Three distinguishable noninteracting particles have available nondegenerate single-particle energies 0, ε, 2ε. If total energy is 2ε, how many distributions are possible?
The occupations can be (n₀,n₁,n₂)=(2,0,1) or (1,2,0). In the first case choose the particle at 2ε: three ways. In the second choose the particle at zero: three ways. Total microstates=3+3=6. Distinguishability is essential to this count.
More Statistical Thermodynamics: Micro-canonical, Canonical and Grand canonical ensembles, Boltzmann distribution, Partition functions and thermodynamic properties. Statistical mechanics of non-interacting systems, ideal monoatomic, diatomic gases, translational, rotational, vibrational and electronic partition functions. questions
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