Answer
See answer below.
Work Step by Step
Relevant Maxwell relation:
$\left(\dfrac{\partial s}{\partial v}\right)_T=\left(\dfrac{\partial P}{\partial T}\right)_v$
From the given equation:
$(P-a/v^2)(v-b)=RT$
$P=\frac{RT}{v-b}+\frac{a}{v^2}$
$\left(\dfrac{\partial P}{\partial T}\right)_v=\dfrac{R}{v-b}$
$\left(\dfrac{\partial s}{\partial v}\right)_T=\dfrac{R}{v-b}$
