A statistical development of entropy for the introductory physics course

Abstract

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.