Problem $4$ Serway & Jewett $20\mathrm{.}14$

A certain molecule has f degrees of freedom. Show that an ideal gas consisting of such

molecules has the following properties:

$($a$)$ its total internal energy is f nRT $/2,$

$($b$)$ its molar specific heat at constant volume is f R$/2,$

$($c$)$ its molar specific heat at constant pressure is $($f $+2)$R$/2,$ and

$($d$)$ its specific heat ratio is $=$ CP $/$CV $=($f $+2)/$f