= Solution
For a high-temperature <linear rigid rotor>, $q_{\rm rot}=T/\theta_{\rm rot}$ up to temperature-independent symmetry/<spin> factors. Therefore $q'/q=1/T$ and $q''=0$, giving
$$
\boxed{\frac{C_{V,m}^{\rm rot}}R=0-1+2=1.}
$$
This agrees with the <equipartition theorem> for two quadratic rotational coordinates. It is the rotational contribution; adding free three-dimensional translation gives $C_{V,m}=5R/2$ when vibrations remain unexcited. A constant <rotational symmetry number> does not affect this derivative.
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