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!

Helmholtz energy of Simple solid

  1. Dec 1, 2013 #1
    The problem is :

    a) Find Helmholtz free energy F(V, T) of a simple solid.
    b) Use the result of part a) to verify that (∂F/∂T)v and (∂F/∂V)T are consistent with S(T, V) and P(V, T) in equation P=a0T-b0ln(V/V0)

    I know:
    Helmholtz free energy is F=U-TS
    and dF=-SdT-PdV
    S=-((∂F/∂T)v)
    P=-(∂F/∂V)T
    Maxwell relation: (∂S/∂V)T=(∂P/∂T)V

    My problem is that the only examples I have here of Helmholtz free energy is for an ideal gas, NOT a simple solid. Is this correct to say internal energy of simple solid is U=ncvT+nu0 ?
    And S=ncvln(T/Tr)+nRln(V/Vr+S(Tr, Vr) ?
    Where you could just substitute the equations for U and S into F and simplify?

    I found the above equations on a power point from another classes slides so I'm not sure on the background if they're accurate or not...
    Any help would be appreciated to get me on the right track!! Thanks!
     
  2. jcsd
  3. Dec 30, 2013 #2
    the trick is to specify second derivatives of F. they are the physical observables. i.e., bulk modulus, KT=-v(dp/dv)v can be chosen as murnaghan's =KTo(v0/v)^n. specific heat, CV=T(ds/dt)v can be 3R and (dp/dt)v=gamma/v*Cv, gamma being the gruneisen's ratio. you can integrate twice to get F, closed form and you can find constants v0,kt0,n,and gamma for many materials in tables. p.s., often gamma/v is assumed constant and experiments bear this out.
     
  4. Dec 30, 2013 #3
    by the way, integration is much easier if you just call the bulk modulus constant. with gamma/v*cv also constant, integration should be a snap.
     
  5. Dec 31, 2013 #4
    typo correction: KT=-v(dp/dv)t
    also, n=1 for linear compression solid
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Helmholtz energy of Simple solid
  1. Helmholtz free energy (Replies: 10)

Loading...