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    HASSANABDULWHAB's Avatar
    HASSANABDULWHAB Posts: 1, Reputation: 1
    New Member
     
    #1

    Jul 23, 2012, 06:33 AM
    Statistical physics assignment
    Statistical physics assignment 1
    1. Fugacity:
    Work out the fugacity of air at 290K (recall that the average molecular weight is 29!). Do we
    need to worry about quantum statistics?
    2. State counting:
    (a) A Bose-Einstein system has k = 2 states a; b with ga = 2; gb = 1 and N = 3 . By
    drawing energy level diagrams and assigning identical balls to represent particles, verify
    the theoretical formulae for
    f3;0g ,
    f0;3g ,
    f2;1g , and
    f1;2g in the BE case. (Hint: to
    aid visualisation, draw the energy levels as 2 lines side by side for the lower two degenerate
    levels, with one line above them for the upper level.)
    (b) Suppose in some related system, b becomes equal to a . Now check that your total count
    in (a), now agrees with
    f3g for the new system.
    (c) Repeat the calculation of each case in (a), this time for a Maxwell-Boltzmann system, by
    allocating distinguishable balls to the levels, and check the formula in each case.
    (d) Draw the single configuration possible for a Fermi-Dirac system with N = 3 , and k = 2
    states a; b with ga = 2; gb = 1 .
    3. Schottky defects:
    Atoms displaced from lattice sites inside a crystalline solid can migrate by thermal creeping
    and eventually arrive at the crystal surface. Consider an crystal with N atoms altogether, of
    which there are n Schottky defects (you may have to assume n  N ). Suppose the energy of
    formation of a single Schottky defect is w.
    (a) Show that the entropy of the system is
    S(n) = kB ln
    N!
    n!(N 􀀀 n)!
    :
    (b) Using this, and maximising S at equilibrium, show that at temperature T the defect density
    is
    n
    N 􀀀 n
    =
    1
    ew=kBT 􀀀 1
    :
    (c) Estimate this density if w = 1 eV and T = 290K or 103K
    Curlyben's Avatar
    Curlyben Posts: 18,514, Reputation: 1860
    BossMan
     
    #2

    Jul 23, 2012, 06:35 AM
    While we're happy to HELP, we won't do all the work for you.
    Please show us what you have done and where you are having problems.

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