanding of hydrostatics and thermal physics and of the underlying concepts from mechanics,” and in C. H. Kautz, “Investigation of student understanding of the ideal gas law,” Ph.D. dissertations, Department of Physics, University of Washington, 1999 (unpublished).

See, for example,

G.

Erickson

, “,” , – ();

G.

Erickson

, “,” , – ();

M.

Reiner

,

J.

Slotta

,

M.

Chi

, and

L.

Resnick

, “,” , – ().

See, for example, A. B. Arons, A Guide to Introductory Physics Teaching (Wiley, New York, 1997), Part III, pp. 118–121.

See, for example,

P. H.

van Roon

,

H. F.

van Sprang

, and

A. H.

Verdonk

, “,” , – ().

See, for example,

S.

Rozier

and

L.

Viennot

, “,” , – ().

R. Resnick, D. Halliday, and K. S. Krane, Physics (Wiley, New York, 1992), 4th ed.

D. C. Giancoli, Physics (Prentice–Hall, Englewood Cliffs, NJ, 1995), 4th ed.

In the courses included in this study, students typically apply the first law of thermodynamics to closed systems, so there is no term for the chemical potential.

For a discussion of important conceptual issues that need to be addressed in teaching this material, see A. B. Arons, Teaching Introductory Physics (Wiley, New York, 1997), Part III, pp. 80–82, 124–129.

A description of the use of the individual demonstration interview by the Physics Education Group can be found in

R. A.

Lawson

and

L. C.

McDermott

, “,” , – () and in other articles in Ref. 3 that report on research by the group. Since 1994, most of the interviews have been both videotaped and audiotaped.

None of the students raised questions about the insulating capabilities of the pump or the speed with which the handle was pushed inward. If any had done so, they would have been told to assume the pump is perfectly insulating.

In both interviews and on written problems, a small number of students gave other explanations that were acceptable. For example, some students in the more advanced courses gave a microscopic work argument. Typically, these students argued that the speed of the gas particles would increase as a result of collisions with the moving piston and that the temperature would therefore increase. A handful of students in these courses also correctly applied the equation $PVγ$=constant for adiabatic processes to predict that the temperature would increase. During interviews, such students were asked to try to account for this relationship between P and V.

All the students assumed (explicitly or implicitly) that they could treat the air in the pump as an ideal gas. If this issue had been raised, the students would have been told to do so.

The version of the first law that was used in that particular student’s course was provided.

Results from three sections of the calculus-based course at the University of Maryland serve as an example of the similarity of student performance before and after instruction. In the two classes in which the question was administered after instruction, a correct prediction concerning the temperature was made by 61% $(N=66)$ and 54% $(N=83),$ respectively. In the class in which the question was given before any instruction, 59% $(N=113)$ of the students made a correct prediction. The variation in the percentages of students giving correct explanations was similarly small.

Additional evidence that student performance on certain types of questions is essentially the same before and after instruction can be found in several of the articles in Ref. 3 that report on research by the Physics Education Group.

Other evidence is reported in

R. R.

Hake

, “,” , – ().

At UIUC, the question was posed in multiple-choice format with no explanations required. Therefore, we have not included this data in Table I. About 65% of the students answered correctly $(N=189),$ a figure consistent with that obtained in other introductory courses.

See Ref. 11.

See, for example,

L. C.

McDermott

and

P. S.

Shaffer

, “,” , – (),

L. C.

McDermott

and

P. S.

Shaffer

, and printer’s erratum to Part I, , ();

P. S.

Shaffer

and

L. C.

McDermott

, “,” , – ().

For a description of similar difficulties, see the article in Ref. 11.

In some classes at the second-year level the instructor discussed in detail collisions between gas molecules and a moving piston. However, a complete microscopic treatment of heat transfer is not typically presented in the courses involved in this study.

We have also seen students use the fact that expressions for both pressure and temperature involve the mean square particle velocity to back up their claims that P and T are directly proportional.

For other examples, see

T.

O’Brien Pride

,

S.

