Cooling of Ideal Gas Reading Reflection

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Write a reading reflection on the two papers atached below. The reflection can be on one paper or something common to both papers. It should address one or more of the reading reflection prompts. Make sure it is focused and coherent (there is a a unifying theme to your reflection). The reading reflection should be around 250 words long.

Reading reflection prompts: what are the author's purpose in writing this article? What can you take from it that can be applied in your own classroom? How does the article impact your own physics content and pedagogical knowledge? What connections do you find with the other content you have encountered this week?

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In the Classroom edited by Resources for Student Assessment John Alexander University of Cincinnati Cincinnati, OH 45221 Three Forms of Energy Sigthór Pétursson Department of Natural Resource Science, University of Akureyri, 600 Akureyri, Iceland; sigthor@unak.is Thermodynamics is of fundamental importance to chemistry. Over one hundred papers in this Journal show the appreciation of this importance by the chemical community in the last five years. Reference to only a few of these papers is given here (1–9). The importance of reactions that are primarily carried out for the production of energy and the principles used to work out the quantity of energy released are well known. Of no less importance are the fundamental principles relating to entropy and the free energy of reactions to determine the spontaneity of reactions and even the equilibrium constant (10, 11). The use of the common thermodynamic equations, as presented in general chemistry courses, is relatively straightforward, even if some of the underlying concepts, covered further in more advanced physical chemistry courses, are difficult for the beginner. The modern students and practitioners of chemistry have at their disposal a vast quantity of thermodynamic data; it is therefore essential that the practical aspects of the subject are not obscured by too much theory. The authors of contemporary books on thermodynamics are aware of this as noted in recent reviews (12, 13). Calculations It is probably true that chemists are more familiar with heat energy than mechanical energy. To appreciate fully the important and common transformation of chemical energy into mechanical energy, for example in the internal combustion engine or in our bodies, it is helpful to compare the energy involved in familiar events. Three different transformations that everybody should be able to envisage are examined. The three forms of energy are described and illustrated in Figures 1–3. We may have our own feelings on which of these three events involves the greatest amount of energy, but let us work it out. Heat What is the energy needed to heat 200 g of water from 7.0 ⬚C to 37.0 ⬚C? specific heat capacity of H2O (c) = 4.184 J ∆t = 37.0 ⬚C − 7.0 ⬚C = 30.0 ⬚C mass of H2O (m) = 200 g What is the energy (heat) involved in warming 200 g of water from 7.0 °C to 37.0 °C? Remember that every time you drink a glass of cold water your body expends this quantity of heat to warm the water up to your body temperature. glass of water 200 g of water heated from 7.0 oC to 37.0 oC Figure 1. Heat. Elevation of a body against Earth’s gravitational force. What is the energy (work) needed to lift a 50.0 kg sack of cement to a height of 10.0 m? This is roughly equal to carrying a sack of cement to the third floor of a building. 50.0 kg elevated by 10.0 m against gravity, g = 9.80 m s-2 cement, 50.0 kg Figure 2. Mechanical energy. What is the work performed in expanding a cylinder by 90.0 L against an external pressure of 1.0 atm? external pressure P = 1.00 atm g᎑1 ⬚C᎑1 area = A The heat energy, q, involved is therefore: q = (m)(∆t)(c) = (200 g) × (30.0 °C) × (4.184 J g᎑1 °C᎑1) = 25104 J = 25.1 kJ 776 piston extracted against external pressure ∆V ∆ = 90.0 L Figure 3. Expansion. Journal of Chemical Education • Vol. 80 No. 7 July 2003 • JChemEd.chem.wisc.edu l In the Classroom Mechanical Energy What is the energy needed to lift a 50.0 kg sack of cement to a height of 10.0 m? The gravitational acceleration, g, is 9.80 m s᎑2. The force acting on the sack is therefore: f = (m)(g) = (50.0 kg) × (9.80 m s᎑2) = 490 kg m s᎑2 = 490 N Mechanical energy or work is by definition the product of force and displacement. The work, w, performed by displacing the sack of cement by 10.0 m against gravity is therefore: w = ( f )(l) = (490 N) × (10.0 m) = 4900 N m = 4.90 kJ Expanding Cylinder What is the work, w, performed to expand a cylinder by 90.0 L against a pressure of 1.00 atm? w = ( f )(d) = ( f )(l); where d is the displacement P = f 兾A; pressure is the force per unit area, A rearranging f = P × A, thus w = (P)(A)(l) Since (A)(l) is the change of volume, ∆V, w = (P)(∆V) w =(1.00 atm) × (90.0 L) = 90.0 atm L The unit atm L must be equivalent to energy (work). We can confirm this and convert the unit to joule by representing the pressure in SI units 1 atm = 1.013 × 105 