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I believe the shape affects how many different shapes or positions the atoms in the molecule can be in. Since entropy is associated with the number of states or positions the atoms in a molecule can take, the shape of the molecule is associated with entropy.
The shape affects entropy because it affects the molar heat capacity, which is part of the equation for a change in temperature (delta S = C*ln(T2/T1)). Depending on the shape the molar heat capacity can be 3/2*R, 5/2*R, or 7/2*R
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