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

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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