Pa or in fundamental SI units 1 atm = 1.013 × 105 kg m᎑1 s᎑2 Thus atm L = 1.013 × 105 kg m᎑1 s᎑2 L Since L = dm3 = 10᎑3 m3, then atm L = (1.013 × 105 kg m᎑1 s᎑2) × (10᎑3 m3) = 101.3 kg m2 s᎑2 = 101.3 joule as kg m2 s᎑2 is equivalent to joule. Therefore the work done on the surroundings is: w = (90.0 atm L) × [101.3 J兾(atm L )] = 9117 J = 9.12 kJ Discussion It is interesting to compare these results, especially the energy involved in heating the water and elevating the sack of cement. It takes a reasonably fit person to carry a mass of 50.0 kg of cement to the third floor of a house. This activity could be considered a good exercise. Do that a few times every day and you would be justified in feeling that you were getting rid of a few excess Calories (capital C is used to denote nutritional calories, equal to 1000 heat calories)! The energy expended in doing this activity is, however, only 19.5% of the energy expenditure in drinking a glass of cold water. Even if we add the body weight of the person, let us say 75 kg, the energy expenditure is still only about 49% of that involved in drinking the water. We can take a more extreme case regarding the heat energy. Consider the example of a person who ingests, perhaps a bit excessively, 1 L of hot (67 ⬚C) liquid daily (coffee, tea, etc.). If that person changed to drinking 1 L of cold (7 ⬚C) water he would be expending 251 kJ per day, since he is switching from heat gain in cooling 1 L at 67 ⬚C to 37 ⬚C to heat expenditure in heating 1 L at 7 ⬚C to 37 ⬚C. Let us look at the expanding cylinder. The thermodynamic importance of the expansion or compression of gases, when reactions take place at constant pressure, is familiar. Keeping in mind Torricelli’s barometer and remembering that mercury has a density of 13.5 g兾cm3, this is equivalent to lifting [(90.0 dm3) × (1000 cm3兾dm3) × (13.5 g兾cm3)] = 1.22 × 106 g = 1.22 × 103 kg or 1.22 metric tons to a height of 760 mm or 0.760 m. This is best appreciated if we think in terms of extracting a piston with a radius of 19.42 cm or 1.942 dm, by 0.760 m or 7.60 dm. The pressure is 1 atm or 760 mm Hg and the volume swept by the process is (1.942 dm)2 × π × 7.60 dm = 90.0 dm3 or 90.0 L. The weight of the mercury is about 24 times the weight of the sack of cement and a much larger force is needed to perform this task, but the displacement is also much smaller. Nutritional Energy Comparison Since two of the examples above led us into comparisons relevant to nutrition we can develop that theme very briefly. First it must be stressed that these examples are not illustrated to trivialize the need for healthful physical activity because we need to exercise our muscles and drinking cold water is not the best way to accomplish that. However the comparison does draw attention to a worthwhile and economical nutritional fact. Consider that the basal metabolic rate—the energy expenditure when lying at complete rest— of an average middle-aged man (180-cm high, 75 kg) is about 7100 kJ (about 1700 kcal or Calories) per 24 hours. The total energy use of the same man doing light physical work during the day is about 8400 kJ (about 2000 Calories) per 24 hours. Thus the energy requirement for physical activity for the man is about 1300 kJ or 310 Calories (14). The extra 251 kJ of energy the man would utilize by switching from drinking a liter of hot drinks to drinking a liter of cold water is about 20% of the energy needed for light physical activity. Literature Cited 1. Mills, Pamela; Sweeney, William V.; Cieniewicz, Waldemar. J. Chem. Educ. 2001, 78, 1360–1361. 2. Weiss, Hilton M. J. Chem. Educ. 2001, 78, 1362–1364. 3. Bartell, Lawrence S. J. Chem. Educ. 2001, 78, 1059–1067. JChemEd.chem.wisc.edu • Vol. 80 No. 7 July 2003 • Journal of Chemical Education 777 In the Classroom 4. Bartell, Lawrence S. J. Chem. Educ. 2001, 78, 1067–1069. 5. Wadsö, Lars; Smith, Allan L.; Shirazi, Hamid; Mulligan, S. Rose; Hofelich, Thomas. J. Chem. Educ. 2001, 78, 1080– 1086. 6. Jacobson, Nathan. J. Chem. Educ. 2001, 78, 814–819. 7. Howard, Irmgard K. J. Chem. Educ. 2001, 78, 505–508. 8. Jansen, Michael P. J. Chem. Educ. 2000, 77, 1578–1579. 9. Jensen, William B. J. Chem. Educ. 2000, 77, 713–717. 10. Masterton, W. L.; Hurley, C. N. Chemistry, Principles and 778 11. 12. 13. 14. Reactions, 4th ed.; Harcourt College Publishers: Orlando, FL, 2001; Chapters 8, 17. Noggle, J. H. Physical Chemistry, 3rd ed.; Harper Collins: New York, 1996; Chapters 2, 3. Gislason, Eric A. J. Chem. Educ. 2001, 78, 1186. Minderhout, Vicky. J. Chem. Educ. 2001, 78, 457. Passmore, R.; Eastwood, M. A. Davidson and Passmore Human Nutrition and Dietetics; Churchill Livingstone: Edinburgh, Scotland, UK, 1986; Chapter 3. Journal of Chemical Education • Vol. 80 No. 7 July 2003 • JChemEd.chem.wisc.edu Student understanding of the ideal gas law, Part II: A microscopic perspective Christian H. Kautz, Paula R. L. Heron, Peter S. Shaffer, and Lillian C. McDermott Citation: American Journal of Physics 73, 1064 (2005); doi: 10.1119/1.2060715 View online: http://dx.doi.org/10.1119/1.2060715 View Table of Contents: http://scitation.aip.org/content/aapt/journal/ajp/73/11?ver=pdfcov Published by the American Association of Physics Teachers Articles you may be interested in Comparing student conceptual understanding of thermodynamics in physics and engineering AIP Conf. Proc. 1513, 102 (2013); 10.1063/1.4789662 Cooling of an ideal gas by rapid expansion Am. J. Phys. 74, 54 (2006); 10.1119/1.2110547 Student understanding of the ideal gas law, Part I: A macroscopic perspective Am. J. Phys. 73, 1055 (2005); 10.1119/1.2049286 Irreversible Adiabatic Compression of an Ideal Gas Phys. Teach. 