5. a) Derive an expression for ground state energy of a completely degenerate FD gas. For copper, take kg101.9 and Js,1062.6,m105.83134328−−−×=×=×=emhVNto calculate Fermi energy. (6,4) b) Show that the partition function of an N-particle system is given by the expression: 2/332NNNNNmhVZZβπ== Obtain expressions for (i) heat capacity at constant volume, (ii) average pressure exerted by the gas, and (iii) Helmholtz free energy F.
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