Calculating entropy, microstate/macrostate probabilities

Click For Summary

Homework Help Overview

The discussion revolves around calculating entropy in the context of statistical mechanics, specifically focusing on the relationship between microstates and macrostates. The original poster attempts to clarify their understanding of the entropy calculation related to a system described as having "half A and half B".

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the validity of the original poster's approach to calculating entropy, questioning the use of a specific probability in the context of entropy calculations. There is mention of Boltzmann's entropy formula as a potentially more appropriate method for the problem at hand.

Discussion Status

Some participants have provided guidance on the correct approach to take, specifically suggesting the use of Boltzmann's entropy formula. The original poster acknowledges the misstep in their calculation and indicates a resolution by adopting the suggested formula.

Contextual Notes

There is an indication that the original poster may have initially misunderstood the relationship between probabilities of states and the calculation of entropy, leading to confusion in their approach.

Flucky
Messages
93
Reaction score
1
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
Question_zpse877aa66.jpg


ANSWER ATTEMPT
20131103_132450_zps4b5b3476.jpg


Cheers,
James
 

Attachments

  • Question_zpse877aa66.jpg
    Question_zpse877aa66.jpg
    10.2 KB · Views: 302
  • 20131103_132450_zps4b5b3476.jpg
    20131103_132450_zps4b5b3476.jpg
    10.2 KB · Views: 421
Physics news on Phys.org
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.
 
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.
 
cool, glad you figured it out in the end :)
 

Similar threads

Finding the probabilities of macrostates for paramagnetic dipoles
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Entropy Real? End of Time? - Veritasium Video
  • · Replies 14 ·
Replies
14
Views
7K
Undergrad Microstate, Macrostate, Probability
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Definition of a system in Boltzmann entropy
  • · Replies 1 ·
Replies
1
Views
2K
Graduate How does the number of microstates affect the entropy of an isolated system?
  • · Replies 39 ·
2
Replies
39
Views
7K
Graduate Could the Laws of Physics Be Proportional to Entropy?
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad What Are the Differences Between Boltzmann and Gibbs Entropies?
  • · Replies 6 ·
Replies
6
Views
5K
How Do Macrostates and Microstates Determine Particle Energy Distribution?
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Does Laplace's demon know about entropy?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Equilibrium, entropy, probability - Release of constraints
  • · Replies 2 ·
Replies
2
Views
2K