DIDACTIfen - Unité de Recherche en Didactique et Formation des Enseignants - ULiège
Disciplines :
Chemistry Education & instruction
Author, co-author :
Natalis, Vincent ; Université de Liège - ULiège > Unités de recherche interfacultaires > Unité de recherche en didactique et formation des enseignants (DIDACTIfen)
Leyh, Bernard ; Université de Liège - ULiège > Département de chimie (sciences) > Laboratoire de dynamique moléculaire
Language :
English
Title :
Improving the teaching of entropy and the second law of thermodynamics : a systematic review with meta-analysis
Alternative titles :
[fr] Améliorer l'enseignement de l'entropie et de la deuxième loi de la thermodynamique : une revue systématique avec méta-analyse
Akbulut F. and Altun Y., (2020). A Holistic Approach to Entropy in Science Education, Int. Online J. Sci. Educ., 7(4), 1913–1932.
Aledo J. C., (2007), Coupled reactions versus connected reactions: coupling concepts with terms, Biochem. Mol. Biol. Educ., 35(2), 85–88, DOI: 10.1002/bmb.5.
Ashbaugh H. S., (2010), Ehrenfest’s Lottery—Time and Entropy Maximization, Chem. Eng. Educ., 44(3), 229–235.
Atarés L., Canet M. J., Trujillo M., Benlloch-Dualde J. V., Paricio Royo J. and Fernandez-March A., (2021), Helping Pregraduate Students Reach Deep Understanding of the Second Law of Thermodynamics, Educ. Sci., 11(9), 539, DOI: 10.3390/ educsci11090539.
Bachelard G., (1938), La formation de l’esprit scientifique [The formation of the scientific mind], Vrin.
Baierlein R., (1994), Entropy and the second law: a pedagogical alternative, Am. J. Phys., 62(1), 15–26, DOI: 10.1119/1.17732.
Bain K., Moon A., Mack M. R. and Towns M. H., (2014), A review of research on the teaching and learning of thermodynamics at the university level, Chem. Educ. Res. Pract., 15(3), 320–335, DOI: 10.1039/C4RP00011K.
Ben-Naim A., (2011), Entropy: Order or Information, J. Chem. Educ., 88(5), 594–596, DOI: 10.1021/ed100922x.
Ben-Naim A., (2012), Entropy and the Second Law: Interpretation and Misss-Interpretationsss, World Scientific Publishing.
Bennett J. M. and Sözbilir M., (2007), A Study of Turkish Chemistry Undergraduates’ Understanding of Entropy, J. Chem. Educ., 84(7), 1204–1208, DOI: 10.1021/ed084p1204.
Ben-Zvi R., (1999), Non-science oriented students and the second law of thermodynamics, Int. J. Sci. Educ., 21(12), 1251–1267, DOI: 10.1080/095006999290057.
Bhattacharyya D. and Dawlaty J. M., (2019a), Teaching Entropy from Phase Space Perspective: Connecting the Statistical and Thermodynamic Views Using a Simple One-Dimensional Model, J. Chem. Educ., 96(10), 2208–2216, DOI: 10.1021/acs.jchemed.9b00134.
Bhattacharyya D. and Dawlaty J. M., (2019b), Teaching Entropy from Phase Space Perspective: Connecting the Statistical and Thermodynamic Views Using a Simple One-Dimensional Model, J. Chem. Educ., 96(10), 2208–2216, DOI: 10.1021/acs.jchemed.9b00134.
Bindel T. H., (1995), Solution-Phase Thermodynamics: A ‘‘Spontaneity’’ Activity, J. Chem. Educ., 72(1), 34–35, DOI: 10.1021/ ed072p34.
Bindel T. H., (2004), Teaching Entropy Analysis in the First-Year High School Course and Beyond, J. Chem. Educ., 81(11), 1585–1594, DOI: 10.1021/ed081p1585.
Bindel T. H., (2007), Discovering the Thermodynamics of Simultaneous Equilibria. An Entropy Analysis Activity Involving Consecutive Equilibria, J. Chem. Educ., 84(3), 449–452, DOI: 10.1021/ed084p449.
