Many introductory physics texts introduce the statistical basis for the definition of entropy in addition to the Clausius definition, ΔS=q/T. We use a model based on equally spaced energy levels to present a way that the statistical definition of entropy can be developed at the introductory level. In addition to motivating the statistical definition of entropy, we also develop statistical arguments to answer the following questions: (i) Why does a system approach a state of maximum number of microstates? (ii) What is the equilibrium distribution of particles? (iii) What is the statistical basis of temperature? (iv) What is the statistical basis for the direction of spontaneous energy transfer? Finally, a correspondence between the statistical and the classical Clausius definitions of entropy is made.

1.
The following texts were surveyed in researching this manuscript. This list is not intended to be exhaustive but merely representative of those texts currently in use. P. M. Fishbane, S. Gasiorowicz, and S. T. Thornton, Physics for Scientists and Engineers (Prentice–Hall, Englewood Cliffs, NJ, 1996), 2nd ed.; D. C. Giancoli, Physics for Scientists and Engineers (Prentice–Hall, Englewood Cliffs, NJ, 2000), 3rd ed.; D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics (Wiley, New York, 1997), 5th ed.; E. Hecht, Physics: Calculus (Brooks/Cole, Pacific Grove, CA, 2000), 2nd ed.; R. D. Knight, Physics, A Contemporary Perspective (Addison–Wesley, Reading, MA, 1997), Vol. 2; L. S. Lerner, Physics for Scientists and Engineers (Jones and Bartlett, Sudbury, MA, 1996); S. M. Lea and J. R. Burke, Physics: The Nature of Things (Brooks/Cole, Pacific Grove, CA, 1997); R. Reese, University Physics (Brooks/Cole, Pacific Grove, CA, 2000); J. Sanny and W. Moebs, University Physics (Wm. C. Brown, Dubuque, IA, 1996); R. A. Serway, Physics for Scientists and Engineers (Saunders College Publishing, Philadelphia, PA, 1996), 4th ed.; P. A. Tipler, Physics for Scientists and Engineers (Freeman, Worth Publishers, New York, 1999), 4th ed.
2.
The idea of entropy as a measure of disorder has been discredited. See, for example,
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R. Baierlein, Thermal Physics (Cambridge UP., Cambridge, 1999), pp. 3–4. The author is indebted to one of the referees for pointing out this definition of temperature as given in this text.
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