## Calculating degeneracy(W)

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

Nancy Le - 1F
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Joined: Fri Sep 29, 2017 7:07 am

### Calculating degeneracy(W)

How do you determine the number of states there are in a system?

Hazem Nasef 1I
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Joined: Tue Oct 10, 2017 7:13 am

### Re: Calculating degeneracy(W)

I believe normally that the number of states possible in a system would be given to you, or you would be able to deduce it from information given (i.e. the number of arrangements of molecules that result in the same energy) and you would have to calculate degeneracy. The degeneracy is given by the number of states raised to a power of the number of particles in the system. So if there are two particles that can be in one of two states, the degeneracy would be two raised to the second power, which is 4.

Nhan Nguyen 2F
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### Re: Calculating degeneracy(W)

From my notes, I have
W = 2^N where N is the number of particles

Rachel Formaker 1E
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### Re: Calculating degeneracy(W)

To modify the equation above,
W=2N for a 2-state system, where N is the number of particles.
The example we used was where each particle could be in one of two bulbs of a flask
This equation can be used for any number of states, just by changing the base.

For a 3-state system:
W=3N

The number of states of a system is the base of the equation, and the number of states is just the number of possible places that a particle could be within the system.

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