Bindel T. H., (2010), Understanding Chemical Equilibrium Using Entropy Analysis: The Relationship Between DStot (sys1) and the Equilibrium Constant, J. Chem. Educ., 87(7), 694–699, DOI: 10.1021/ed100192q.
Black P. J., Davies P. and Ogborn J. M., (1971), A Quantum Shuffling Game for Teaching Statistical Mechanics, Am. J. Phys., 39(10), 1154–1159, DOI: 10.1119/1.1976594.
Brady K. T., (1989), Shine some light on entropy of mixing, J. Chem. Educ., 66(4), 339–341, DOI: 10.1021/ed066p339.
Brosnan T., (1989), Teaching chemistry using spreadsheets—I: Equilibrium Thermodynamics, School Sci. Rev., 70(252), 39–47.
Canagaratna S. G., (2008), Zeroth Law, Entropy, Equilibrium, and All That, J. Chem. Educ., 85(5), 732–736, DOI: 10.1021/ ed085p732.
Carson E. M. and Watson J. R., (2002), Undergraduate Students’ Understandings of Entropy and Gibbs Free Energy, Univ. Chem. Educ., 6, 4–12.
Cartier S. F., (2009), An Integrated, Statistical Molecular Approach to the Physical Chemistry Curriculum, J. Chem. Educ., 86(12), 1397–1402, DOI: 10.1021/ed086p1397.
Castellón E., (2014), Application of the Second Law of Thermodynamics To Explain the Working of Toys, J. Chem. Educ., 91(5), 687–691, DOI: 10.1021/ed400085z.
Chinaka T. W., (2021), Introducing the second law of thermodynamics using Legitimation Code Theory among first year chemistry students, Cypriot J. Educ. Sci., 16(3), 981–994, DOI: 10.18844/cjes.v16i3.5772.
Christensen W. M., Meltzer D. E. and Ogilvie C. A., (2009), Student ideas regarding entropy and the second law of thermodynamics in an introductory physics course, Am. J. Phys., 77(10), 907–917, DOI: 10.1119/1.3167357.
Cochran M. J. and Heron P. R. L., (2006), Development and assessment of research-based tutorials on heat engines and the second law of thermodynamics, Am. J. Phys., 74(8), 734–741, DOI: 10.1119/1.2198889.
Cohen J., (1988), Statistical Power Analysis for the Behavioral Sciences, Lawrence Erlbaum Associates.
Craig N. C., (1988), Entropy analyses of four familiar processes, J. Chem. Educ., 65(9), 760–764, DOI: 10.1021/ed065p760.
Dachet D., (2024), Umbrella Review: De sa méthodologie aux considérations méthodologiques relatives à son application dans le champ des sciences de l’Éducation [Umbrella Review: From its methodology to methodological considerations relating to its application in the field of educational sciences] [Doctoral dissertation, University of Liège (Belgium)].
De Abreu R. and Guerra V., (2012), Introducing thermodynamics through energy and entropy, Am. J. Phys., 80(7), 627–637, DOI: 10.1119/1.3698160.
Donnelly J. and Hernández F. E., (2018), Fusing a reversed and informal learning scheme and space: student perceptions of active learning in physical chemistry, Chem. Educ. Res. Practice, 19(2), 520–532, DOI: 10.1039/C7RP00186J.
Dreyfus B. W., Geller B. D., Meltzer D. E. and Sawtelle V., (2015), Resource Letter TTSM-1: Teaching Thermodynamics and Statistical Mechanics in Introductory Physics, Chemistry, and Biology, Am. J. Phys., 83(1), 5–21, DOI: 10.1119/1.4891673.
Eisen L., Marano N. and Glazier S., (2014), Activity-Based Approach For Teaching Aqueous Solubility, Energy, and Entropy, J. Chem. Educ., 91(4), 484–491, DOI: 10.1021/ ed4005563.
Ellis F. B. and Ellis D. C., (2008), An Experimental Approach to Teaching and Learning Elementary Statistical Mechanics, J. Chem. Educ., 85(1), 78–82, DOI: 10.1021/ed085p78.
