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I could be wrong, but I'm pretty sure residual entropy is the entropy at T=0K. Because although the third law states that deltaS=0 at T=0K, this is theoretical and can only happen if the substance is a perfect crystal. So, in reality, there will be some entropy.
Residual and positional entropy are the same thing. I would like to add that molar residual entropy is different than residual/positional entropy. When determining the degeneracy of molar residual entropy, the exponent used in Avogadro's constant. This makes sense because molar residual entropy represents the entropy in one mole of a certain compound.
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