### degeneracy

Posted:

**Sun Feb 10, 2019 5:17 pm**Can someone explain the concept of W (degeneracy) and how to solve for it?

Created by Dr. Laurence Lavelle

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

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=132&t=41839

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Posted: **Sun Feb 10, 2019 5:17 pm**

Can someone explain the concept of W (degeneracy) and how to solve for it?

Posted: **Sun Feb 10, 2019 5:34 pm**

Degeneracy is how different particles can be in different positions but have the same energy levels. To calculate W you take the number of possible positions or orientations available and raise it the power of the number of particles. so if you had 4 particles that could be in 2 different positions W would equal 2^4.

Posted: **Sun Feb 10, 2019 5:39 pm**

Simply put, degeneracy is the number of different ways energy can exist, or the different configurations (microstates) a substance can take in a particular state. For example, gases have high degeneracy (the molecules are largely free to bounce around whatever container they're in), whereas solids have low degeneracy (molecules are locked into a crystal structure, in the case of a salt, and are not able to move very much).

To relate this to entropy, let's refer to the Boltzmann equation. S = kBln(W), where W represents degeneracy (the number of microstates of a substance). S and W are directly proportional - as W is larger, S is also larger, and vice versa. Referring back to our earlier example, this means that a gas has both higher degeneracy and entropy than a solid.

Hope it helps!

To relate this to entropy, let's refer to the Boltzmann equation. S = kBln(W), where W represents degeneracy (the number of microstates of a substance). S and W are directly proportional - as W is larger, S is also larger, and vice versa. Referring back to our earlier example, this means that a gas has both higher degeneracy and entropy than a solid.

Hope it helps!