Help with Adiabatic Derivation

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  • #1
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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
 
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  • #2
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[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]
 
  • #3
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Thanks quydau35 :)
 

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