An Introduction to Statistical Mechanics and Thermodynamics by Robert H. Swendsen

By Robert H. Swendsen

This article offers the 2 complementary features of thermal physics as an built-in idea of the homes of topic. Conceptual realizing is promoted by means of thorough improvement of simple thoughts. unlike many texts, statistical mechanics, together with dialogue of the mandatory chance conception, is gifted first. this gives a statistical beginning for the concept that of entropy, that's vital to thermal physics. a distinct function of the e-book is the advance of entropy in response to Boltzmann's 1877 definition; this avoids contradictions or advert hoc corrections present in different texts. specific basics supply a average grounding for complicated subject matters, comparable to black-body radiation and quantum gases. an in depth set of difficulties (solutions can be found for academics in the course of the OUP website), many together with particular computations, enhance the middle content material by means of probing crucial innovations. The textual content is designed for a two-semester undergraduate direction yet may be tailored for one-semester classes emphasizing both element of thermal physics. it's also appropriate for graduate study.

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The total volume is V = VA + VB . The number of particles in A is NA , with NB = N − NA being the number of particles in B. We can either constrain the number of particles in each box to be fixed, or allow the numbers to fluctuate by making a hole in the wall that separates the boxes. The total number of particles N is constant in either case. We are interested in the probability distribution for the number of particles in each subsystem after the constraint (impenetrable wall) is released (by removing the wall or making a hole in it).

No quantum mechanical concepts are used. All the ideas will follow directly from Boltzmann’s work. We will use more modern mathematical methods than he did to derive the entropy of the classical ideal gas, but we will make no assumptions with which he was not familiar. In Chapters 7 and 8 the formal expression for the entropy will be extended to classical systems with interacting particles. Although the expression we obtain can rarely be evaluated exactly, the formal structure will be sufficient to provide a basis for the development of thermodynamics in Part II.

This misinterpretation is so common that many scientists are under the impression that Boltzmann defined the entropy as the logarithm of a volume in phase space. Going back to the original meaning of W and Boltzmann’s 1877 definition eliminates much of the confusion about the statistical interpretation of entropy. The main differences between Boltzmann’s treatment of entropy and the one in this book lie in the use of modern mathematical methods and the explicit treatment of the dependence of the entropy on the number of particles.

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