41, 450 (2003); 10.1119/1.1625202 Student understanding of the first law of thermodynamics: Relating work to the adiabatic compression of an ideal gas Am. J. Phys. 70, 137 (2002); 10.1119/1.1417532 This article is copyrighted as indicated in the article. Reuse of AAPT content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 68.232.23.162 On: Fri, 12 Feb 2016 17:14:09 Student understanding of the ideal gas law, Part II: A microscopic perspective Christian H. Kautz,a兲 Paula R. L. Heron, Peter S. Shaffer, and Lillian C. McDermott Department of Physics, University of Washington, Seattle, Washington 98195 共Received 6 April 2005; accepted 29 July 2005兲 Evidence from research indicates that many undergraduate science and engineering majors have seriously flawed microscopic models for the pressure and temperature in an ideal gas. In the investigation described in this paper, some common mistaken ideas about microscopic processes were identified. Examples illustrate the use of this information in the design of instruction that helped improve student understanding of the ideal gas law, especially its substance independence. Some broader implications of this study for the teaching of thermal physics are noted. © 2005 American Association of Physics Teachers. 关DOI: 10.1119/1.2060715兴 I. INTRODUCTION This paper is the second of two that report on an investigation of student understanding of the ideal gas law 共PV = nRT兲.1 The emphasis in the first is on the macroscopic variables and their relationship to one another through the ideal gas law.2 We found that many of the student difficulties that we identified at the macroscopic level seem to be rooted in incorrect, or incomplete, microscopic models. 共The use of the term model to characterize some related ideas does not mean that students have the robust, self-consistent conceptual structure that physicists associate with this term.兲 In this paper, we describe some common student models, and discuss how the insights gained from this study have guided the development and assessment of tutorials to improve student learning.3 The research, which was conducted by the Physics Education Group at the University of Washington 共UW兲, involved more than 1000 students. The participants were mostly undergraduate science and engineering majors enrolled in introductory algebra- or calculus-based physics courses at UW and other universities and a sophomore-level thermal physics course at UW. Most of these students had taken, or were concurrently taking, introductory chemistry. We obtained additional information from graduate students who were pursuing a Ph.D. in physics at UW. The ideal gas law and the kinetic theory of gases are covered in many introductory physics and chemistry courses and, at a somewhat more advanced level, in thermal physics courses. Often, relatively little time is spent on a macroscopic perspective. The emphasis is mostly on the microscopic model. The underlying assumptions are often stated explicitly and presented in detail. An expression for pressure is derived in terms of the number of particles, their mass and average speed, and the volume of the gas. Temperature is identified with the average kinetic energy of the particles. For most students, this instructional sequence is not the first exposure to the microscopic view of a gas. They are usually aware of the particulate nature of matter before they take an undergraduate science course. II. METHODS OF INVESTIGATION The present study builds on related research in which we examined the ability of students to apply the first law of thermodynamics and the ideal gas law.2,4 We began the in- vestigation with individual demonstration interviews.5 As these progressed, misinterpretations of microscopic processes seemed to underlie many of the errors that the students made. To verify this impression, we conducted additional interviews in which we asked students from the thermal physics course to respond to tasks specifically designed to elicit their ideas about microscopic processes in an ideal gas. For example, students were asked to compare the number of molecules in three hypothetical identical balloons, each filled with a different ideal gas, but all with the same volume and temperature. Fewer than half of the students realized that the pressure in all three balloons must be the same and, hence, the number of molecules must be equal. Most assumed that the size, mass, and structure of the gas particles required different values for the pressure or number of molecules. The analysis of responses to the interview tasks yielded information