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Find the equation of state (thermo)

  1. Oct 28, 2008 #1
    1. The problem statement, all variables and given/known data
    A hypothetical substance has an isothermal compressibility k = a/v and an expansivity B = 2bT/v where a and b are constants and v is the molar volume. Show that the equation of state is v-bT2+aP = g where g is a constant.

    2. Relevant equations
    k= -v(dP/dv)T
    B = 1/v(dV/dT)P
    (dP/dT)v = -(dv/dT)P/(dv/dP)T

    3. The attempt at a solution
    I went about it 2 different ways; neither seem to work:
    1) B = 1/v(dV/dT)P = 2bT/v
    => (dV/dT)P = 2bT
    => v = bT2 + g'

    k = -v(dP/dv)T = a/v
    => (dP/dv)T = -a/v2
    => P = a/v + g"

    And I don't know what to do from here...

    or
    2)
    dP = (dP/dv)T dv + (dP/dT)V dT
    = -(dv/dT)p/(dv/dP)T dT - k/v dv
    = Bv/ (dv/dP)^(-1)T - k/v dV
    = -Bk dT - k/v dv
    = -2bTa/v^2 dT - a/v^2 dv
    P = (1/v^2)baT^2 + a/v + g


    Thanks
     
  2. jcsd
  3. Oct 28, 2008 #2

    olgranpappy

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    Homework Helper

    this is wrong.

     
  4. Oct 28, 2008 #3

    olgranpappy

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    Homework Helper

    should be
    [tex]
    k=-\frac{1}{V}\left(\frac{dV}{dP}\right)_T
    [/tex]
     
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