The Differential Equations Of Thermodynamics

A Concise Handbook of Mathematics, Physics, and Engineering Sciences takes a practical approach to the basic notions, formulas, equations, problems, theorems, methods, and laws that most frequently occur in scientific and engineering applications and university education. The authors pay special attention to issues that many engineers and students find difficult to understand.

Classic Lectures on Thermodynamics, A+ for Clarity These lectures by Enrico Fermi make great reading for undergraduates in chemistry or physics, particularly those undergoing the rigors of physical chemistry and chemical thermodynamics. Fermi writes with clarity, always carefully laying the appropriate groundwork for each topic.
The mathematics assumes familiarity with calculus, including partial differentiation. Fermi provides clear explanations and motivation for the mathematics and the derivations are complete and easy to follow. For example, he carefully explained the form of a perfect differential of two variables and how it can be more readily integrated. I appreciated this help.

The first four chapters will be familiar to students of physics: Thermodynamic Systems, First Law of Thermodynamics, Second Law of Thermodynamics, and Entropy. The derivation of the Clapeyron equation and the Van der Waals equation may be new to some students.

Thereafter, the text begins to look more like physical chemistry with chapters titled Thermodynamic Potentials, Gaseous Reactions, Thermodynamics of Dilute Solutions, and the Entropy Constant. I found these last chapters to be more difficult, but not overly so.

At some points Thermodynamics becomes a real page-turner, but not in the sense of a fast-paced action story. The page-turning is necessary to retrieve earlier mathematical expressions. Occasionally, you will encounter statements like "the expression for the free energy is immediately obtained from equations (111), (29), and (86)." Fermi does not allow the reader to forget earlier derivations and discussions.

This book offers an in-depth verification of numerical solutions for differential equations modeling heat transfer phenomena, where the smoothed particle hydrodynamics (SPH) method is used to discretize the mathematical models. Techniques described in this book aim to speed up the convergence of numerical solutions and increase their accuracy by significantly reducing the discretization error.

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