Boltzmann Equation for Entropy:
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Degenerate describes states that have the same energy level, but different positions/configurations. For example, the three p-orbitals of a given energy level are degenerate. Calculating it is complicated because it depends on the number of particles and the types of particles in the system.
I think the problem he did in his lecture was a good example. You have to identify the number of orientations the molecule can be in. Lets say its 3. Then you raise this number to the power of how many molecules of it there are. That is your W (degeneracy) in the boltzmann equation.
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