The third law of thermodynamics says that at T=0 the entropy of a system must be 0. I'm confused to how to corresponds to the statistical/quantum mechanical treatment of systems, which seems to say that S doesn't have to be 0 at T=0 when degenerate energy levels are considered.
Some materials have mulitple degenerate ground states, like iron has two. So if T=0 and all atoms of iron are in the ground state, then the multiplicity of the ground state is $W_g=2$. So $S=k lnW_g=9.5654*10^{-24}J/K$, which isn't 0. Can someone clarify what my mistake is?