[ian123]

A box is divided into two compartments of equal volume. N ideal gas molecules are confined to one half of the box and the other half is empty. The divider between the compartments is removed so that the particles are free to move around the box. What is the probability that all the molecules spontaneously move into one side of the box? Explain your reasoning, please.

I can't get my head around it.

[Borek]

What is probability that N tosses of a coin produce only heads?

[ian123]

2/2^N but I'm not sure about how to explain my reasoning.

[ian123]

A box is divided into two compartments of equal volume. N ideal gas molecules are confined to one half of the box and the other half is empty. When divider is removed what is the change in entropy of the system? Explain your reasoning.

So far this is what I've done
Ssubscript(AB)=ksubscript(b)*ln(2m*2m)
  =ksubscript(b)*ln((2m)^2)
  =2ksubscript(b)*(ln(m)+ln(2))

Once the divider is removed the number of micro states of a particle doubles to 2m

m=microstate(s)

Thanks for the help in advance.

[ian123]

What is probability that N tosses of a coin produce only heads?

1/2

[ian123]

I'm not sure if my answer is correct or not?
How to explain my reasoning?

[Arkcon]

ian123:, I've merged two posts of yours, with different titles, but the same question.  As you can see, it makes this thread a mess, with previous answers to one thread appearing before questions in the next thread.  You've had some time to read the rules, but I'm going to spell it out for you:  Stop cross posting, just ask your question once, and put your further questions, and your work, in the same thread.  If you think you're going to fool someone into doing all the work for you by posting again, you're mistaken, anyone can click on you name and see all your posts.  And if they stay separate, and people didn't notice, you can't use the posting from one thread in another thread, people will get annoyed at that rapidly.

Don't ask us to write explanations for you.  And if you think you're just asking for "help" in writing an explanation, then you have to actually write some of that explanation in that posting.

And please don't bμmp up a thread with frequent "Am I right?" postings.

[Borek]

2/2^N but I'm not sure about how to explain my reasoning.

Have you heard about binomial distribution?

Disclaimer: as you have later added another question, dealing with entropy, I am not convinced this is a correct approach; I don't remember enough statistical mechanics. But binomial distribution is how I would solve this problem.

[Corribus]

This is just a basic probability problem.

Instead of N molecules, let's just say there is 1 molecule. What is the probability it is in one chamber or the other? Now do it for 2 molecules, then 4 molecules. You should easily be able to see the pattern, then solve for N molecules.

There's no real explanation to be had. If every molecule is randomly located, and you restrict your possible locations to 1 chamber or the other, it's just straightforward statistics.

[ian123]

A box is divided into two compartments of equal volume. N ideal gas molecules are confined to one half of the box and the other half is empty. When divider is removed what is the change in entropy of the system? Explain your reasoning.

Once the divider is removed the number of micro states of a particle doubles to 2m

m=microstate(s)

Thanks for the help in advance.

[ian123]

Number of microstates is omega 2 at the end and number of microstates at the is omega 1 at the beginning. Place this inside Delta S =kln(omega2/omega1) and you get the change in entropy.

Any opinions?