Problem $2(10$ pts$)$

$($a$)$ Derive the following equations for $c_p$ and $c_v($recall$,=\frac{c_p}{c_v})$:

$c_p=\frac{R}{-1}$

$c_v=\frac{R}{-1}$

$($b$)$ For what assumptions are these equations valid?