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Thermodynamics: polytropic processes

  1. Nov 19, 2009 #1
    1. The problem statement, all variables and given/known data
    "During some actual expansion and compression processes in piston-cylinder devices, the gases have been observed to satisfy the relationship [tex]PV^n=c[/tex] where n and C are constants. Calculate the work done when a gas expands from 150kPa and .03 m^3 to a final volume of .2m^3 for the case of n = 1.3


    2. Relevant equations
    [tex]W = \int_{1}^{2} {P}dV[/tex]


    3. The attempt at a solution
    [tex]PV^n=C \Rightarrow P=CV^{-n} \Rightarrow
    W = \int_{.03}^{.2} {150V^{-1.3}}dV = 621 kJ[/tex]
    Which...is wrong :(

    The solution the book offers is:
    [tex] P_{2} = P_{1}\frac{V_{1}}{V_{2}}^n = (150)\frac{.03}{.2}^{1.3} = 12.74 kPa
    \Rightarrow W = \int_{1}^{2} {P}dv = \frac{P_{2}V_{2} - P_{1}V_{1}}{1-n}
    =\frac{(12.74 \cdot .2 - 150 \cdot .03)}{1-1.3} = 6.51 kJ[/tex]

    Could someone explain why the way i did it is "unacceptable"?
     
    Last edited: Nov 20, 2009
  2. jcsd
  3. Nov 19, 2009 #2

    Mapes

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    Science Advisor
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    Gold Member

    Because [itex]C\neq150[/itex]; check your integrand.
     
  4. Nov 20, 2009 #3
    Oh...woops
    I put in 150 cuz i was still thinking that [tex]W = P\Delta V[/tex] and I put in 150
    then what would i put in? the question does not supply C though
     
  5. Nov 20, 2009 #4

    Borek

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    Staff: Mentor

    You can calculate C from initial state.

    --
    methods
     
  6. Nov 20, 2009 #5
    oh lol!
    ok, i got the answer, thanks :)
     
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