Consider a sample containing $2\mathrm{.}30$ mol of an ideal diatomic gas.

$($a$)$ Assuming the molecules rotate but do not vibrate, find the total heat capacity of the sample at constant volume.

nCv $=$ J$/$K

$($b$)$ Assuming the molecules rotate but do not vibrate, find the total heat capacity of the sample at constant pressure.

nCp $=$ J$/$K

$($c$)$ Assuming the molecules both rotate and vibrate, find the total heat capacity of the sample at constant volume.

nCv $=$ J$/$K

Assuming the molecules both rotate and vibrate, find the total heat capacity of the sample at constant pressure.

nCp $=$ J$/$K