Consider N massless non-interacting spin-s fermions in a three-dimensional box of volume V . (a) Find...

Consider N massless non-interacting spin-s fermions in a three-dimensional box of volume V .
(a) Find the Fermi energy E_F as a function of N, V , and s.
(b) For zero temperature, find the pressure in terms of N, V , and E_F .
(c) Plot the occupation of states as a function of the energy at a temperature of T =E_F /(10k). Your graph can be a sketch by hand. However, the effect of the finite temperature should be indicated clearly.
(d) Suppose that you start with a gas of these particles in a box of volume V near T = 0.
Now suppose that a valve is opened such that the gas can undergo a free expansion, allowing it to come to equilibrium at a new volume that is twice as large as the initial volume. Assuming no work or heat transfer occurs during the expansion, does the temperature of the gas go up, down, or stay the same? Explain your reasoning.

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genius_generous answered 2 years ago

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