Answer to Question #125032 in Physical Chemistry for INDRAJIT SOMNATH WADGAVE

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