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**Unformatted text preview: **b) Using the result of part a), derive an expression for the entropy. c) From the expression of for the energy, Eq. (1) above, and the answer to part b), show that the Helmholtz free energy of a degenerate Fermi gas can be written in the form F = U o- A 2 (2) and give an explicit expression for the function A in terms of D( F ). 6 . Free energy of a degenerate Fermi gas II. The Sommerfeld expansion gives that the chemical potential of a degenerate Fermi gas is given by = F-1 3 2 2 2 F . (3) a) From this expression, derive the Helmholtz free energy. (It should be the same result as part c of problem 5.) b) Find the pressure of a degenerate Fermi gas. c) Give a physical reason for the non-zero value of the pressure at =0....

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