The occupation numbers are N0, N1, N2 and N3. The total energy of the system amounts to 3ε 1. They are allowed to occupy 4 different energy states: ε 0 = 0, ε 1, ε 2 = 2ε 1 and ε 3 = 3ε 1 (e.g. Ludwig Boltzmann concluded from the 2nd law of Thermodynamics that the macro-state with the most micro-states is the most stable in equilibrium (remember S = k B ln Ω ).Ī simple example There are 3 (distinguishable, independent and identical) particles A, B and C. recap: micro-state: macro-state:Ĭertain assignment of particles to certain (energy) state realised by many micro-states („sum of micro-states“) The Boltzmann distribution was introduced in the last section of part I (see Dr. Baierlein: "Thermal Physics", Cambridge University Press, 1999 Mandl, "Statistical Physics", Wiley, 1988 Recommended Books / Background Reading for this second part: 88 Superconductivity and superfluidity, BEC. 83 The perfect photon gas - black-body radiation. 68 Systems with variable particle number. 64 Comparison of Boltzmann, BE and FD statistics. 45 4.1.2 Debye's theory of an ideal crystal. 45 4.1.1 Einstein's theory of an ideal crystal. 38 3.4.3 Rotational specific heat of diatomic molecules- ortho/para 1H2. 35 3.4.2 Maxwell velocity distribution in a classical gas. Validity and Limit of the Semi-Classical Description. 31 3.3.3 The principle of the equipartition of energy. 29 3.3.2 The entropy of mixing-the Gibbs paradox. 29 3.3.1 Entropy of a mon-atomic gas, the Sackur-Tetrode equation. 28Įntropy and Energy of the Semi-Classical Gas. 24 Partition functions and comparison to experimental data. 21 Partition function of (molecular) vibration, Zvib. 20 Partition function of (molecular) rotation, Zrot. Partition function of internal motion, Zint. 14ģ.2.5 Partition function for translational motion, Z1tr. 9 Contributions of different types of motion to Z1. 8 Distinguishable / indistinguishable particles?. The Boltzmann Distribution (derived!).2 3.1.1 A simple example. PH 605 Thermal and Statistical Physics Part II: Semi-Classical Physics Quantum Statistics course-webpage: ĭr.
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