## Microstates

Boltzmann Equation for Entropy: $S = k_{B} \ln W$

ng1D
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### Microstates

What is the relationship between microstates and degeneracy? Are they the same thing or are the number of microstates related to degeneracy?

Nathan Rothschild_2D
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### Re: Microstates

They are not the same thing, just related
W=X^n
Where W= Degeneracy, X=the number if possible microstates, n=number of available particles

Alan Cornejo 1a
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### Re: Microstates

Nathan Rothschild_2D wrote:They are not the same thing, just related
W=X^n
Where W= Degeneracy, X=the number if possible microstates, n=number of available particles

This is correct, they are two distinct things but they can be related with an equation

Janet Nguy 2C
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### Re: Microstates

Like what was said, degeneracy is related to microstates by the equation W = X^n; this is just because degeneracy describes all of the possible positions that a particle can exist in, so intuitively you would take the # of microstates to the power of the # of particles there are.

SVajragiri_1C
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### Re: Microstates

Degeneracy is exponentially related to microstates.

arisawaters2D
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### Re: Microstates

In Lavelle's lecture from today (2/3), he talks about a 2 particle system with 4 microstates and says the degeneracy would be W=4=2^2. I'm a little confused by this, because in the discussion above, it says that W=X^n, where X is the number of microstates and n is the number of particles. So, wouldn't W be 4^2?
Last edited by arisawaters2D on Wed Feb 03, 2021 12:14 pm, edited 1 time in total.

Lucy_Balish_3G
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### Re: Microstates

arisawaters2D wrote:In Lavelle's lecture from today (2/3), he talks about a 2 particle system with 4 microstates and says the degeneracy would be W=4=2^2. I'm a little confused by this, because in the discussion above, it says that W=X^n, where X is the number of microstates and n is the number of particles. So, wouldn't W be 4^2 =8?

If the example you are referencing is 4 CO molecules, I think you just switched the two. Because there are 2 microstates for the C and the O (either left or right) and 4 molecules, you would find W=2 microstates ^ (4 number of particles). 2^4=16.

DMaya_2G
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### Re: Microstates

Degeneracy is connected to microstates by the equation W = X^n. Degeneracy describes all of the possible positions that a particle can exist at.

MinjooPark_3I
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### Re: Microstates

arisawaters2D wrote:In Lavelle's lecture from today (2/3), he talks about a 2 particle system with 4 microstates and says the degeneracy would be W=4=2^2. I'm a little confused by this, because in the discussion above, it says that W=X^n, where X is the number of microstates and n is the number of particles. So, wouldn't W be 4^2?

I believe he was saying that when there are two states (L and R in this case) and there are two particles, there are 4 arrangements/microstates/distributions which would mean it has a degeneracy of 4 (2^2).

Please correct me if I'm wrong!

Norah Gidanian 3D
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### Re: Microstates

DMaya_2G wrote:Degeneracy is connected to microstates by the equation W = X^n. Degeneracy describes all of the possible positions that a particle can exist at.

X would be equal to the number of microstates in this equation. n would be equal to the number of possible states

AJForte-2C
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### Re: Microstates

are states/micro states/atomic states all basically the same thing when calculating degeneracy?

Xinying Wang_3C
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### Re: Microstates

AJForte-2C wrote:are states/micro states/atomic states all basically the same thing when calculating degeneracy?

I think they are basically the same thing, just different names used in different circumstances.

Mursall M 2A
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### Re: Microstates

Microstates are all the different possible positions a molecule could be in. To to find the degeneracy you take the microstates^#of molecules you have.

AJForte-2C
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### Re: Microstates

Xinying Wang_3C wrote:
AJForte-2C wrote:are states/micro states/atomic states all basically the same thing when calculating degeneracy?

I think they are basically the same thing, just different names used in different circumstances.

thanks so much! Just wanted to make sure.

Taylor Newville 1C
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### Re: Microstates

Degeneracy is the number of possible microstates of a system raised to the number of particles in that system.

Joshua Eidam 2A
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### Re: Microstates

I am confused about how to identify microstates. In Lavelle's lecture, he consistently used 2 for the value of microstates but I am assuming that is not always the case. In a given problem or example, what are you looking for when trying to identify the number of microstates?

Matlynn Giles 2E
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### Re: Microstates

two different things but an equation can relate the two!

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