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# Solve for the Fairness Function

**Keywords:**Energy and Entropy, Statistical Mechanics, Thermodynamics

### Highlights of the activity

- For this activity, students are placed into small groups and asked to solve the fairness function in terms of several variables.
- Each group will receive experience manipulating quantum mechanical terms such as the probability, the internal energy, and terms that evolve from using the Lagrangian.

### Reasons to spend class time on the activity

After being introduced to multiple terms frequently used in statistical mechanics, making connections between how the terms can be used to answer a thermodynamics problem is important. This activity provides students with an exercise in manipulating common statistical mechanical variables to find the solution to a problem. Ultimately, the solution from this exercise can also lead to a solution for the internal energy in terms of the number of eigenstates possible in the system.