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Consider a free fermion gas of N particles in a volume V at zero temperature. The...

Consider a free fermion gas of N particles in a volume V at zero temperature. The total kinetic energy of the gas is U = (3/5)N epsilon-F with epsilon-F

= (hbar^2/2m)((3(π^2)N)/V )^ 2/3 .

(a) Using the thermodynamic identity show that the pressure of the gas is given by p = − (∂U/∂V )σ,N .

(b) Derive an expression of the degenerated-gas pressure and express your final result in terms of U and V .

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