Thermodynamic assembly - Statistical Thermodynamics

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SUMMARY

The discussion focuses on a model thermodynamic assembly with four distinguishable particles and a total energy of U = 6ε, where the allowed energy states are 0, ε, 2ε, and 3ε. The user initially identified five possible distributions of particles among these energy levels but was unable to find the remaining four distributions. The conversation highlights the importance of distinguishing between labeled and unlabeled particles, leading to a total of 44 distinguishable states when considering particle labeling.

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Homework Statement


Consider a model thermodynamic assembly in which the allowed (nondegenerate) states have energies 0, ε, 2ε, 3ε.The assembly has four distinguishable (localized) particles and a total energy U = 6ε. Tabulate the nine possible distributions of the four particles among the energy levels nε where n = 0, 1...

Homework Equations

The Attempt at a Solution


I have tried tabulating it but I can only find five possible distributions that add up to 6ε.

3ε...2...1...1...
2ε.....1.....2...3
ε...1...3...2...
0...2...1......1

I'm stumped as to where to go form now and I cannot find the other four. Is there some part of the theory I'm getting wrong or I'm not understanding?
 
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It looks correct to me. The other possibility is if you consider the particles distinguishable, then you need to label the particle at a given energy level. If that is the case, and I counted correctly, I get 44 different states.
 

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