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Ideal Gas Law Question

  1. Apr 17, 2009 #1
    1. The problem statement, all variables and given/known data
    A vertical cylinder has a piston of mass "m" on top that is free to move without friction. If
    there are "n" moles of an ideal gas in the cylinder at absolute temperature "T", what is the
    height "h" of the piston above the bottom of the cylinder so that it will be in equilibrium
    under its own weight?


    2. Relevant equations
    PV=nRT
    P=F/A
    V=A*h


    3. The attempt at a solution
    I worked this through summing the forces on the piston and got F_gas - F_atm -mg =0 or P_gas*A - P_atm*A = mg

    this gives P_gas = mg/A + P_atm

    from here I looked at the Ideal Gas Law Equation,

    PV=nRT, solving for V and substitution we get

    A*h = nRT/(P_gas)

    so h = nRT/(P_gas*A)

    plugging in the P_gas I got:

    h = nRT/(mg + P_atm*A)

    The thing is, the area was not mentioned in the question and I don't believe we're supposed to have area in the final answer (which is in variable form). I know the work I did above is correct, but is there a way to get rid of the A, as I am 90% sure it isn't supposed to be there. Thanks!
     
  2. jcsd
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