Entropy and Degeneracy [ENDORSED]

[Isabel Gutierrez 2G]

Hello,
I understand that degeneracy is the number of ways of achieving an energy state but I don't understand how that is related to entropy. Can someone please explain?

[Vincent Tse 2B]

Recall that Entropy (S) --an extensive property that relies on the number of particles--describes the likelihood or probability that the system will be in a particular state. Or, in more common terms, entropy describes how "disordered" a system is.

In explaining how "disordered" a system is and the number of ways in achieving a particular energy state, which can vary in combinations/arrangements in microstates, degeneracy is used and denoted as W = 2^N (where N = the number of particles in those states) and the base 2 is used to indicate two possible states.

The relationship between W and entropy can be found through the Boltzmann equation: S = K_b * ln(W) where K_b is the Boltzmann constant.

In the very equation it self, it shows that entropy relies on the number of all possible states in achieving a given energy state (remember that W describes all possible states in different arrangements). This also reaffirms the idea of entropy being an extensive property.