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Homework Help: Leaking gas (Effusion)

  1. Jan 10, 2006 #1
    I'm working on a question where gas is leaking out of a container from a small pinhole. I have a differential equation dN/dt = (Constants)*N. I solved this to get an exponential. The exponent is that group of constants, which are A/2V*(kT/m)^1/2. Shouldn't the exponent have something to do with time? Because if they don't, the dimensions don't work out. Can anyone clear this up for me?
     
  2. jcsd
  3. Jan 10, 2006 #2
    dN/dt = C * N
    yields
    N = N0 * exp (C * t)
    ,where t is time

    BTW, this is not "Advanced Physics" ;-)
     
  4. Jan 10, 2006 #3
    You're right, that's not advanced physics, its simple DE. But that's not what I asked.
    For that equation to make sense, the exponent should be dimensionless. C*t is not. That's the part I don't understand
     
  5. Jan 10, 2006 #4

    lightgrav

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    N is a count ... dN/dt has units counts/sec ... C must have units 1/sec.
     
  6. Jan 11, 2006 #5
    If A is area and V is volume (and yes, they are) then dimension of your constant is
    m2/m3 * m/s = 1/s
    and no problem.
    I advise to use more precise formula
    dN/dt = -1/4 n*<v>*A = -1/4 AN/V * sqrt[kT/(2*3.1416*m)]
     
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