### Degeneracy

Posted:

**Sat Feb 03, 2018 7:42 pm**What is degeneracy and how can we use it?

Created by Dr. Laurence Lavelle

https://lavelle.chem.ucla.edu/forum/

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=75&t=26802

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Posted: **Sat Feb 03, 2018 7:42 pm**

What is degeneracy and how can we use it?

Posted: **Sat Feb 03, 2018 7:53 pm**

Degeneracy, denoted by W, is the number of ways of achieving a given energy state. We use degeneracy (W) in the Boltzmann equation, which is S = k x ln(W).

Posted: **Sat Feb 03, 2018 7:56 pm**

Degeneracy refers to microstates of the same energy. Looking at Dr. Lavelle's example with the two-sided flask from 01/22 lecture, we can see that the four microstates arise from the two particles going to two different sides of the flask while still at equivalent energy states. We assign degeneracy to the variable W, which gives us the number of ways to achieve a given energy state. Note that we use degenerate microstates to [censored] entropy, and the two are related by the Boltzmann equation.

Posted: **Sat Feb 03, 2018 8:28 pm**

Some of the examples we were given for finding the degeneracy,W, are:

For 2 particles both in one of two states: W=(2)^2=4

For 1 particle in one of two states: W=(2)^1=2

From this we can get the general idea that W = # of states^# of particles

For 2 particles both in one of two states: W=(2)^2=4

For 1 particle in one of two states: W=(2)^1=2

From this we can get the general idea that W = # of states^# of particles

Posted: **Sun Feb 04, 2018 10:52 pm**

these are all correct, but the way that I find it easiest to remember it is basically the different ways we can arrange particles