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Thermodynamics- pV^n = constant.

  1. Sep 8, 2009 #1
    1. The problem statement, all variables and given/known data
    A closed system consisting of 2 lb of a gas undergoes a process in which pV^n=constant. For: p1=20 lb/in^2 , V1=10 ft^3 and p2=100lb/in^2 V2=2.9 ft^3.

    Find n.


    2. Relevant equations

    pV^n=constant
    3. The attempt at a solution

    Im just having trouble realizing how to find n. This seems very basic and maybe im just rusty from having the summer off, this is a review question.

    (p1)(V1)^n = (p2)(V2)^n

    Now Im having trouble realizing how to re-arrange that to find n... Ive tried using the relation p1V1^n=5P1(.29V1)^n but everything keeps canceling out. Can someone push me in the right direction?

    Ive also tried solving for n in terms of C and plugging that back in and that just gives me a jumbled mess.
     
  2. jcsd
  3. Sep 8, 2009 #2

    Mapes

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    The logarithm function turns exponential factors into multiplicative factors...
     
  4. Sep 8, 2009 #3
    Yah I understand that. But Even if I do that wont I be left with:

    n*ln(P1V1)=n*ln(P2V2)

    So... All I can do is cancel things out. I cant really isolate n... right? unless I want #n=0.

    Feel free to call me a moron if im missing something obvious :tongue:
     
  5. Sep 8, 2009 #4

    Mapes

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    You're not taking the logarithm correctly.
     
  6. Sep 8, 2009 #5
    Oh God I suck....

    So does this sound good to you?

    ln(P1(V1)^n)=ln(P2(V2)^n)

    ln(P1) + n*ln(V1) = ln(P2) + n*ln(V2)
     
  7. Sep 8, 2009 #6

    Mapes

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    Better!
     
  8. Sep 8, 2009 #7
    Awesome, thanks Mapes! How did I not see that :blushing:

    I gotta say, I appreciate your help. I havent been on the boards in quite a while but i remember you helping me in the past as well. Thanks again Mapes!
     
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