## Homework 9.21

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

Katie Blann 1E
Posts: 29
Joined: Tue Nov 15, 2016 3:00 am

### Homework 9.21

How would you know to use the equation w= 1^64 for this problem?

Posts: 32
Joined: Thu Jul 13, 2017 3:00 am

### Re: Homework 9.21

Since the molecules are all aligned in the same direction, the number of possible states is 1. In turn we use the formula (# of possible states)^# of particles. This yields 1^64 as there are 64 molecules.

Nancy Dinh 2J
Posts: 59
Joined: Fri Sep 29, 2017 7:07 am

### Re: Homework 9.21

Adding on to that, for this specific problem the number of states will be the number of orientations. In a, all of the molecules face the same way and therefore have only one possible orientation. In b, you will have four orientations so w = ln(4^# of molecules).

Sandhya Rajkumar 1C
Posts: 50
Joined: Fri Jun 23, 2017 11:40 am

### Re: Homework 9.21

The problem asks us to calculate entropy and gives us the number of molecules and the number of arrangements. Using these 2 things, we an calculate the degeneracy(W). To calculate the degeneracy: (# of arrangements)^(# of molecules). For part (a), we know there are 64 molecules aligned in the same direction, so we get W = 1^64. And to calculate entropy from that, we have to plug it into the Boltzmann equation: S = kB*ln(W) = kB*ln(1^64).

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