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    Pressure of Ideal Bose and Fermi Gas Satisfy PV = 2/3 E

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    In class we wrote down the thermodynamical potential for a gas of non-interacting (non- relativistic) fermions in three dimensions. We found a simple result for fermions of the form (see attached).

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    In 2a) you have obtained:

    PV = - Omega

    According to Eqs. (1) and (2):

    Omega = +/- kT Integral over e de g(e)Ln{1 -/+ Exp[-beta(epsilon - mu)]}

    Partial integration:

    Integral over e de g(e)Ln{1 -/+ Exp[-beta(epsilon - mu)]} =

    Lim e--> infinity of [ eg(e)Ln{1 -/+ Exp[-beta(epsilon - mu)]} ]

    - [ eg(e)Ln{1 -/+ Exp[-beta(epsilon - mu)]} ] at e = 0

    - Integral over e de e g'(e) Ln{1 -/+ Exp[-beta(epsilon - mu)]}

    - Integral over e de e g(e) d/de Ln{1 -/+ Exp[-beta(epsilon - mu)]} ...

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