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Deflating tire, thermodynamics problem

  1. May 10, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the size of the hole in the tire after it has taken 60minutes to become flat.


    2. Relevant equations
    Impulse = F*Deltat = DeltaN*Deltap (N=molecules, p=momentum) , P = F/A (A is area of hole), Equipartition for gas in 1-d -> 1/2kT = 1/2mv^2
    Derivative of ideal gas law (assuming T and V are constant) = dPV=dNkT


    3. The attempt at a solution
    the general equation i came up with that describes the decrease in pressure as a function of time is P = e^-((Aroot(kT)/(2Vroot(m)) *t) + P(initial)) actually ill upload a typed image
    flkqyv.jpg

    Using a known volume of a tire i am trying to find the initial pressure but im having trouble figuring out how to do it any help would be appreciated. Also im not sure if i have made a mistake in deriving this equation

    Ummm have i explained well enough? Is there more i need to include? Or is the answer not simple? Im sort of waiting for an update if someone could clarify it would be nice.
     
    Last edited: May 10, 2010
  2. jcsd
  3. May 10, 2010 #2
    Oh i see where i made the mistake. After the integration there should be 1 constant on each side to be combined into another constant which is not P(initial). What a silly mistake. From there it is pretty straightforward.
     
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