## Calculating Entropy using S=kb*ln W

Jake Ney lecture 1 discussion 1F
Posts: 26
Joined: Fri Sep 25, 2015 3:00 am

### Calculating Entropy using S=kb*ln W

Question 9.21 asks to 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 one of four orientations with the same energy.

For part (a) I assume that there is only one possible state, while for part b there are 4 different micro states among 64 different molecules .

How would you calculate the change in entropy for part a and part b given this information?

GabiFujita_1B
Posts: 17
Joined: Fri Sep 25, 2015 3:00 am

### Re: Calculating Entropy using S=kb*ln W

RE: How would you calculate the change in entropy for part a and part b given this information?

To approach this problem, you need to use the Boltzmann equation: S=kblnW, which relates the number of ways of achieving a given energy state (degeneracy) and entropy.

Your kb is a constant for both a & b: 1.3806 x 10^-23 J/K

The main component to calculating the entropy is solving W, or the degeneracy.

For part a, since all the molecules are aligned in the same direction, your W=1^64
Using the Boltzmann equation: S=(1.3806 x 10^-23 J/K)ln(1)=0

For part b, the molecules can lie in any of four arrangements; W=4^64
Using the Boltzmann equation: S=(1.3806 x 10^-23 J/K)ln(3.403x10^38)=1.22x10^-21 J/K