Calculating degeneracy

[Anya Holbrook 1E]

What exactly is the equation to calculate degeneracy (W)? I saw in a lecture a few weeks ago he wrote W = 2^(NA), but I'm still confused.

[Jonathan Batac - 2D]

Degeneracy(W) is equal to the number of positions (let's call it "x") raised to the power of the number of particles, molecules, etc (let's call it "n"). Therefore "W = x^n". The "NA" that you wrote down is Avogadro's number; so that "2^NA" would be the degeneracy of a whole mole of some substance if there are two available positions.

[NayeliPlayas_1L]

Hi, I believe that for degeneracy it is states/positions^molecules. For example in 4G.1 it said "Calculate the entropy of a solid nanostructure made of 64 molecules in which the molecules (a) are all aligned in the same direction (b) lie in any of the four orientations with the same energy." In this case for (a) W=1^64 and (b) would be W=4^64. I hope that makes sense or helps clarify any confusion.

[Lea Baskin Monk 1F]

The equation is W = (possible positions)^(# of particles). Degeneracy (W) is the number of ways of achieving a given energy state.

In the example you gave, the number of possible positions is 2 (like in a molecule such as CO). The number of particles is denoted NA because Lavelle was talking about a mole of molecules where NA = Avogadro's Number.

Using the CO molecule as an example, lets say we have a 3 molecules of CO. The degeneracy (W) would be ....
W = (2)^(3) = 8

The degeneracy equation is used in the Boltzmann equation [S = Kbln(W)] which relates degeneracy to entropy. You can see from this relationship that more particles = higher degeneracy = more entropy.

[Raashi Chaudhari 3B]

Hi!
For calculating degeneracy I like to remember that W (disorder)= (# of possible positions)^(# of molecules)
After calculating the degeneracy you can plug that into the equation S=kB*lnW to calculate entropy.
Hope this helped!

[Emerald Wong 1B]

Degeneracy (W) is (# positions)^(# molecules). You can use this to calculate entropy using the equation from the formula sheet.

[Chris 1C]

W=(# of equal energy positions)^(number of particles) with S=(Boltzmann's constant)*lnW

[Sofia Lombardo 2C]

Degeneracy (W) = (# of positions)^(# of molecules). Then you can just plug this into the S=KblnW equation.

[Joshua Eidam 2A]

Just to clarify, the direction of a molecule also falls under the category of position? Meaning it could be in the same exact spot but facing a different direction and still count as a separate position?

[Charlie Russell 2L]

Does the direction of the particle matter? Does that count as another state?

[Uyenvy Nguyen 1D]

W=(# of possible states)^(# of particles). For example, 64 molecules all aligned in the same direction would have a degeneracy of 1^64.

[Aarushi Verma 2I]

W = (number of equal energy states) ^ (the number molecules). You would then plug this W value into the S = Kb ln W equation to get positional/residual entropy.

[LeanneBagood_2F]

is 'W' in any specific units?

[BoparaiAdeshsurjit2F]

The best way to find degeneracy is the (# of positions)^molecules

[Eliana Carney 3E]

Hey Anya!

Personally, how I like to calculate degeneracy is with the formula W=x^n where x is the number of positions and n is the number of molecules. For example, if you have a mole of molecules with five possible positions, W=(5)^(6.022x10^23). Hope this helps!

[Crystal Hsueh 2L]

The way to find degeneracy (W) is basically:

the number of possible positions ^(# of molecules)

For example, if you had 2 of the same molecules with 4 possible positions, it'd be 4^2.

[Lesly Lopez 3A]

From what I understand:
Degeneracy (W) = (# of positions)^(# of molecules). Then you can just plug this into the S=KblnW equation.

[Jacob Schwarz-Discussion 3I]

The equation to calculate degeneracy (W) is the following: W=(possible positions)^the number of particles

[Ritika Prasad 1A]

Also, to provide more clarification on what degeneracy itself is, it is the number of ways of achieving a given energy state, so the different configurations something can take to achieve the same end state. Thus, in regards to states of matter, gases have a higher degeneracy since the particles can take up more space in a given container, whereas a liquid can take up less space in that same container, and a solid even less. The greater amount of space taken up contributes to a greater number of configurations, resulting in varying degeneracies. This has a direct relationship with entropy through the Boltzmann equation S=kBln(W), as a greater degeneracy results in greater entropy. This makes sense with what we know about entropies, as we know that gases have the highest entropies/greatest disorder, while solids have the lowest entropies/least disorder.