Firetto C. M., Van Meter P. N., Kottmeyer A. M., Turns S. R. and Litzinger T. A., (2021), An extension of the Thermodynamics Conceptual Reasoning Inventory (TCRI): measuring undergraduate students’ understanding of introductory thermodynamics concepts, Int. J. Sci. Educ., 43(15), 2555–2576, DOI: 10.1080/09500693.2021.1975847.
Fuchs H. U., (1987), Entropy in the teaching of introductory thermodynamics, Am. J. Phys., 55(3), 215–219, DOI: 10.1119/ 1.15216.
Gary R. K., (2004), The Concentration Dependence of the DS Term in the Gibbs Free Energy Function: Application to Reversible Reactions in Biochemistry, J. Chem. Educ., 81(11), 1599–1604, DOI: 10.1021/ed081p1599.
Geller B. D., Dreyfus B. W., Gouvea J., Sawtelle V., Turpen C. and Redish E. F., (2014), Entropy and spontaneity in an introductory physics course for life science students, Am. J. Phys., 82(5), 394–402, DOI: 10.1119/1.4870389.
Gislason E. A. and Craig N. C., (2013), Criteria for Spontaneous Processes Derived from the Global Point of View, J. Chem. Educ., 90(5), 584–590, DOI: 10.1021/ed300570u.
Grassian V. H., Meyer G., Abruña H., Coates G. W., Achenie L. E., Allison T., Brunschwig B., Ferry J. and Garcia-Garibay M., (2007), Viewpoint: Chemistry for a Sustainable Future, Environ. Sci. Technol., 41(14), 4840–4846, DOI: 10.1021/ es0725798.
Gwet K., (2002), Kappa Statistic is not Satisfactory for Assessing the Extent of Agreement Between Raters, https://api.semanticscholar.org/CorpusID:140400911.
Haber-Schaim U., (1983), The role of the second law of thermodynamics in energy education, Phys. Teacher, 21(17), 17–20, DOI: 10.1119/1.2341180.
Haglund J., (2017), Good Use of a ‘Bad’ Metaphor: Entropy as Disorder, Sci. Educ., 26(3–4), 205–214, DOI: 10.1007/s11191-017-9892-4.
Haglund J. and Jeppsson F., (2012), Using self-generated analogies in teaching of thermodynamics, J. Res. Sci. Teach., 49(7), 898–921, DOI: 10.1002/tea.21025.
Haglund J. and Jeppsson F., (2014), Confronting Conceptual Challenges in Thermodynamics by Use of Self-Generated Analogies, Sci. Educ., 23(7), 1505–1529, DOI: 10.1007/s11191-013-9630-5.
Hattie J., (2008), Visible Learning. A Synthesis of Over 800 Meta-Analyses Relating to Achievement, Routledge.
Hayes J. C. and Kraemer D. J. M., (2017), Grounded understanding of abstract concepts: the case of STEM learning, Cogn. Res.: Princ. Implic., 2(1), 7, DOI: 10.1186/s41235-016-0046-z.
Hazelhurst T. A., (1931), Exorcising a Spectre: Entropy. J. Chem. Educ., 8(3), 498–503.
Hill C. J., Bloom H. S., Black A. R. and Lipsey M. W., (2008), Empirical Benchmarks for Interpreting Effect Sizes in Research, Child Dev. Perspectives, 2(3), 172–177, DOI: 10.1111/j.1750-8606.2008.00061.x.
Iyengar S. S. and deSouza R. T., (2014), Teaching Thermodynamics and Kinetics to Advanced General Chemistry Students and to Upper-Level Undergraduate Students Using PV Diagrams, J. Chem. Educ., 91(1), 74–83, DOI: 10.1021/ed400480t.
Jadrich J. and Bruxvoort C., (2010), Investigating Diffusion and Entropy with Carbon Dioxide-Filled Balloons, Phys. Teacher, 48(6), 388–390, DOI: 10.1119/1.3479716.
Jameson G. and Brüschweiler R., (2020), Active Learning Approach for an Intuitive Understanding of the Boltzmann Distribution by Basic Computer Simulations, J. Chem. Educ., 97(10), 3910–3913, DOI: 10.1021/acs.jchemed.0c00559.
