The Boltzmann distribution is a central concept in chemistry and its derivation is usually a key component of introductory statistical mechanics courses. However, the derivation, as outlined in most standard physical chemistry textbooks, can be a particularly daunting task for undergraduate students because of the mathematical and conceptual difficulties involved in its presentation. A simple alternative derivation that links familiar concepts from thermodynamics to concepts from statistical mechanics is presented here.
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Sean A. C. McDowell (1999) studied this question.