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