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erogard
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Homework Statement
Consider a 3D gas of N non-interacting fermions in a volume V at temperature T << Ef / k.
Suppose that the particles in the energy range [0.25 Ef, 0.5 Ef] are suddenly removed.
Calculate the Fermi energy of the remaining particles after the system reaches its new thermal equilibrium, and the energy releases to its surrounding.
Homework Equations
So correct me if I'm wrong, but here the occupation number should be given by
[tex] <n_\epsilon> = \frac{1}{\exp[(\epsilon-\mu)kT]+1} [/tex]
Now in the limit of low T (which I suppose is what is implied by the given inequality), this should be 1 for energies less than the Fermi energy, and 0 otherwise.
So, to compute the energy corresponding to the removed particles, should I integrate this equation times epsilon over that interval? ANd knowing what the new N is. how do I then compute the adjusted Fermi energy?
Any hint/explanation would be more than welcome. Thanks!
EDIT: Ok, so I think I got both the released energy and the new number of particles by integrating with the appropriate DoS function. Now wondering how to get the new Ef.
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