why the explosion causes a decrease in temperature, they tend to adopt the ideal-gas law (PV = nRT), and claim that decreas-ing pressure leads to a drop in temperature. The reasoning is not sound because the third variable, volume (V), increases significantly.5 Therefore, PV = nRT is insufficient to explain the cooling effect of the sudden explosion.

After illustrating the ineffectiveness of PV = nRT, the first law (Q+W = ∆U) is introduced along with a review of the concept of work defined in mechanics. The sudden explosion can be regarded as an adiabatic process. During the explosion, work is done by the gas on the atmosphere. From the first law (Q+W = ∆U), the work done by gas causes a decrease of internal energy. Then, combining the first law and the kinetic theory, ∆U = ∆Ek ~ ∆T, where Ek is the total kinetic energy of the gas and ∆T is temperature change. Thus, decreasing internal energy results in a drop in temperature, which is illus-trated by the condensation. The demonstration and in-class dialogue take about 10 minutes to complete.

Since the notion that “work results in change of internal energy” in the first law is not intuitive, more examples are needed for students to practice. After two to three hours of instructing on the definition of the first law and solving sev-eral problems, a worksheet containing five real-life questions is distributed and group discussion is undertaken. Two are described below.

Air conditioning for aircraft cabins

Question: Jet aircraft fly at altitudes above 30,000 ft, where the air is very cold. However, when exchanging the air outside with that inside the cabin, why is air conditioning used, rather than heaters, to obtain a comfortable cabin temperature? (Hint: Think about the outside air pressure at high altitude compared with that of the cabin.)

Answer: Since the outside pressure at high altitude is far lower than that in the cabin, the outside air needs to be quickly (adiabatically) compressed before being delivered into the cabin. From the first law (Q+W = ∆U), work is done on the air owing to the sudden compressing process; thus, the internal energy of the air increases, and the tem-perature rises dramatically.

Despite having considered related examples, most students still had difficulty with this example and needed a hint to see the answer.

Teaching the First Law of Thermodynamics via Real-Life ExamplesWheijen Chang, Feng-Chia University, Taiwan

The literature has revealed that many students encoun-ter substantial difficulties in applying the first law of thermodynamics. For example, university students

sometimes fail to recognize that heat and work are indepen-dent means of energy transfer.1 When discussing adiabatic processes for an ideal gas, few students can correctly refer to the concept of “work” to justify a change in temperature.1 Some students adopt the notion that “collisions between molecules produce heat” to explain the rise in temperature for an adiabatic compression process.2 When explaining pro-cesses entailing temperature variation, students tend to adopt the ideal-gas law.1,2 Although most university students have acquired a reasonable grasp of the state-function concept, which is valid for variation of internal energy, they fail to grasp the concept that work depends not only on the states but also the processes. Thus, they are unable to use the first law effectively.3 In order to help students comprehend the meaning, usages, and value of the first law, and to realize that the ideal-gas law itself is insufficient to analyze many real-life examples, this paper introduces four examples, some of which can be demonstrated in the classroom. The examples have been devised and gradually modified over a period of several years based on implementation in a calculus-based introductory physics course. Details of when, how, and why each example is adopted, along with the students’ pitfalls, are described below.

Exploding bottle

The first demonstration is introduced after completing the topics of the ideal-gas law and kinetic theory. It provides a bridge from the ideal-gas law to the first law (Q+W=∆U), where Q is the heat absorbed by gas systems,W is the work done on the gas, and ∆U is the change of internal energy of the system.

A bottle is damped with a small amount of water, sealed, compressed with air [Fig. 1(a)], then suddenly opened, caus-ing an explosion. As shown in Fig. 1(b), a white “cloud” ap-pears, indicating the condensation of water vapor, implying a drop in temperature.4 When the students are asked to explain

Fig. 1. (a) Exploding bottle. (b) condensation of exploding bottle.

a) b)

DOI: 10.1119/1.3566034 The Physics Teacher ◆ Vol. 49, April 2011 231

C, where γ is Cp/Cv). The “surprise” of igniting a fire using your bare hands may stimulate students’ interest, retain their attention, and render the abstract symbols sensible.

Solving problemsIn order to encourage students to review these examples af-

ter class, conceptual questions such as those posed above can be devised as manipulating problems. For example,

Problem 1: Recalling the fire syringe demon-stration, assume that the room temperature and air pressure are 20oC, 1.00 atm. The ignition point of the tissue is 630 K.6 The inner diameter of the cylinder is 0.800 cm, and the original height of the piston is 11.0 cm. Regard the air as being composed of O2 and N2 only (γ = Cp/Cv =1.40). Evaluate (a) the number of moles of gas in the system, (b) the work done on the gas to ignite the tissue, (c) the compression ratio (Vi /Vf ), (d) the final pressure, and (e) the force required for igniting the tissue.

Answers: (a) n = 2.29×10-4 mole (b) W=∆U = ∆Ek= 5

2nR T∆ =1.60 J

(c) TVγ-1= C, Vi /Vf = 6.78 (d) PVγ = C, Pf =14.6 atm (e) (Pf – Pair)A = 69.0 N.

