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Probability for N molecules

  1. Nov 8, 2013 #1
    Estimate the probability that in a room of volume V, all the N molecules of air are found in volume [itex]\frac{3V}{4}[/itex] and none at all in the reaining volume V/4
    My take to the solution is

    Pr of finding N molecules in [itex]\frac{3V}{4}[/itex] : [itex]\frac{N}{3V/4}[/itex]= [itex]\frac{4N}{3V}[/itex]
    Pr finding none in V/4: 1-[itex]\frac{4N}{3V}[/itex] = [itex]\frac{3V-4N}{3V}[/itex]

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    I used coin toss logic. No idea i did it correct. I'm new at staistical mechanics. I'm kinda lost just give me hints.
     
    Last edited: Nov 8, 2013
  2. jcsd
  3. Nov 8, 2013 #2

    stevendaryl

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    That's not a very good estimate. Think about it this way: You divide the room into two parts, call them section A and section B. Section A is 3 times as large in volume as section B.

    Suppose you start off with an empty room (no air at all). Then you introduce a single molecule into the room at a random location. Then the probability will be 3/4 that the molecule will be placed into section A. Now introduce a second molecule. The probability that it will be in section A is again 3/4. So the probability that the first two molecules will be released into section A is:

    [itex]P_2 = (3/4)*(3/4) = (3/4)^2[/itex]

    So if you keep on releasing molecules into the room at a random location, then the probability that the first [itex]N[/itex] molecules will all be in section A is:

    [itex]P_N = ?[/itex]
     
  4. Nov 8, 2013 #3
    Thx!
     
    Last edited: Nov 9, 2013
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