Vokos

, and

L. C.

McDermott

, “,” , – ();

R. N.

Steinberg

and

M. S.

Sabella

, “,” , – ().

See the article mentioned in Ref. 16 and the first article in Ref. 29.

See Refs. 2, 3, 4, and 11.

See, for example,

M.

Zemansky

, , – ();

J. W.

Warren

, , – ();

R.

Bauman

, , – ();

R. H.

Romer

, “,” , – ().

Failure to understand the role of insulation has also been documented among younger students. For example, some studies have found that children often say that materials like wool will make objects hot, rather than preventing heat transfer. See Refs. 2, 4, and 8.

For a discussion of the confusion between heat and work in the context of frictional processes see the last article in Ref. 1 and Ref. 9, Part III, pp. 137–142.

See Ref. 10.

Reference 13, p. 425.

Reference 12, p. 557. The fifth edition of this text, which was not yet in print at the time of the study described in this article, defines the work done on the gas as $−∫p dV$ and states that “…if the gas expands, dV is positive and W is negative, p being a scalar quantity having only positive values. Conversely, if the gas is compressed, dV is negative and the work done on the gas is positive.” R. Resnick, D. Halliday, and K. S. Krane, Physics (Wiley, New York, 2002), 5th ed., pp. 526–527.

We found similar results in a different set of interviews with a small number of students. In the physical situation on which the interviews were based, no object was readily identifiable as “responsible” for the motion. We asked students to consider the following two cases. In case I, a sample of gas is enclosed in a cylinder with a piston that is free to move. The cylinder is placed inside an insulating box with some ice water. Case II is identical in every respect to case I except that the cylinder’s piston is locked in place. The students were asked to predict how the amounts of ice melted would compare after both systems are allowed to reach thermal equilibrium. In case I, positive work is done on the gas as the piston lowers at constant pressure. In case II the piston does not move so no work is done. It follows that, in case I, greater heat transfer is required to lower the temperature of the gas by the same amount and therefore more ice is melted. Only two of the five students interviewed took into account the work done in case I, despite having covered in their course the difference between heat capacity at constant volume $(Cv)$ and at constant pressure $(Cp).$ It is possible that students failed to regard the piston as doing work because it was not “active.”

The version given at UIUC was multiple choice. No explanations were required.

For a discussion of some of the relevant research, see, in addition to articles listed in Ref. 3,

L. C.

McDermott

, “,” (), – ().

See, for example,

J.

Minstrell

, “,” , – ().

See, for example,

D. P.

Maloney

, “,” , – ().

In this and other cases we have found little or no systematic variation between responses on graded and ungraded versions of the same question.

We found that many students did not treat “work done=0” and “there is no such work” as equivalent statements. Therefore we explicitly allowed for both possibilities.

See Ref. 44.

In one version, the students were asked explicitly about the relationship between the two pages.

For articles in which the failure to use energy principles in mechanics is documented and discussed, see the section in Ref. 3 on problem-solving performance.

See the article mentioned in Ref. 16 and the first article in Ref. 29.

We have posed the bicycle pump task in informal situations to a number of friends and colleagues who are physicists.

There have been several articles that support the introduction of microscopic models during the study of topics in classical physics. For examples in the context of thermal physics, see the first two articles in Ref. 1. For an example in the context of electric circuits, see

B. A.

Thacker

,

U.

Ganiel

, and

D.

Boys

, “,” , – (). In the article, data are presented that indicate that students who had been given a microscopic model outperformed others who had not. However, there is additional evidence that students who had developed a sound macroscopic model performed as well on the questions posed in this study as those who had been given a microscopic model.

K.

Wosilait

,

P. R. L.

Heron

,

P. S.

Shaffer

, and

L. C.

McDermott

, “,” , – ().

See Ref. 32.

For other tutorials developed by the Physics Education Group, see 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).

For illustrations of the iterative process used by the Physics Education Group in the development of curriculum, see the second article in Ref. 25, the first article mentioned in Ref. 29, and articles in Ref. 3 by the Physics Education Group.