we have non relativistic electrons at absolute zero. we need to show that the total energy is 3N*Ef/5 where Ef is the Fermi energy. this calculation I can do. we then need to show that the Pressure is equal to 2U/3V where U is the total energy. I did this by noting the dU=TdS - PdV and at absolute zero, S=0 therefore dS=0, so P = -dU/dV. using the explicit expression for U in terms of V you can get the required answer easily. I originally tried deriving this by finding the partition function for the fermions explicitly, then finding the helmholtz free energy, and then finding the pressure from this, using e.g(adsbygoogle = window.adsbygoogle || []).push({});

F=-Kb*T*ln(Zn)

however this method did not appear to work (it gave me very messy mathmatical expressions that did not look right). I'm not too sure why you can't get the answer this way. Is it because the equations for U,S,F in terms of the partition function only apply to Boltzmann statistics, and not quantum stats?

Sachi

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# Homework Help: Fermi energy of non relativistic electrons

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