Estimate the molar heat capacity (at constant volume) of sulfur dioxide gas. In addition to translational and rotational motion, there is vibrational motion. Each vibrational degree of freedom contributes R to the molar heat capacity at high temperature. The temperature needed for the vibrational modes to be accessible can be approximated by θ = hn_vib/k, where k is Boltzmann’s constant. The vibrational modes have frequencies 35 THz, 41 THz, and 16 THz (1 THz = 1 * 10¹² Hz).

(a) What is the high-temperature limit of the molar heat capacity at constant volume?

(b) What is the molar heat capacity at constant volume at 1000. K?

(c) What is the molar heat capacity at constant volume at room temperature?