Consider N non-interacting fermions of mass m confined to a 3-dimensional cubic box of dimensions L XL XL (a) Calculate

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Consider N Non Interacting Fermions Of Mass M Confined To A 3 Dimensional Cubic Box Of Dimensions L Xl Xl A Calculate 1 (90.01 KiB) Viewed 54 times

Consider N non-interacting fermions of mass m confined to a 3-dimensional cubic box of dimensions L XL XL (a) Calculate the Fermi energy assuming the fermions in the box move ultra-relativistically and express your answer in terms of the volume of the box V = L3. (In the ultra- relativistic limit E ~ pc = ħkc). (6) Find an expression for the total energy Etot of this system in the ultra-relativistic limit. - = (c) Find an expression for the pressure as a function of volume, employing the thermody- namic relation p -(@E/V), where E is the internal energy (total energy of the system).