about the microscopic models that students commonly use to predict and explain the behavior of ideal gases. We found that these models often are so seriously flawed that they inhibit the development of a functional understanding of important concepts in thermal physics, including operational definitions of pressure and temperature, conservation of energy as expressed by the first law of thermodynamics, and substance independence of the ideal gas law. These findings laid the foundation for the development of written problems that enabled us to explore in greater detail some of the difficulties that we had identified and also to estimate their prevalence. The problems were administered on course examinations or on nongraded written quizzes. All involved qualitative questions for which explanations of reasoning were required. In presenting the data, we have combined the results from multiple sections of the same course, rounded the numbers of students, and given the percentages of correct and incorrect responses to the nearest 5%. Our research methods and justification for this approach are discussed in greater detail in Ref. 2. III. PROBLEMS DESIGNED TO PROBE STUDENT UNDERSTANDING We designed three types of problems to probe student understanding of the ideal gas law from a microscopic perspective. Some involved several tasks. Unless otherwise noted, they were administered after standard instruction, but before 1064 Am. J. Phys. 73 共11兲, November 2005 http://aapt.org/ajp © 2005 American Association of Physics Teachers 1064 This article is copyrighted as indicated in the article. Reuse of AAPT content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 68.232.23.162 On: Fri, 12 Feb 2016 17:14:09 any research-based instruction. Thus, they can also be considered as pretests for the type of instruction that we will describe. For each problem we give a proper response and note the prevalence of correct answers. A more detailed analysis follows later. A. Isobaric expansion or compression problems In one set of problems, students were asked about microscopic aspects of an isobaric process. In each case, a fixed amount of an ideal gas undergoes a specified change in volume at constant pressure. Usually the students were asked to compare the initial and final equilibrium states in order to avoid the issue of whether the process could be considered quasi-static. Students were sometimes first asked to sketch the process in a PV diagram. Most drew correct diagrams. 1. Kinetic-energy task The students were asked whether the average kinetic energy per molecule increases, decreases, or remains the same as the result of an isobaric expansion. To answer correctly the students could first recognize that the increase in volume at constant pressure must correspond to an increase in temperature. The average kinetic energy per molecule is proportional to the temperature, which therefore also increases. Alternatively they could realize that an expansion results in a decrease in number density. Therefore, the average speed of the gas particles must increase to maintain the same pressure. Consequently, the average kinetic energy 共and hence temperature兲 must increase. About 70% of the introductory students 关N ⬃ 155兴 and about 80% of the thermal physics students 关N ⬃ 40兴 recognized that the average kinetic energy increases. Many gave the right answers for a variety of incorrect reasons. On a similar task involving a compression, about 55% of the introductory students realized that the kinetic energy decreases 关N ⬃ 60兴. 2. Change-in-momentum and particle-flux tasks Students were also asked whether the average change in momentum of a single particle as the result of a collision with a wall would be different after the isobaric expansion. This question, which is admittedly difficult, was not asked primarily to assess understanding, but rather to help the students think in terms of a microscopic model in which gas pressure can be expressed as the product of the average change in momentum per collision of a single particle and the particle flux incident on the wall.6 In the second task, the students were asked whether the number of particles incident on a container wall per unit time interval per unit area 共the particle flux兲 would be greater than, less than, or equal to the number before the expansion.7 To answer this question, students could recognize that in the standard elementary microscopic treatment of an ideal gas, elastic collisions are assumed.8 Therefore, the average change in momentum of a particle in a single collision is proportional to the average initial momentum of the particle, which in turn is a 共monotonically increasing兲 function of the temperature. In the process described, the average change in momentum increases due to the increase in the temperature. Because the product of the average change in momentum and the particle flux remains constant in an isobaric process, the particle flux must be less after the expansion. In the introductory co ...
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Cooling of ideal gas
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