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This textbook introduces chemistry and chemical engineering students to molecular descriptions of thermodynamics, chemical systems, and biomolecules.
- Equips students with the ability to apply the method to their own systems, as today's research is microscopic and molecular and articles are written in that language
- Provides ample illustrations and tables to describe rather difficult concepts
- Makes use of plots (charts) to help students understand the mathematics necessary for the contents
- Includes practice problems and answers
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1
Introduction
Section 1.1 looks at the similarities and differences between classical thermodynamics and statistical thermodynamics. Then, in Section 1.2, we see several examples of phenomena that are beautifully described by statistical mechanics. Section 1.3 lists practices of notation adopted by this book.
1.1 Classical Thermodynamics and Statistical Thermodynamics
Classical thermodynamics, when applied to a closed system, starts with two fundamental laws. The first law of thermodynamics accounts for a balance of energy:
1.1
where the system receives heat dâ˛Q and work dâ˛W to change its internal energy by dU (see Figure 1.1). The prime in âdâ˛â indicates that the quantity may not be a thermodynamic variable, i.e. not expressed as a total derivative. When the volume of the system changes from V to V + dV, dâ˛W = âp dV, where p is the pressure.
The second law of thermodynamics expresses dâ˛Q by a thermodynamic variable, but only when the change is reversible:
1.2
where T is the temperature. The second law introduces the entropy S.
In classical thermodynamics, we try to find relationships between macroscopic variables, S, T, U, V, and p. The equation of state is one of the relationships. We also learned different types of energy, specifically, enthalpy H, Helmholtz free energy F, and Gibbs free energy G. These measures of energy are convenient when we consider equilibria under different constraints. For example, at constant T and V, it is F that minimizes when the system is at equilibrium. Certainly, we can always maximize S of the universe (system + the surroundings), but knowing the details of the surroundings is not feasible or of our concern. Rather, we want to focus on the system, although it is the maximization of the entropy of the universe that dictates the equilibrium of the system. People have devised F for that purpose. If we minimize F of the system under given T and V, we are equivalently maximizing S of the universe. Likewise, G minimizes when the system's temperature and pressure are specified.
As you may recall, classical thermodynamics does not need to assume anything about the composition of the system â whether it is a gas or liquid, what molecules constitute the system, and so on. The system is a continuous medium; and it is uniform at all length scales, if it consists of a single phase. In other words, there are no molecules in this view.
Statistical thermodynamics, in contrast, starts with a moleculeâlevel description of the system â what types of molecules make up the system, wheth...
Table of contents
- Cover
- Table of Contents
- Preface
- Acknowledgments
- About the Companion Website
- Symbols and Constants
- 1 Introduction
- 2 Review of Probability Theory
- 3 Energy and Interactions
- 4 Statistical Mechanics
- 5 Canonical Ensemble of Gas Molecules
- 6 Indistinguishable Particles
- 7 Imperfect Gas
- 8 Rubber Elasticity
- 9 Law of Mass Action
- 10 Adsorption
- 11 Ising Model
- 12 Helical Polymer
- 13 HelixâCoil Transition
- 14 Regular Solutions
- Appendix A: Mathematics
- References
- Index
- End User License Agreement