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Sudden decompression

  1. Nov 6, 2008 #1
    Imagine an infinitely long square box of side L. This box is isolated from the ambient and contains a number of N molecules of an ideal gas in a volume L^3 in thermal equilibrium located at one end of the box at time t=0.

    I found that the evolution of this system can be modelled by the decay equation

    n(t) = N e^{-At}.

    Where n is the number of particles in the volume L^3 and A is a scalling constant.

    My question is: Is there a better model for this system? (maybe hopefuly including absolute temperature T, L and Boltzman constant k_B)
     
    Last edited: Nov 7, 2008
  2. jcsd
  3. Nov 19, 2008 #2
    Please, help. I'm stuck a long time in this.

    So far I got the following formula which gives the time the i-th particle takes to reach the barrier at x=L:

    [tex]
    t_i = \frac{2 L - x_i}{\overline{v} \cos(a_i)}
    [/tex]

    where

    [tex]x_i[/tex] is a random variable between 0 and L
    [tex]a_i[/tex] is a random variable between 0 and [tex]\pi /2[/tex]
    [tex]\overline{v}[/tex] is the average speed of a gas particle

    What I need is [tex]n(t) = f(N, L, \overline{v},t)[/tex]

    where

    N is the total number of particles
    n(t) is the the number of particles in the original volume [tex]L^3[/tex] after time t

    Any reference book or article?

    Thanks
     
  4. Nov 19, 2008 #3
    Perhaps a Google search of "sudden decompression equations" with an additional search term of NASA, LANL or something similar might give some insight.
     
  5. Nov 26, 2008 #4
    Thank you for you suggestion, pallidin, but I couldn't find anything.

    I'm checking the consistency of the following formula I worked out:

    [tex]
    \boxed{
    \;\;n(t) = N exp\left[-\left(\frac{4\ln{2}\sqrt{\frac{3k_BT}{m}}}{\pi L}\right)t\right].\;\;
    }
    [/tex]

    where [tex]k_B[/tex] is Boltzmann constant, T is the absolute temperature and m is the atomic weight of the monoatomic gas molecule.
     
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