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Thermo: Isentropic expansion

  1. Sep 7, 2009 #1
    1. The problem statement, all variables and given/known data

    I have a system u =Av-2exp(s/R)

    N moles of this substance initially at T0 and P0 are expanded isentropically until the pressure is halved. What is the final temperature?

    2. Relevant equations

    du = [tex]\partial[/tex]u[tex]\partial[/tex]s ds + [tex]\partial[/tex]u[tex]\partial[/tex]v dv
    du = Tds - Pdv


    3. The attempt at a solution

    If this function is changing isentropically, ds would have to be zero, correct? The derivative of v would have to be such as to multiply P times 1/2, correct? But, if ds --> zero, how do I find my final temperature as a multiple of my initial temperature? Do I have to start plugging values which would satisfy these conditions back into the original equation?
     
  2. jcsd
  3. Sep 7, 2009 #2

    Mapes

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    How about expressing T as [itex](\partial U/\partial S)_V[/itex] and P as [itex]-(\partial U/\partial V)_S[/itex] and looking at how the volume changes during the process?
     
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