Equilibrium in a Gas Box: How Do Molecule Distributions Change?

[FourierX]

Homework Statement

A box is separated by a partition which divides its volume in the ratio 3:1. The larger portion of the box contains 1000 molecules of Neon gas, the smaller box contains 100 molecules of Helium gas. A small hole is made in the partition, and one waits until equilibrium is attained.

i) Find the mean number of molecules of each type on either side of the partition.
ii) What is the probability of finding 1000 molecules of of Neon gas in the larger portion and 100 molecules of Helium gas in the smaller (i.e. the same distribution as in the initial system) ?

Homework Equations

P_i = $$\Omega$$_i/$$\Omega$$_f

where,
$$\Omega$$_i = initial number of accessible state
$$\Omega$$_f = final number of accessible state

The Attempt at a Solution

I used the idea of equilibrium, reversible and irreversible processes.


"Berkeley"

 

[FourierX]

For the probability portion, here is what i did:

Since the partition exists with a ratio 3:1
Probability of finding N Neon gas in the larger portion = (1/3)^N
where,
(1/3) is the probability of finding 1 molecule of Neon gas in the larger portion
N = 1000

Probability of finding N Helium gas in the smaller portion = (2/3)^N
where,
(2/3) is the probability of finding 1 molecule of Helium gas in the smaller portion
N = 100


I believe this is correct, but please help me be sure

thanks