# 4 Statistical Mechanics

We learn several fundamental concepts of statistical mechanics – states, phase space, ensemble, and partition function – in this chapter. There are a few assumptions or hypotheses in statistical mechanics, and from them we can derive all the thermodynamics functions such as pressure, heat capacity, free energy, and chemical potential. The expression of the pressure gives the equation of state. When you finish this chapter, you will have learned all the necessary tools for applying statistical mechanics to different chemical systems.

## 4.1 Basic Assumptions, Microcanonical Ensembles, and Canonical Ensembles

### 4.1.1 Basic Assumptions

Statistical mechanics is founded on a few assumptions stated in simple words. Starting with these assumptions, various laws of thermodynamics that we learned in undergraduate physical chemistry courses are derived. So far, no phenomena that go against the laws have been discovered. That is why we accept the basic assumptions of statistical mechanics as the first principles, just as the Schrödinger equation is accepted in quantum mechanics. Recall that, in the physical chemistry courses, many of the laws were given, not derived.

In the first eight sections of this chapter, we consider a closed system that consists of *N* particles – a fixed number of particles. A closed system can exchange heat and work with its surroundings. The particles are molecules, atoms, electrons, etc. They can be in any phase – vapor, liquid, or solid. ...

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