Jeppsson, F., Haglund, J., Amin, T. G. and Strömdahl, H., (2013), Exploring the Use of Conceptual Metaphors in Solving Problems on Entropy, J. Learn. Sci., 22(1), 70–120, DOI: 10.1080/10508406.2012.691926.
Johnstone A. H., (1991), Why is science difficult to learn? Things are seldom what they seem, J. Comput. Assisted Learn., 7(2), 75–83, DOI: 10.1111/j.1365-2729.1991.tb00230.x.
Jungermann A. H., (2006), Entropy and the Shelf Model: A Quantum Physical Approach to a Physical Property, J. Chem. Educ., 83(11), 1686, DOI: 10.1021/ed083p1686.
Kang D.-Y., Liou K.-H. and Chang W.-L., (2015), Investigating Friction as a Main Source of Entropy Generation in the Expansion of Confined Gas in a Piston-and-Cylinder Device, J. Chem. Educ., 92(10), 1667–1671, DOI: 10.1021/acs.jchemed. 5b00361.
Kattmann U., (2018), A biologist’s musing on teaching about entropy and energy: towards a better understanding of life processes, School Sci. Rev., 99(368), 61–68.
Kaufman R. and Leff H., (2022), Interdependence of the First and Second Laws of Thermodynamics, Phys. Teacher, 60(6), 501–503, DOI: 10.1119/5.0074493.
Keifer D., (2019), Enthalpy and the Second Law of Thermodynamics, J. Chem. Educ., 96(7), 1407–1411, DOI: 10.1021/ acs.jchemed.9b00326.
Kiatgamolchai S., (2015), A Graphical Proof of the Positive Entropy Change in Heat Transfer Between Two Objects, Phys. Teacher, 53(2), 95–96, DOI: 10.1119/1.4905807.
Kincanon E., (2013), How I teach the second law of thermodynamics, Phys. Educ., 48(4), 491–496, DOI: 10.1088/0031-9120/48/4/491.
Kozliak E. I., (2004), Introduction of Entropy via the Boltzmann Distribution in Undergraduate Physical Chemistry: A Molecular Approach, J. Chem. Educ., 81(11), 1595–1598, DOI: 10.1021/ed081p1595.
Kozliak E. I., (2009), Overcoming Misconceptions about Configurational Entropy in Condensed Phases, J. Chem. Educ., 86(9), 1063–1068, DOI: 10.1021/ed086p1063.
Kozliak E. I., (2014), Entropy of Mixing of Distinguishable Particles, J. Chem. Educ., 91(6), 834–838, DOI: 10.1021/ ed4007666.
Kozliak E. I. and Lambert F. L., (2005), ‘‘Order-to-Disorder’’ for Entropy Change? Consider the Numbers! Chem. Educ., 10, 24–25, DOI: 10.1333/s00897050864a.
Laird B. B., (1999), Entropy, Disorder, and Freezing, J. Chem. Educ., 76(10), 1388–1390, DOI: 10.1021/ed076p1388.
Lambert F. L., (1999), Shuffled Cards, Messy Desks, and Disorderly Dorm Rooms – Examples of Entropy Increase? Nonsense! J. Chem. Educ., 76(10), 1385–1387, DOI: 10.1021/ed076p1385.
Lambert F. L., (2002), Entropy Is Simple, Qualitatively, J. Chem. Educ., 79(10), 1241–1246, DOI: 10.1021/ed079p1241.
Lambert F. L., (2007), Configurational Entropy Revisited, J. Chem. Educ., 84(9), 1548–1550, DOI: 10.1021/ed084p1548.
Lambert F. L., (2011), The Conceptual Meaning of Thermodynamic Entropy in the 21st Century, Int. Res. J. Pure Appl. Chem., 1(3), 65–68, DOI: 10.9734/IRJPAC/2011/679.
Lambert F. L. and Leff H. S., (2009), The Correlation of Standard Entropy with Enthalpy Supplied from 0 to 298.15 K, J. Chem. Educ., 86(1), 94–98, DOI: 10.1021/ed086p94.
Landis J. R. and Koch G. G., (1977), The Measurement of Observer Agreement for Categorical Data, Biometrics, 33(1), 159–174, DOI: 10.2307/2529310.
