Derive the formula for the single particle partition function for a dilute monoatomic gas and use that to show that P is proportional to V^(-5/3).

See attached file.

Pressure excerted by a Fermi gas, at absolute zero

Show that the pressure exerted by a Fermi gas at absolute zero is p = (2NEf)/(5V) where N is the total number of particles, Ef the fermi energy and V is the volume. ((If you need to use the relation for the mean energy of particles obeying Fermi-Dirac statistics at absolute zero temperature, you can just quote it's = 3Ef/5 I derived it earlier in this problem, so you don't have to derive it again))

Describe the temperature dependence of the heat capacity of a diatomic gas.

Describe the temperature dependence of the heat capacity of a diatomic gas.