## 9.21

Volume: $\Delta S = nR\ln \frac{V_{2}}{V_{1}}$
Temperature: $\Delta S = nC\ln \frac{T_{2}}{T_{1}}$

Kelly Kiremidjian 1C
Posts: 62
Joined: Fri Sep 29, 2017 7:04 am

### 9.21

In #21, where do they get the value of Kb? Also can someone explain this question I'm confused what we are calculating

Chem_Mod
Posts: 17949
Joined: Thu Aug 04, 2011 1:53 pm
Has upvoted: 406 times

### Re: 9.21

Hannah Chew 2A
Posts: 76
Joined: Fri Sep 29, 2017 7:05 am
Been upvoted: 2 times

### Re: 9.21

Kb is Boltzmann's constant, which is given to us on exams. The question is essentially asking for the entropy based on how many ways can you arrange the molecules. For part a), there is only 1 way to arrange it because they are all the same molecules aligned the same way. Part b), there is 4^64 ways because there are 4 different orientations and 64 molecules. Substitute into S = kblnW.

torieoishi1A
Posts: 32
Joined: Sat Jul 22, 2017 3:00 am

### Re: 9.21

a) Entropy of a solid made of 64 molecules in which they are all aligned in the same direction.
First you need to solve for W (orientation^#molecules). therefore, W=1^64=1. Then use the Boltzmann formula: S=klnW. (k=1.381x10^-23J/K #this is a constant that is given). Snce we know ln1=0, S=0.
b) Entropy of a solid made of 64 molecules in which they lie in any one of four orientations with the same energy.
Using the same formula and constant from part a, W=4^64=3.403x10^38. Then S=(1.381x10^-23J/K)ln(3.403x10^38)=1.22x10^-21J/K