statistical thermodynamics fundamentals and applications

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statistical thermodynamics fundamentals and applications


My intention in this textbook is to provide a self-contained exposition of the fundamentals
and applications of statistical thermodynamics for beginning graduate students in the engineering
sciences. Especially within engineering, most students enter a course in statistical
thermodynamics with limited exposure to statistics, quantum mechanics, and spectroscopy.
Hence, I have found it necessary over the years to “start from the beginning,” not leaving
out intermediary steps and presuming little knowledge in the discrete, as compared to
the continuum, domain of physics. Once these things are done carefully, I find that good
graduate students can follow the ideas, and that they leave the course excited and satisfied
with their newfound understanding of both statistical and classical thermodynamics.
Nevertheless, a first course in statistical thermodynamics remains challenging and
sometimes threatening to many graduate students. Typically, all their previous experience
is with the equations of continuum mechanics, whether applied to thermodynamics, fluid
mechanics, or heat transfer. For most students, therefore, the mathematics of probability
theory, the novelty of quantum mechanics, the confrontation with entropy, and indeed
the whole new way of thinking that surrounds statistical thermodynamics are all built-in
hills that must be climbed to develop competence and confidence in the subject. For this
reason, although I introduce the ensemble method at the beginning of the book, I have
found it preferable to build on the related Maxwell–Boltzmann method so that novices
are not confronted immediately with the conceptual difficulties of ensemble theory. In
this way, students tend to become more comfortable with their new knowledge earlier in
the course. Moreover, they are prepared relatively quickly for applications, which is very
important to maintaining an active interest in the subject for most engineering students.
Using this pedagogy, I find that the ensemble approach then becomes very easy to teach
later in the semester, thus effectively preparing the students for more advanced courses
that apply statistical mechanics to liquids, polymers, and semiconductors.
To hold the students’ attention, I begin the book with the fundamentals of statistical
thermodynamics, pause to recover needed knowledge from quantum mechanics and
spectroscopy, and then move on to applications involving ideal gases, the solid state, and
radiation. An important distinction between this book and previous textbooks is the inclusion
of an entire chapter devoted to laser-based diagnostics, as applied to the thermal
sciences. Here, I cover the essentials of absorption, emission, and laser-induced fluorescence
techniques for the measurement of species concentrations and temperature. A full
xvi ! Preface
introduction to kinetic theory is also provided, including its applications to transport phenomena
and chemical kinetics.
During the past two decades, I have developed many problems for this textbook that are
quite different from the typical assignments found in other textbooks, which are often either
too facile or too ambiguous. Typically, the students at Purdue complete eight problem sets
during a semester, with 4–6 problems per set. Hence, there are enough problems included
in the book for approximately three such course presentations. My approach has been to
construct problems using integrally related subcomponents so that students can learn the
subject in a more prompted fashion. Even so, I find that many students need helpful hints
at times, and the instructor should indeed be prepared to do so. In fact, I trust that the
instructor will find, as I have, that these interactions with students, showing you what they
have done and where they are stuck, invariably end up being one of the most rewarding
parts of conducting the course. The reason is obvious. One-on-one discussions give the
instructor the opportunity to get to know a person and to impart to each student his or her
enthusiasm for the drama and subtleties of statistical thermodynamics.