Problem 2: Assuming that a jet plane flies at a high altitude, where T = −40.0oC and P = 0.280 atm, evaluate (a) the final temperature, (b) the compression ratio (Vi /Vf), when quickly compressing the air to P =1.00 atm.7

Answer: (a) TVγ–1= C, Tf = 335 K = 62oC (too hot to survive!)

(b) 2.48

These two problems are context rich and integrate several principles, i.e., the first law, ideal-gas law, kinetic theory, and adiabatic state functions.

ConclusionsDespite its simple mathematical form, the first law is not

easy for students to comprehend. By analyzing ample real-life conceptual questions, students may gradually appreciate the crucial role of the first law in thermodynamics and grasp its key concepts, particularly the notion that “work can alter internal energy of a gas system,” as suggested by Meltzer.3 Through the use of such examples, the basic physics principle can become sensible, relevant, and meaningful to students’

Hair spray

Question: When the compressed liquid in a can of hair spray is released as a mist (Fig. 2), why would the container cool down? In what ways are the explanation of this phenomenon similar to and different from the exploding bottle?

Answer: Similar to the exploding bottle, this demonstration is an adiabatic expansion process. Using the first law we see that since work is done by the hair spray in the expansion process, the internal energy of the spray decreases. However, the hair spray involves the heat of vaporization exaggerating the cooling effect. This is only a minor factor in the explod-ing bottle. Therefore, this demonstration involves both the first law and the concept of latent heat.

After some additional discussion and practice, the last demonstration is done and in-class dialogue is undertaken.

Fire syringeA fire syringe is an appealing

demonstration to further reinforce the concept of the first law. Put a small piece of tissue into the cyl-inder, press the piston forcefully, and the temperature can be raised dramatically to ignite the tissue, as shown in Fig. 3. The process is quick enough to be treated as an adiabatic process (Q = 0). Work is done on the system via the com-

pression. Thus, based on the first law, the internal energy in-creases and the temperature rises.

When hearing this demonstration explained, a few stu-dents are found to attribute the burning to the heat caused by the friction of the piston. This response indicates that when explaining the temperature variation, these students continue to seek sources of thermal energy rather than work, consistent with the “collision model” found by Rozier and Viennot.2 Although the first law is defined, and many examples and problems have been practiced, the notion of work may still be overlooked by some students. Thus, providing abundant real-life examples to highlight this counterintuitive concept is helpful.

In addition to enhancing the concept of the first law, this demonstration can also serve as an “appetizer” to initiate the derivation of adiabatic state-functions (e.g., PVγ= C, TVγ-1=

Fig. 2. Hair spray.

Fig. 3. Fire syringe.

232 The Physics Teacher ◆ Vol. 49, April 2011

daily lives. We emphasize that real-life examples or demon-strations should not only perform the role of entertainment, but provoke thinking and discussion.8,9

AcknowledgmentThis paper was supported by the National Science Council Grant NSC-97-2511-5-035-001-MY3.

References1. M. E. Loverude, C. H. Kautz, and P. R. L. Heron, “Student un-

derstanding of the first law of thermodynamics: Relating work to the adiabatic compression of an ideal gas,” Am. J. Phys. 70(2),137–148 (2002).

2. S. Rozier and L. Viennot, ‘‘Students’ reasoning in thermody-namics,’’ Int. J. Sci. Educ. 13, 159–170 (1991).

3 D. E. Meltzer, “Investigation of students’ reasoning regarding heat, work, and the first law of thermodynamics in an introduc-tory calculus-based general physics course,” Am. J. Phys. 72, 1432–1446 (2004).

4. Some students might regard white “smoke” as an indication of heating, i.e., smoke due to heating. Thus, instructors need to explicitly link the smoke (cloud) to cooling.

5. The author’s finding is consistent with Loverude et al.’s (see Ref. 1) and Rozier and Viennot’s (see Ref. 2) studies.

6. C. H. Haynm and S. C. Baird, “Adiabatic compression in a fire syringe,” Phys. Teach. 23, 101–102 (1985).

7. The problem was adopted in the 2008 final examination, with-out prior instruction. Among the 113 first-year engineering students taught by the author, the percentages of correct re-sponses in each sub-question were: (a) 38%, (b) 42%, of which 11% misused V ~ 1/ P (isothermal process) in (b).

8. M. C. Buncick, P. G. Betts, and D. D. Horgan, “Using demon-strations as a contextual road map: Enhancing course continu-ity and promoting active engagement in introductory college physics,” Int. J. Sci. Educ. 23(12), 1237–1255 (2001).

9. C. Crouch, A. P. Fagen, J. P. Callan, and E. Mazur, “Classroom demonstrations: Learning tools or entertainment?” Am. J. Phys. 72, 835–838 (2004).

Wheijen Chang is a professor at Feng-Chia University in Taiwan. She has taught introductory physics since receiving an MS from Ohio State University in 1984. Since obtaining a PhD in 2000 in science education from Waikato University, New Zealand, she has conducted research on improving teaching and learning of introductory physics.wjnchang@gmail.com

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