Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Probabilities and binomial theorem

  1. Sep 27, 2011 #1
    1. The problem statement, all variables and given/known data

    Consider an ideal gas of N identical particles in a volume V, and a subvolume v. The chance a molecule is in inside the subvolume is P = v/V.

    a) What is the chance the subvolume contains n particles?

    b) Use the binomial theorem [tex](p + q)^N = \sum_{n = 0}^N p^n q^{N-n} \frac{N!}{n!(N-n)!}[/tex] for random p and q to calculate the average number of particles [tex]\langle n\rangle[/tex] and the variance [tex]\sigma^2 = \langle n^2 \rangle - \langle n \rangle^2[/tex]

    Anyone who could give me a nudge in the right direction?
  2. jcsd
  3. Sep 27, 2011 #2
    As the gas is ideal, the particles can go inside the subvolume independently. Thus, the answer is (v/V)^N =p^N. Part (b) follows from straightforward but long calculations.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook