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Thermodynamics Questions

  1. Jan 17, 2010 #1
    1. The problem statement, all variables and given/known data

    Hi, I got a set of problems to do and there are a few I am having trouble with: (edit: I had more questions before but I figured them out)

    1. A hypothetical substance has an isothermal compressibilty [tex]\kappa[/tex]=a/v and an expansivity [tex]\beta[/tex]=2bT/v, where a and b are constants, and v is the specific volume.
    a) Show that the equation of state is given by v-bt2 + aP=constant
    b) If at a pressure P0 and temperature T0, the specific volume is v0, evaluate the constant.



    3. The attempt at a solution

    1. Ok I figured out 2a), but I don't know how to evaluate the constant for 2b)...what I did was just replace v, T, and P with v0, t0, and P0, but I don't think that is right.

    I think it may be something with an exact differential equation, I am not sure though. I have ([tex]\beta\nu[/tex]/[tex]\partial[/tex]P)[tex]\partial[/tex]T = -([tex]\kappa\nu[/tex]/[tex]\partial[/tex]T)[tex]\partial[/tex]P
    Help for that one please



    Btw how do you make the kappa symbol on the same level as everything else?
     
    Last edited: Jan 18, 2010
  2. jcsd
  3. Jan 17, 2010 #2
    Ok number 3 I figured out
     
  4. Jan 18, 2010 #3
    Any help?
     
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