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Homework Help: Alternative Real Gas Equation of State

  1. Sep 8, 2011 #1
    1. A friend suggests to you an alternative to the Virial equation of state: P=(RT/Vm)-(B/Vm2)+(C/Vm3)

    a.) Show that this equation is useful by proving that it demonstrates critical behavior.
    b.) Find the critical constants Pc, Vm,c, and Tcin terms of B, C and R.
    c.) Calculate the compressibility factor Zc.

    Vm=molar volume, P=pressure, T=temp, and B&C would normally be the first and second virial constants.




    2. I know that first and second derivatives of pressure with respect to volume should be zero at the critical temperature.



    3. Through an algebraic nightmare, I figured out that Tc is equal to (6Vm^3(B+C)-12C+2BVm^2)/(RVm^2(2+Vm)) by taking the first and second derivatives, then setting them equal to each other since they should both be zero at Tc. I have no idea how to find Pc, Vc or Vm since it doesn't appear possible to isolate Vm. How should I proceed?
     
  2. jcsd
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