Langbeheim E., Abrashkin A., Steiner A., Edri H., Safran S. and Yerushalmi E., (2020), Shifting the learning gears: redesigning a project-based course on soft matter through the perspective of constructionism, Phys. Rev. Phys. Educ. Res., 16(2), 020147, DOI: 10.1103/PhysRevPhysEducRes.16.020147.
Langbeheim E., Safran S. A. and Yerushalmi E., (2014), Visualizing the Entropy Change of a Thermal Reservoir, J. Chem. Educ., 91(3), 380–385, DOI: 10.1021/ed400180w.
Lechner J. H., (1999), Visualizing Entropy, J. Chem. Educ., 76(10), 1382–1385, DOI: 10.1021/ed076p1382.
Leff H. S., (1996), Thermodynamic entropy: The spreading and sharing of energy, Am. J. Phys., 64, 1261–1271, DOI: 10.1119/ 1.18389.
Leff H. S., (2007), Entropy, Its Language, and Interpretation, Found. Phys., 37(12), 1744–1766, DOI: 10.1007/s10701-007-9163-3.
Leff H. S., (2012), Removing the Mystery of Entropy and Thermodynamics—Part I, Phys. Teacher, 50(1), 28–31, DOI: 10.1119/1.3670080.
Leff H. S., (2020), Energy and Entropy: A Dynamic Duo, CRC Press.
Leinonen R., Asikainen M. A. and Hirvonen P. E., (2015), Grasping the second law of thermodynamics at university: the consistency of macroscopic and microscopic explanations, Phys. Rev. Spec. Top.–Phys. Educ. Res., 11(2), 020122, DOI: 10.1103/PhysRevSTPER.11.020122.
Makahinda T. and Mawuntu V. J., (2023), Development of Thermodynamics Learning With Empirical Approach and Portfolio Assessment Techniques, Studies Learn. Teach., 4(2), 285–295, DOI: 10.46627/silet.v4i2.263.
Mayorga L. S., López M. J. and Becker W. M., (2012), Molecular Thermodynamics for Cell Biology as Taught with Boxes, CBE—Life Sci. Educ., 11(1), 31–38, DOI: 10.1187/cbe.11-07-0053.
Michalek B. and Hanson R. M., (2006), Give Them Money: The Boltzmann Game, a Classroom or Laboratory Activity Modeling Entropy Changes and the Distribution of Energy in Chemical Systems, J. Chem. Educ., 83(4), 581–588, DOI: 10.1021/ed083p581.
Moore T., (2022), Connecting Energy Dispersal and the Classical Definition of Entropy, Chem. Eng. Educ., 56(3), 175–180.
Moore T. A. and Schroeder D. V., (1997), A different approach to introducing statistical mechanics, Am. J. Phys., 65(1), 26–36, DOI: 10.1119/1.18490.
Morris, S. B., (2008), Estimating Effect Sizes From Pretest-Posttest-Control Group Designs, Org. Res. Methods, 11(2), 364–386, DOI: 10.1177/1094428106291059.
Muller E. A., (2012), What Carnot’s Father Taught His Son About Thermodynamics, Chem. Eng. Educ., 46(3), 165–170.
Munakata M., Vaidya A. and Vanderklein D., (2022), Interdisciplinary Lessons on Energy and Entropy, J. College Sci. Teach., 51(5), 10–15, DOI: 10.1080/0047231X.2022.12290576.
Novak I., (2003), The Microscopic Statement of the Second Law of Thermodynamics, J. Chem. Educ., 80(12), 1428–1431, DOI: 10.1021/ed080p1428.
Page M. J., McKenzie J. E., Bossuyt P. M., Boutron I., Hoffmann T. C., Mulrow C. D., Shamseer L., Tetzlaff J. M., Akl E. A., Brennan S. E., Chou R., Glanville J., Grimshaw J. M., Hróbjartsson A., Lalu M. M., Li T., Loder E. W., Mayo-Wilson E., McDonald S., McGuinness L. A., Stewart L. A., Thomas J., Tricco A. C., Welch V. A., Whiting P. and Moher D., (2021), The PRISMA 2020 statement: an updated guideline for reporting systematic reviews, BMJ, 372(71), DOI: 10.1136/bmj.n71.
