1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Virial equation of state

  1. Jan 25, 2015 #1
    1. The problem statement, all variables and given/known data
    It's just that in my textbook, for section titled "Second virial coefficients can be used to determine intermolecular potentials," I have an equation that I do NOT understand how it was derived---I tried to do it over and over, but couldn't quite figure how. If anyone could explain, thank you!!!

    B2v(T) = RT * B2p(T), where B2v(T) and B2p(T) are virial coefficient

    2. Relevant equations

    B2v(T) = RT * B2p(T), where B2v(T) and B2p(T) are virial coefficient

    3. The attempt at a solution
    I assume the equation comes from Z, the compressibility factor:

    Z = PV/RT, where it can be expanded to:

    Z = 1 + B2v(T)/V + B3v(T)/V2 + ...
    Z = 1 + B2p(T)*P + B3p(T)*P2 + ...

    So, I equivocated 1 + B2v(T)/V + ... = 1 + B2p(T)P + ...
    B2v(T)/V + ... = B2p(T)P + ...
    ...and tried multiplying both side by V or divide by P to cancel out other virial coefficients with numbers larger than 2 (meaning B3v and B3p), but I don't know how to progress anymore.......pls give me hints! I want to understand how the original equation B2v(T) = RT * B2p(T) was obtained!
     
  2. jcsd
  3. Jan 25, 2015 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Perhaps the idea isn't to let all higher order terms cancel, just to equate the first order coefficients ?
     
  4. Jan 25, 2015 #3

    Quantum Defect

    User Avatar
    Homework Helper
    Gold Member

    What happens if you use the compressibility (written in the volume version of the virial expansion) to solve for P. Take this series expansion for P and plug into the pressure version of the virial expansion. Compare this equation with the virial expansion in terms of volume. Coefficients in front of the same powers of 1/V must be the same for the two expressions to be the same:

    A x + B x^2 + ... = alpha x + beta x^2 + ... is true iff A = alpha, B = beta, ....
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted