Answer
See answer below.
Work Step by Step
Relevant Maxwell relation
$\left(\dfrac{\partial s}{\partial v}\right)_T=\left(\dfrac{\partial P}{\partial T}\right)_v$
For an ideal gas: $P=\frac{RT}v$
$\left(\dfrac{\partial s}{\partial v}\right)_T=\left(\dfrac{\partial P}{\partial T}\right)_v=\dfrac Rv$
