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Nonlinear molecules have 3 rotational degrees from the 3 axes of rotation. Since there is symmetry about only one axis, linear molecules have 2 rotational degrees. The degrees of freedom contribute to the heat capacity.
I'm pretty sure that generally, nonlinear molecules will have higher molar heat capacities than linear molecules. For example, in 4C.1 from the textbook, NO2 (bent) has higher molar heat capacity than NO (linear).
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