Explaining the entropy concept and entropy components
Abstract
Total entropy of a thermodynamic system consists of two components: thermal entropy due to energy, and residual entropy due to molecular orientation. In this article, a three-step method for explaining entropy is suggested. Step one is to use a classical method to introduce thermal entropy STM as a function of temperature T and heat capacity at constant pressure Cp: STM = ∫(Cp/T) dT. Thermal entropy is the entropy due to uncertainty in motion of molecules and vanishes at absolute zero (zero-point energy state). It is also the measure of useless thermal energy that cannot be converted into useful work. The next step is to introduce residual entropy S0 as a function of the number of molecules N and the number of distinct orientations available to them in a crystal m: S0 = N kB ln m, where kB is the Boltzmann constant. Residual entropy quantifies the uncertainty in molecular orientation. Residual entropy, unlike thermal entropy, is independent of temperature and remains present at absolute zero. The third step is to show that thermal entropy and residual entropy add up to the total entropy of a thermodynamic system S: S = S0 + STM. This method of explanation should result in a better comprehension of residual entropy and thermal entropy, as well as of their similarities and differences. The new method was tested in teaching at Faculty of Chemistry University of Belgrade, Serbia. The results of the test show that the new method has a potential to improve the quality of teaching.
References
Atkins, P. & de Paula, J. (2011). Physical Chemistry for the Life Sciences, 2nd ed. New York: W. H. Freeman and Company.
Boltzmann, L. (1974). The second law of thermodynamics. In B. F. McGuinness (Ed.), Theoretical physics and philosophical problems (pp. 13- 33). New York: Springer-Verlag.
Carson, E.M. & Watson, J.R. (2002). Undergraduate students’ understandings of entropy and Gibbs free energy, University Chemistry Education, 6, 4-12.
Chang, R. (2000). Physical Chemistry for the Chemical and Biological Sciences, 3rd ed. Sausalito: University Science Books.
Clausius, R. (1867). The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies. London: John van Voorst.
Clausius, R. (1870). On a Mechanical Theorem Applicable to Heat, Philosophical Magazine, 40(265), 122–127.
Clausius, R. (1865). Ueber verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie, Annalen der Physik, 201(7), 353–400.
Clayton, J.O. & Giauque, W.F. (1932). The heat capacity and entropy of carbon monoxide. Heat of vaporization. Vapor pressures of solid and liquid. Free energy to 5000°K from spectroscopic data, Journal of the American Chemical Society, 54(7), 2610-2626.
Edington, A.S. (1928). The nature of the physical world. Cambridge: Cambridge University Press.
Gillet, S.L. (2006). Entropy and its misuse, I. Energy, free and otherwise, Ecological Economics, 56(1), 58–70.
Johari, G. (2010). Configurational and residual entropies of nonergodic crystals and the entropy's behavior on glass formation, The Journal of Chemical Physics, 132, 124509.
Kostic, M.M. (2014). The Elusive Nature of Entropy and Its Physical Meaning, Entropy, 16(2), 953-967.
Kozliak, E. (2007). Consistent Application of the Boltzmann Distribution to Residual Entropy in Crystal, Journal of Chemical Education, 84(3), 493-498.
Kozliak, E.I. (2009). Overcoming Misconceptions about Configurational Entropy in Condensed Phases, Journal of Chemical Education, 86(9), 1063-1068.
Kozliak, E. & Lambert, F. (2008). Residual Entropy, the Third Law and Latent Heat, Entropy, 10(3), 274-284.
Lambert, F. L. (2007). Configurational entropy revisited, Journal of Chemical Education, 84(9), 1548−1550.
Langbeheim, E.; Safran, S.A. & Yerushalmi, E. (2014). Visualizing the Entropy Change of a Thermal Reservoir, Journal of Chemical Education, 91(3), 380-385.
Popovic, M. (2014). Comparative study of entropy and information change in closed and open thermodynamic systems, Thermochimica Acta, 598, 77-81.
Popovic, M. (2015). Are Shannon entropy and Residual entropy synonyms? . In Proceedings of the 2nd Int. Electron. Conf. Entropy Appl., Sciforum Electronic Conference Series, 2, A004. doi:10.3390/ecea-2-A004
Sestak, J.; Mares, J.J. & Hubik, P. (2011). Glassy, Amorphous and Nano-Crystalline Materials: Thermal Physics, Analysis, Structure and Properties. New York: Springer.
Shultz, T. R. & Coddigton, M. (1981). Development of the concept of energy conservation and entropy, Journal of Experimental Child Psychology, 31(1), 131−153.
Smirnova, N.N.; Kulagina, T.G.; Markin, A.V.; Shifrina, Z.B. & Rusanov, A.L. (2005). Thermodynamics of phenylated polyphenylene in the range from T → 0 to 640 K at standard pressure, Thermochimica Acta, 425(1-2), 39-46.
Sozbilir, M. & Bennet, J.M. (2007). A Study of Turkish Chemistry Undergraduates’ Understandings of Entropy, Journal of Chemical Education, 84(7), 1204-1208.
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