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Which should I use to prove this?

  1. Nov 23, 2012 #1
    (∂s/∂P) at constant volume =1/T ×(∂u/∂T)at constant volume × (∂T/∂P) at constant volume

    s(P,v)
    Tds= du +pdv
    h= u + pv
    h(P,v)
    u(P,v)
    or other formula?
    How am I going to choose ? Please guide

    Thank
     
  2. jcsd
  3. Nov 23, 2012 #2

    haruspex

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    I'm not expert on gas theory, so I'll just treat this as an algebraic question.
    Of those 'formulae', only two are equations. One of those two involves h, not mentioned anywhere else. So that leaves Tds= du +pdv as the only candidate.
    What would the constant volume version of that equation look like?
     
  4. Nov 23, 2012 #3
    The others also can become equation like s is function of v and p
    So ∂s=(∂s/∂p)dp + (∂s/∂v)dv
    Then h=u + pv , can be dh= du + Pdv + vdp
    This is all just dealing with mathematics , please teach me how to choose
    Do you mean why did I put constant volume there? It means by keeping volume constant then only differentiate.
    Thank
     
  5. Nov 23, 2012 #4
    Have you considered using the Maxwell relations?

    BiP
     
  6. Nov 23, 2012 #5

    haruspex

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    No, I mean take this equation: Tds= du +pdv
    and turn it into an equation involving partial derivatives, v being constant.
     
  7. Nov 24, 2012 #6
    I am not really understand what is Maxwell ,
    I only can get (∂s/∂P) at constant volume = (1/T)(∂h/∂P)constant volume -(v/T)
     
  8. Nov 24, 2012 #7

    haruspex

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    Please post your working to get that.
     
  9. Nov 24, 2012 #8
    Trial
     

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  10. Nov 24, 2012 #9
    This first , only that second deriavative
     

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  11. Nov 25, 2012 #10
    You need to follow BiP's advice and familurize yourself with the derivation and application of the Maxwell equations.
     
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