I Thermal Physics: Fermi Gas and chemical potential

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Hi all, I have an issue trying to understand the following paragraph from Blundell's book.

Screenshot 2019-03-17 at 9.16.08 PM.png


How, exactly, does the definition of ##\mu_0 = E_F## "make sense"? In the sentence after 30.21, it seems to say that the mean energy for a system with ##N## particles differs from that of a system with ##N-1## particles by the highest occupy-able energy level at ##T = 0##, which is ##E_f##. What does this mean?

Many thanks in advance.
 

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DrClaude

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The chemical potential can be seen as the (Gibbs free) energy per particle, or the energy necessary to add one more particle to the system. With fermions at T = 0, all states up to ##E_F## are occupied, therefore the next fermion will add an energy of ##E_F## to the system. It does make sense to equate ##\mu(T=0) = E_F##.
 

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