Final answer:
The heat capacity of polyatomic molecules at room temperature increases from the value R due to the contribution of vibrational degrees of freedom, which allows the molecules to store additional thermal energy.
Step-by-step explanation:
When considering the heat capacity of polyatomic molecules in relation to the value R (the gas constant), the introduction of vibrational degrees of freedom at room temperature would increase their heat capacity beyond R. Each translational and rotational degree of freedom contributes R/2 to the heat capacity (Cv) of a gas.
For vibrational modes, each mode effectively counts as two degrees of freedom, due to both potential and kinetic energy contributions, and hence contributes R to Cv. The presence of these vibrational degrees indicates the capacity of the molecules to store more thermal energy and therefore increases heat capacity.
Polyatomic molecules at room temperature typically possess translational and rotational degrees of freedom, and some vibrational modes may be populated as well. According to the information given, the heat capacities of real gases are somewhat higher than those predicted for gases without vibrational motion, implicating the significance of vibrational energy at these temperatures.
Therefore, with additional degrees of freedom beyond translational and rotational motion, one would expect the heat capacity of polyatomic molecules to be higher than the predictions using Cv = d (R/2) where d is the number of non-vibrational degrees of freedom only.