Van der Waals gas is not real gas?

  1. From van der Waals , (P+a/v^2)(v-b)=RT,
    At critical temperature, I get (∂P/∂V)at constant temperature =0
    and (∂^2P/∂V^2) at constant temperature ,T=0.
    then critical pressure,P = a/(27b^2)--------1
    critical volume,v=3b-----------2
    critical temperature=8a/(27Rb)----------3
    then simultaneous equation 1 and 3,
    I get b=(RT/8P), b=(v/3) ------------------4
    But from the experiment, we get T,P,v and then substitute into the two equation from 4,both b have different values. Why?

    Thank you
  2. jcsd
  3. mfb

    Staff: Mentor


    Using your equations:
    P = a/(27b^2)

    I get
    8/(27b) = 8/(27b)

    Looks fine.

    Are you sure your real gas is a perfect van-der-Waals gas?
  4. I though all real gas is van der Waals ? Then what do you mean by perfect van der Waals?
  5. Philip Wood

    Philip Wood 1,180
    Gold Member

    On other threads which you've started, it's been made clear (I think) that the V der W equation is a theoretical equation based on some quite crude assumptions. No actual gas obeys the V der W equation perfectly. [The confusion may be caused because 'real gas' is sometimes used to mean non-ideal gas, even a theoretical non-ideal gas, and not necessarily an actual gas.]
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