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Next: 5. Statistical Quantum Mechanics Up: 4. Statistical Thermodynamics Previous: 4.3 Grand canonical ensemble


4.4 Problems for Chapter 4



EXERCISES:

4.1 Canonical phase space density: Considering the Maxwell-Boltzmann distribution in a classical 3D fluid, show that
a) with increasing kinetic energy $E_{k}$ the density of states decreases as $\exp \left[ - E_{k}/kT \right]$;
b) in spite of this the most probable kinetic energy is not zero.
Apply this to the general canonical phase space.

4.2 Grand canonical ensemble: Using the grand partition function, derive the mean number of particles in one $m^{3}$ of an ideal gas at standard conditions.


TEST YOUR UNDERSTANDING OF CHAPTER 4:

4.1 Temperature and entropy: What happens if two systems are put in contact with each other such that they may exchange energy?

4.2 Changes of state: What is a quasistatic change of state?

4.3 Equipartition theorem: Formulate the equipartition theorem; to which microscopic variables does it apply? Give two examples.

4.4 Canonical ensemble: What are the macroscopic conditions that define the canonical ensemble? When is it equivalent to the microcanonical ensemble?

4.5 Grand canonical ensemble: What are the macroscopic conditions defining the grand canonical ensemble? What is needed to make it equivalent to the canonical and microcanonical ensembles?
next up previous
Next: 5. Statistical Quantum Mechanics Up: 4. Statistical Thermodynamics Previous: 4.3 Grand canonical ensemble
Franz Vesely
2005-01-25