The classical distribution function 
f () = e
^{(μ)/τ
} = λe
^{/τ
}

The chemical potential of an ideal gas 
μ = τ log

The free energy of an ideal gas 
F = Nτ
log
 1

The pressure of an ideal gas is given by the ideal gas law 
p =

The entropy of an ideal gas 
σ = N
log
+

The energy of an ideal gas 
U =
Nτ

The heat capacities for an ideal gas 
C
_{V} =
N
C
_{p} =
N

The FermiDirac Distribution function 
f () =

The Fermi energy of a degenerate Fermi gas 
= (3Π
^{2}
n)^{2/3}

The energy of the ground state of a Fermi gas 
U
_{gs} =
N

The BoseEinstein Distribution Function 
f () =
