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Calculating pressure fromV1 to V2 with a polytropic exponent

  1. Nov 6, 2011 #1
    1. The problem statement, all variables and given/known data

    I have a bicycle pump where I need to calculate the pressure in a certain volume. No heat is lost during compression so this is a isentropic system

    initial volume is 0.3L
    final volume is 0.0195
    Gas is air
    n=k


    2. Relevant equations
    I don't know, that's the problem. I recognise this as a fairly simple question but I just don't know


    3. The attempt at a solution

    non
     
  2. jcsd
  3. Nov 6, 2011 #2

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    Welcome to PF, metiz1! :smile:

    An adiabatic process (for an ideal gas) has [itex]P V^\gamma = constant[/itex], where [itex]\gamma = {7 \over 5}[/itex] for air (as a diatomic ideal gas).
    Combined with the initial pressure as standard pressure, you can calculate the final pressure.
     
  4. Nov 6, 2011 #3
    Thank you for your reply.

    I can't say I realy understand your reply though...Shouldn't I enter the initial temperature (lets say 20C, 293K) somewhere in the equation?
     
  5. Nov 6, 2011 #4

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    No, you don't need the temperature.

    Let me rephrase:
    [tex]P_{initial} (V_{initial})^{7 \over 5} = P_{final} (V_{final})^{7 \over 5}[/tex]

    Solve for [itex]P_{final}[/itex].


    You can find the formula for instance here:
    http://en.wikipedia.org/wiki/Adiabatic_process
    (Shouldn't it be in your notes or something? :confused:)
     
  6. Nov 6, 2011 #5
    Thanks for your help! I had to use a hypotetical situation (n=1.4) for my calculations and see how the real word measurements stacked up....The n value I got was like 0.8....I dun goofed the measurement I think :P
     
  7. Nov 6, 2011 #6

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    Hmm, I just realized... you're talking about a pump.
    I suppose that means the amount of air changes?
    Kind of relevant, since the formula only works when the amount of air remains constant...
     
  8. Nov 6, 2011 #7
    Yes you are right, however, in this situation I had to asume all the air was being compressed in a smaller volume withouth any air or heat escaping, so all is good.
     
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