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Van der Waals derivation

  1. Oct 12, 2009 #1
    QUESTION:

    Van der Waals derived the expression:
    (P+(a/v^2))(v-b)=RT
    which is a useful approximation of the equation of state of a real gas. Here a and b are gas
    dependent constants and v =V/n is the specific volume (Volume V divided by the # of
    moles of gas molecules)
    Show that at constant volume V and temperature T but decreasing number N=n NA (NA:
    Avogadro’s constant) of particles the Van der Waals equation of state approaches the
    equation of state of an ideal gas.


    I know that I have to rearrange the VdW equation into the P=P(v,T) form and then use a Taylor series.

    I have rearranged the eqution:

    (P+(a/v2))(v-b)=RT
    P=P(v,T)
    P(v,T)=a0T - b0ln(v/v0)

    thus,

    a0T - b0ln(v/v0) + (a/v2))(v-b)= RT

    but I'm uncertain what to do next....

    Is this even correct thus far?
    Any tips on where to go from here?

    Thanks!
     
  2. jcsd
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