Problem 13.2: The function TV defined by G = PV - N is called the grand potential.
a) Show that dG = -SdT - PdV - NdN.
b) The grand potential for a gas (found in Chapter 25) is given by:
Ω(T,V) = -kBT ln(Z) + PV,
where kB is the Boltzmann constant and Z = (1/N!) (2Ï€mkBT/h^2)^(3/2)V is the partition function.