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Homework Help: Ideal gas, pistons and water

  1. May 4, 2010 #1
    1. The problem statement, all variables and given/known data

    An upright cylinder 1.00m tall and closed at it's lower end is fitted with a light piston that is free to slide up and down. Initially the piston is in the centre. Above the piston, the cylinder forms a cup-like cavity which water is poured into until it is full. Assuming that the lower portion of the cylinder contains an ideal gas, determine the position of the piston when the upper cavity is full of water.


    2. Relevant equations

    Density of water = 1000 kg/m^3

    3. The attempt at a solution

    I have tried doing this in so many different ways, here is but one (I have a very strong feeling i am barking up the wrong tree, this question is only worth 5 marks out of 100 on an exam paper. I must be overcomplicating it)

    let h be the final distance from the base to the piston when the upper cavity is filled with water

    let A be the area of the piston

    Theory:
    When the upper cavity is full of water, the preassure of the water acting down must be equal to the preassure of the gas acting up for equilibrium.
    So find and equate the final equilibrium Preassures:

    For the Water:

    the preassure exerted is force/area

    Pw = {mg}/{A}

    since the mass of water m = \rho V

    where the volume V = A(1-h)

    so:

    Pw = {g \rho A(1-h)} / A = g \rho (1-h)
    Now for the gas:

    ???

    I have no idea, this is where i confused myself.
    After this, i tried doing it using relationships between the Work done on the gas and the work done by the water on the piston.

    I'm thoroughly stuck and if anyone's seen anything like this before then i'd be glad of a kick in the right direction. (If you know please dont post the entire answer, I just need to know what i've missed or where to start. Thanks)

    Edit: Sorry about the formatting, I tried to make it look pretty but my Latex is pretty rusty
     
  2. jcsd
  3. May 4, 2010 #2
    What do you know about the pressure and volume of an ideal gas?
     
  4. May 5, 2010 #3
    PV = nRT = NkT

    so:

    P is proportional to V^-1
     
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