Partanen L., (2016), Student oriented approaches in the teaching of thermodynamics at universities – developing an effective course structure, Chem. Educ. Res. Practice, 17(4), 766–787, DOI: 10.1039/C6RP00049E.
Phillips J. A., (2016), The Macro and Micro of it Is that Entropy Is the Spread of Energy, Phys. Teacher, 54(6), 344–347, DOI: 10.1119/1.4961175.
Pirker J., Gutl C. and Astatke Y., (2015), Enhancing online and mobile experimentations using gamification strategies, 2015 3rd Experiment International Conference (Exp.at’15), 224–229, DOI: 10.1109/EXPAT.2015.7463270.
Plumb R. C., (1964), Teaching the entropy concept, J. Chem. Educ., 41(5), 254–256, DOI: 10.1021/ed041p254.
Poggi V., Miceli C. and Testa I., (2017), Teaching energy using an integrated science approach, Phys. Educ., 52(1), 015018, DOI: 10.1088/1361-6552/52/1/015018.
Read J. R. and Kable S. H., (2007), Educational analysis of the first year chemistry experiment ‘Thermodynamics Think-In’: An ACELL experiment, Chem. Educ. Res. Pract., 8(2), 255–273, DOI: 10.1039/B6RP90034H.
Rodriguez J.-M. G., Nardo J. E., Finkenstaedt-Quinn S. A. and Watts F. M., (2023), The use of frameworks in chemistry education research, Chem. Educ. Res. Practice, 24(4), 1109–1126, DOI: 10.1039/D3RP00149K.
Rogers B. A. and Zhang Y., (2020), Project-Based Experiment in a Physical Chemistry Teaching Laboratory: Ion Effects on Caffeine Partitioning Thermodynamics, J. Chem. Educ., 97(11), 4173–4178, DOI: 10.1021/acs.jchemed.0c00961.
Ross K., (1988), Matter scatter and energy anarchy. The Second Law of Thermodynamics is simply common experience, Sch. Sci. Rev., 69(248), 438–445.
Salagaram T. and Chetty N., (2011), Enhancing the understanding of entropy through computation, Am. J. Phys., 79(11), 1127–1132, DOI: 10.1119/1.3623416.
Samuelsson C. R., Elmgren M., Xie C. and Haglund J., (2019), Going through a phase: infrared cameras in a teaching sequence on evaporation and condensation, Am. J. Phys., 87(7), 577–582, DOI: 10.1119/1.5110665.
Schoepf D. C., (2002), A statistical development of entropy for the introductory physics course, Am. J. Phys., 70(2), 128–136, DOI: 10.1119/1.1419097.
Schwedler S. and Kaldewey M., (2020), Linking the submicroscopic and symbolic level in physical chemistry: how voluntary simulation-based learning activities foster first-year university students’ conceptual understanding, Chem. Educ. Res. Practice, 21(4), 1132–1147, DOI: 10.1039/C9RP00211A.
Souza J. D., Passos C. G. and Netz P. A., (2023), Exploring Bachelard’s Epistemological Obstacles in Physical Chemistry Textbooks: The Case of Thermodynamics Concepts, Acta Sci., 25(5), 30–58, DOI: 10.17648/acta.scientiae.7781.
Sözbilir M., (2004), What Makes Physical Chemistry Difficult? Perceptions of Turkish Chemistry Undergraduates and Lecturers, J. Chem. Educ., 81(4), 573–578, DOI: 10.1021/ ed081p573.
Spencer J., Moog R. and Gillespie R., (1996), Demystifying Introductory Chemistry. Part 4. An Approach to Reaction Thermodynamics through Enthalpies, Entropies, and Free Energies of Atomization, J. Chem. Educ., 73(7), 631–636, DOI: 10.1021/ed073p631.
Sreenivasulu B. and Subramaniam R., (2013), University Students’ Understanding of Chemical Thermodynamics, Int. J. Sci. Educ., 35(4), 601–635, DOI: 10.1080/09500693. 2012.683460.
