(adsbygoogle = window.adsbygoogle || []).push({}); a) Consider a system that may be unoccupied with energy zero or iccuped by one particle in either of two states, one of zer oeenrgy and one of energy epsilon. Show taht the Gibbs sum for this system is

[tex] z = 1 + \lambda / \lambda\exp(-\epsilon/\tau) [/tex]

b) Show that the thermal average occupancy of the ssytem is

[tex] <N> = \frac{\lambda + \lambda\exp(-\epsilon/\tau)}{z} [/tex]

c) show that the thermal average occupancy of the state at eneryg = epsilon is

[tex] <N(\epsilon)> = \lambda\exp(-\epsilon/\tau)/z [/tex]

d) Find an expression for the theram laverage eneryg of the system

e) Allow the possibility tat the orbital at 0 and at epslon may be occupied each by one particle at the same time, show that

[tex] z = 1 + \lambda + \lambda\exp(-\epsilon/\tau) + \lambda^2 \exp(-\epsilon/\tau) = (1+ \lambda) [1 + \lambda \exp(\epsilon/\tau)] [/tex]

I will post my attempted solutions in a seaparate post.

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# Gibbs sum

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