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Help with Adiabatic Derivation

  1. Mar 7, 2010 #1
    Using [tex]dU = dW[/tex],

    [tex]\frac{f}{2}NkdT = -PdV[/tex]

    I eventually came to

    [tex]T^\frac{f}{2}V = \mbox{constant}[/tex]

    I tried to then get it to the form in the book - [tex]PV^\frac{f+2}{f}=\mbox{constant}[/tex] using the formula [tex]PV = NkT[/tex]:

    [tex]\left(\frac{PV}{Nk}\right)^\frac{f}{2}V=\mbox{constant}[/tex]

    [tex]P^\frac{f}{2}V^\frac{f+2}{2}=\mbox{constant}[/tex]

    How do I get it in the right form? Thanks
     
    Last edited: Mar 7, 2010
  2. jcsd
  3. Mar 7, 2010 #2
    [tex]P^{\frac{f}{2}} V^{\frac{f+2}{2}}=const[/tex]
    so i have:
    [tex]\frac{f}{2}lnP+\frac{f+2}{2}lnV=constant[/tex]
    then:
    [tex]lnP+\frac{f+2}{f}lnV=constant[/tex]
     
  4. Mar 7, 2010 #3
    Thanks quydau35 :)
     
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