Strnad J., (1984), The second law of thermodynamics in a historical setting, Phys. Educ., 19, 94–100, DOI: 10.1088/0031-9120/19/2/317.
Strong L. E. and Halliwell H. F., (1970), An alternative to free energy for undergraduate instruction, J. Chem. Educ., 47(5), 347–352, DOI: 10.1021/ed047p347.
Styer D., (2019), Entropy as Disorder: History of a Misconception, Phys. Teacher, 57(7), 454–458, DOI: 10.1119/1.5126822.
Styer D. F., (2000), Insight into entropy, Am. J. Phys., 68(12), 1090–1096, DOI: 10.1119/1.1287353.
Taber K. S., (2013), Revisiting the chemistry triplet: drawing upon the nature of chemical knowledge and the psychology of learning to inform chemistry education, Chem. Educ. Res. Practice, 14(2), 156–168, DOI: 10.1039/C3RP00012E.
Talanquer V., (2011), Macro, Submicro, and Symbolic: the many faces of the chemistry ‘‘triplet’’, Int. J. Sci. Educ., 33(2), 179–195, DOI: 10.1080/09500690903386435.
Teichert M. A. and Stacy A. M., (2002), Promoting understanding of chemical bonding and spontaneity through student explanation and integration of ideas, J. Res. Sci. Teach., 39(6), 464–496, DOI: 10.1002/tea.10033.
Tro N., (2019), Chemistry: A Molecular Approach, Financial Times Prentice Hall.
Tsaparlis G., (2007), Teaching and Learning Physical Chemistry: A Review of Educational Research, Advances in Teaching Physical Chemistry, American Chemical Society, vol. 973, pp. 75–112.
Tsaparlis G., (2016), The logical and psychological structure of physical chemistry and its relevance to graduate students’ opinions about the difficulties of the major areas of the subject, Chem. Educ. Res. Practice, 17(2), 320–336, DOI: 10.1039/C5RP00203F.
Velasco J., Buteler L., Briozzo C. and Coleoni E., (2022), Learning entropy among peers through the lens of coordination class theory, Phys. Rev. Phys. Educ. Res., 18(1), 010127, DOI: 10.1103/PhysRevPhysEducRes.18.010127.
Volfson A., Eshach H. and Ben-Abu Y., (2019), Introducing the idea of entropy to the ontological category shift theory for conceptual change: the case of heat and sound, Phys. Rev. Phys. Educ. Res., 15(1), 010143, DOI: 10.1103/PhysRevPhys EducRes.15.010143.
software What Works Clearinghouse Procedures and Standards Handbook, Version 5.0., (2022), U.S. Department of Education.
Williams D. and Glasser D., (1991), An Introduction to Equilibrium Thermodynamics. A Rational Approach to Its Teaching. Part 2: Internal Energy, Entropy, and Temperature, Chem. Eng. Educ., 25(2), 164–172.
Wood A., (1975), Graphical Representation of Thermodynamic Functions, J. Coll. Sci. Teach., 5(2), 102–104.
Wu G. and Wu A. Y., (2020), A new perspective of how to understand entropy in thermodynamics, Phys. Educ., 55(1), 015005, DOI: 10.1088/1361-6552/ab4de6.
Wu G. and Wu A. Y., (2021), Analogies between momentum current, electric current and entropy current, Phys. Educ., 56(3), 035019, DOI: 10.1088/1361-6552/abe83f.
Yu T. H., (2020), Teaching Thermodynamics with the Quantum Volume, J. Chem. Educ., 97(3), 736–740, DOI: 10.1021/acs. jchemed.9b00742.
Zhang K., (2020), Illustrating the Concepts of Entropy, Free Energy, and Thermodynamic Equilibrium with a Lattice Model, J. Chem. Educ., 97(7), 1903–1907, DOI: 10.1021/acs. jchemed.0c00225.
Zimmerman S., (2010), An instructive model of entropy, Int. J. Math. Educ. Sci. Technol., 41(6), 805–818, DOI: 10.1080/ 0020739X.2010.486447.
Zinman W. G., (1973), Demonstration of Entropy and of the Second Law of Thermodynamics, Am. J. Phys., 41(11), 1284–1285, DOI: 10.1119/1.1987545.
