b) The grand potential for a system of non-interacting spin-z fermions which can occupy single-particle states of energy

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B The Grand Potential For A System Of Non Interacting Spin Z Fermions Which Can Occupy Single Particle States Of Energy 1 (94.86 KiB) Viewed 121 times

I only need part ii.) and iii.) of part b.
b) The grand potential for a system of non-interacting spin-z fermions which can occupy single-particle states of energy bi, at chemical potential u, is Þg = –kist In (e(1-4)ß +1). - i) For a 3D gas of massless fermions moving ultra-relativistically, show that we can write the grand potential in the continuum limit as: kpTV Φα -EB Fisches [* In (e6--18 + 1) ede, [5 marks] ii) By considering the limit of the integrand as T +0 separately for the two cases E<ll and € > H, show that at zero temperature, Vu4 Φα 127²(hc)3 [7 marks] iii) Hence show that the internal energy per particle of the gas is žu. [3 marks)