Statistical mechanics

1. Feb 15, 2009

LocationX

In adjacent containers of volume V1 and V2, there contains a gas of N molecules. The gas is free to move between the containers through a small hole in their common wall.

What is the probability to find k molecules in the V1?

Probability of one molecule to be in V1 is given by:
$$P=\frac{V_1}{V_1+V_2}$$

Using the Poisson distribution, I think the probability that k molecules are in V1 should be:

$$p_{poisson}(k)=\frac{a^k}{k!} e^{-a}$$
$$p(k)=\frac{\left( \frac{N V_1}{V_1+V_2} \right) ^k}{k!} e^{-\frac{N V_1}{V_1+V_2}}$$

Is this correct?

My next step is to find the probability when V2 -> infinity, and N->infinity such that $$N/V=\rho$$ is finite.

For this, I get:
$$p(k)=\frac{\left( \rho \right) ^k}{k!} e^{-\rho}$$

Does this work make any logical sense at all? Comments are appreciated, thanks for the help!

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?