Question

using the equipartition of energy concept estimate the ideal gas Cp(not Cv) in units KB for the low temperature regime where no vibrational modes are activated(if you calculate Cp=42KB, enter 42 as your answer )

Answer 1

Since vibrational modes are inactive, energy of ideal gas molecules is that of moving in 3 directions and rotations (for molecules consisting of 2 and more atoms). Each type of moving and rotation has average energy 1/2 KB. Number of rotational modes is 2 for linear molecules and 3 for other complex molecules. Cp = Cv + KB = N*1/2KB + KB = (N + 2)/2 KB

where N is the total number of modes.

Thus,

Cp = 5/2 KB for monoatomic gas,

Cp = 7/2 KB for linear gas molecules,

Cp = 4 KB for non-linear gas molecules