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Finding work for a gas in a piston cylinder

  1. Oct 9, 2015 #1
    1. The problem statement, all variables and given/known data
    A gas in a piston-cylinder assembly undergoes a process for which the relationship between pressure and volume is pV2=Constant. The initial pressure is 1 bar, the initial volume is 0.1 m3, and the final pressure is 9 bar. Determine the final volume and the work for the process.

    2. Relevant equations


    3. The attempt at a solution
    V2=sqrt((p1)(V12)/(p2))
    V2= 0.03333 m3

    W=∫ pdV
    W=∫ C/(V2) dV
    =C[-1/V]
    =C[-1/(V2-V1)]
    =[(p2V22)-(p1V12)][-1/(V2-V1)]

    =[((900000Pa)(0.0333m3)2)-((100000Pa)(0.1m3)2))][-1/(0.0333-0.1)]

    I think the answer is supposed to be W= -19.97KJ, I'm not sure what I'm doing wrong.
     
  2. jcsd
  3. Oct 9, 2015 #2
    Your integration is incorrect, and your determination of the constant C is incorrect. ##C=p_1V_1^2=p_2V_2^2##
     
  4. Oct 9, 2015 #3
    Oh ok, the constant part makes sense. How is the integration wrong though?
    I thought ∫1/x^2 dx = -1/x ?
     
  5. Oct 9, 2015 #4
    Yes, that's correct, but you substituted the integration limits incorrectly.

    Chet
     
  6. Oct 9, 2015 #5
    Thanks for your help!
     
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