Consider the multiplicity of a classical gas of N non-interacting molecules (not necessarily monatomic). Since they don't interact,their positions are not correlated, so the multiplicity of each will be simply proportional to the volume, with the result that the total multiplicity Ω = VNfN(U), where fN is some function of the total internal energy. Show that this implies the two conditions for an ideal gas.
Ω(N,n) = N!/[n!(N-n)!]
PV = NkT
The Attempt at a Solution
I'm not really certain how to go about this. Would the two conditions be referring to the ideal gas law PV = NkT = nRT and that a entropy and multiplicity increase?