### Georg Job

# An elementary approach to quantum statistical problems (I)

Lecture at the "Physical Chemistry Seminar" of the Institute for Physical Chemistry of the University of Hamburg, on May 5, 1991

### Summary

In order to derive the relation between macroscopic thermodynamic quantities and the quantum mechanical properties of atoms or atomic unions, statistical thermodynamics is usually applied. It is considered a necessary means of solving problems of this type because "phenomenological thermodynamics as a macroscopic theory is on principle not able to make statements about atomic systems". To correct this entrenched prejudice that is even made relevant by standardized exams, is the aim of this presentation. Various important results of quantum statistics will be derived for which, apart from the well-known relations of quantum mechanics, only the chemical potential and its concentration and energy dependence are needed.

### Table of Contents

- Summary
- Introduction
- First acquaintance with molecular statistics
- Prerequisite formulas
- Contribution of vibrations to the chemical potential
- Contribution of rotation to the chemical potential
- Molecular velocity distribution
- Barometric Formula
- Equilibrium of sedimentation in a centrifuge
- Probability of an energy state
- Outlook