Calculating entropy, microstate/macrostate probabilities

[Flucky]

Hi all, could somebody look over my answer please. I'm pulled the equation I used off the internet but can't remember where so I'm not sure what it's called.

I took a picture of my answer as I thought it would be easier to read than fiddling with symbols here.

QUESTION

ANSWER ATTEMPT

Cheers,
James

 

[BruceW]

I don't really understand your calculation. I would agree that 0.144 is the probability of finding the system in the macrostate of "half A and half B". But then after that, you try to use this probability to calculate entropy... That doesn't really make sense to me. When you calculate entropy, you should be summing over each of the possible states, and using the probability of each of these states. I don't see how your calculation does that.

Also, I think maybe you are making things more difficult than you need to. You know Boltzmann's entropy formula, right? why not use that? The problem says to calculate the entropy associated with the macrostate "half A and half B", so Boltzmann's entropy formula is ideal.

 

[Flucky]

Hi BruceW, yeah turned out I was using the wrong equation so sending myself in circles. You were right I did need to use the Boltzmann entropy formula which came out with the correct result.

 

[BruceW]

cool, glad you figured it out in the end :)