0
Show that the equation of state
holds for both free bosons and fermions (and also in the classi- cal case). Show that an ideal ultrarelativistic gas, given by the energy spectrum ε = shk, still obeys the same equation of state.
Physics
For fermions, we have
In the thermodynamic limit, for free fermions, we can write
from which we prove that pV = 2U/3. The same manipulations can be carried out for bosons, but we should pay special atten- tion to the h = 0 state. For the classical gas, this result is trivial.
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