Thermodynamic assembly - Statistical Thermodynamics

In summary, there are nine possible distributions of four distinguishable particles among the energy levels in a model thermodynamic assembly with a total energy of 6ε. If the particles are labeled, there are 44 different states. However, it seems that you have correctly identified five possible distributions and may need to further explore the theory to find the other four.
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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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  • #2
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.
 

Related to Thermodynamic assembly - Statistical Thermodynamics

1. What is thermodynamic assembly?

Thermodynamic assembly is a concept in thermodynamics that refers to the process of combining individual components or systems to create a larger, more complex system. This process allows for the study and analysis of the properties and behavior of the larger system as a whole.

2. What is statistical thermodynamics?

Statistical thermodynamics is the branch of thermodynamics that uses statistical methods to analyze and predict the behavior of microscopic particles in a system. It provides a deeper understanding of how thermodynamic properties arise from the collective behavior of individual particles.

3. How are thermodynamic assembly and statistical thermodynamics related?

Thermodynamic assembly and statistical thermodynamics are closely related as the former allows for the study of the properties of a larger system, while the latter provides a theoretical framework for understanding the behavior of individual particles within the system. Together, they provide a comprehensive understanding of the behavior of complex systems.

4. What are the main principles of statistical thermodynamics?

The main principles of statistical thermodynamics include the idea that the properties of a system can be described by the collective behavior of its constituent particles, and that the distribution of particles in a system is governed by the laws of probability. Additionally, statistical thermodynamics also considers the concept of entropy and its role in predicting the behavior of systems.

5. What are some practical applications of thermodynamic assembly and statistical thermodynamics?

Thermodynamic assembly and statistical thermodynamics have numerous practical applications in fields such as chemistry, physics, and engineering. They are used to study and design complex systems, analyze phase transitions and chemical reactions, and develop new materials with specific thermodynamic properties.

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