1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Regarding quantum physics(fermi energy)

  1. May 2, 2009 #1
    The average electron energy in an electron gas is known to be <e>=3E(f)/5. The energy for N such electrons would be 3NE(f)/5. Find the pressure in terms of U and V, where V is the volume of the electron gas.

    My solution.

    Fermi energy
    therefore E(F) is proportional to V^(-2/3)
    since it is proportional i just have to plug into 3NE(f)/5 or the other one correct?


    so which formula do i plug V^(-2/3) into E(F)? The 3NE(f)/5 or 3E(f)/5.
  2. jcsd
  3. May 2, 2009 #2
    Hah, you have me confused. Lets write down what you have:

    [tex]E_F = C V^{-2/3}[/tex]

    where I stuck all those nasty constants that don't depend on V in the term C.

    So, you also know [tex]P=-dU/dV[/tex].

    You have all the pieces, just put them together now.
  4. May 2, 2009 #3
    but the pressure needs to be in terms of U and V.
  5. May 2, 2009 #4
    First use substitution to remove the Fermi energy from the first equation. Then take the derivative with respect to V. And substitute back in U to get the pressure in terms of U and V.
  6. May 3, 2009 #5
  7. May 3, 2009 #6
    after i take derivative i have p=-dU/dV=(6/15)NC*(V^(-5/3))
    you can't substitue this into U because it isn't=U to derivative of du/dv.
  8. May 3, 2009 #7
    First, 6/15 can be simplified. Second, you can pull a U out of that final equation of yours. Just remember what U is equal to, and factor that out of the equation above, and then make it U.
  9. May 3, 2009 #8
    Can i do this U=3/5*N*C*(V^(-2/3)). so solve for N and plug into p=-dU/dV=(6/15)NC*(V^(-5/3))? don't really understand what you mean by pull out U from -du/dv.
  10. May 3, 2009 #9
    You can do that as well, or even solve for C and plug it in. All the constants will cancel out in the end and you will be left with U and V for your pressure equation.
  11. May 3, 2009 #10
    thank you so much.
  12. May 3, 2009 #11
    now he asks to find bulk modulus. B=-V*(dp/dv) but he wants it in terms on U only and if i take derivative and simplify i am left with 2U/3V again but am unsure of how to get further in terms of plugging in for V.
  13. May 3, 2009 #12
    You need to show some work. And remember that U also depends on V.
  14. May 3, 2009 #13
    so use U=(3/5*N*C*V^(-2/3)) solve for V and substitute?
  15. May 3, 2009 #14
    here's what i did B=-V(dp/dv)=-V((d/dV(2U/3V))=2U/3V. But i need my answer in terms of of only U.
  16. May 3, 2009 #15
    You didn't take the derivative of U with respect to V in that formula. But that formula may not be the best to take the derivative of. Try a formula you quoted earlier...

    Take the derivative of that pressure with respect to volume, then substitute the U back in.

    Edit: Nevermind, I see your problem. What does the problem ask for exactly?
    Last edited: May 3, 2009
  17. May 3, 2009 #16
    The bulk modulus, B, is defined to be B=-V(dp/dv). Find expression of B in terms of U.
  18. May 3, 2009 #17
    Well, I get a similar answer as with the U/V, except I get a different coefficient than you. But I still also get the volume in my bulk modulus. So not sure how to express it only as U.
  19. May 3, 2009 #18
    thanks for help i will just ask teacher tom.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook